ENGINEERING TECHNOLOGY

ENGINEERING TECHNOLOGY: Is It More Expensive To Be Single?

2010-09-14T08:25:00.000-07:00

ENGINEERING TECHNOLOGY: Is It More Expensive To Be Single?: "Have you ever considered how much it costs to be single versus the cost of being in a relationship? It may seem strange, but being single ca..."

FLUID MECHANICS

2010-09-07T11:27:00.000-07:00

Fluid mechanics is the study of fluids and the forces on them. (Fluids include liquids, gases, and plasmas.) Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms. Fluid mechanics, especially fluid dynamics, is an active field of research with many unsolved or partly solved problems. Fluid mechanics can be mathematically complex. Sometimes it can best be solved by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach to solving fluid mechanics problems. Also taking advantage of the highly visual nature of fluid flow is particle image velocimetry, an experimental method for visualizing and analyzing fluid flow.
Contents
1 Brief history
2 Relationship to continuum mechanics
3 Assumptions
3.1 The continuum hypothesis
4 Navier–Stokes equations
4.1 General form of the equation
5 Newtonian versus non-Newtonian fluids
5.1 Equations for a Newtonian fluid
6 See also
7 Notes
8 References
9 External links
//
[edit] Brief history
Main article: History of fluid mechanics
The study of fluid mechanics goes back at least to the days of ancient Greece, when Archimedes investigated fluid statics and buoyancy. Medieval Persian & Arab natural philosophers, including Abū Rayhān al-Bīrūnī and Al-Khazini, combined that earlier work with dynamics [1] to presage the later development of fluid dynamics. Rapid advancement in fluid mechanics began with Leonardo da Vinci (observation and experiment), Evangelista Torricelli (barometer), Isaac Newton (viscosity) and Blaise Pascal (hydrostatics), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in Hydrodynamica (1738). Inviscid flow was further analyzed by various mathematicians (Leonhard Euler, d'Alembert, Lagrange, Laplace, Poisson) and viscous flow was explored by a multitude of engineers including Poiseuille and Gotthilf Heinrich Ludwig Hagen. Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl), while various scientists (Osborne Reynolds, Andrey Kolmogorov, Geoffrey Ingram Taylor) advanced the understanding of fluid viscosity and turbulence.
[edit] Relationship to continuum mechanics
Fluid mechanics is a subdiscipline of continuum mechanics, as illustrated in the following table.
Continuum mechanicsThe study of the physics of continuous materials
Solid mechanicsThe study of the physics of continuous materials with a defined rest shape.
ElasticityDescribes materials that return to their rest shape after an applied stress.
PlasticityDescribes materials that permanently deform after a sufficient applied stress.
RheologyThe study of materials with both solid and fluid characteristics.
Fluid mechanicsThe study of the physics of continuous materials which take the shape of their container.
Non-Newtonian fluids
Newtonian fluids
In a mechanical view, a fluid is a substance that does not support shear stress; that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress.
[edit] Assumptions
Like any mathematical model of the real world, fluid mechanics makes some basic assumptions about the materials being studied. These assumptions are turned into equations that must be satisfied if the assumptions are to be held true. For example, consider an incompressible fluid in three dimensions. The assumption that mass is conserved means that for any fixed closed surface (such as a sphere) the rate of mass passing from outside to inside the surface must be the same as rate of mass passing the other way. (Alternatively, the mass inside remains constant, as does the mass outside). This can be turned into an integral equation over the surface.
Fluid mechanics assumes that every fluid obeys the following:
Conservation of mass
Conservation of energy
Conservation of momentum
The continuum hypothesis, detailed below.
Further, it is often useful (at subsonic conditions) to assume a fluid is incompressible – that is, the density of the fluid does not change. Liquids can often be modelled as incompressible fluids, whereas gases cannot.
Similarly, it can sometimes be assumed that the viscosity of the fluid is zero (the fluid is inviscid). Gases can often be assumed to be inviscid. If a fluid is viscous, and its flow contained in some way (e.g. in a pipe), then the flow at the boundary must have zero velocity. For a viscous fluid, if the boundary is not porous, the shear forces between the fluid and the boundary results also in a zero velocity for the fluid at the boundary. This is called the no-slip condition. For a porous media otherwise, in the frontier of the containing vessel, the slip condition is not zero velocity, and the fluid has a discontinuous velocity field between the free fluid and the fluid in the porous media (this is related to the Beavers and Joseph condition).
[edit] The continuum hypothesis
Main article: Continuum mechanics
Fluids are composed of molecules that collide with one another and solid objects. The continuum assumption, however, considers fluids to be continuous. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at "infinitely" small points, defining a REV (Reference Element of Volume), at the geometric order of the distance between two adjacent molecules of fluid. Properties are assumed to vary continuously from one point to another, and are averaged values in the REV. The fact that the fluid is made up of discrete molecules is ignored.
The continuum hypothesis is basically an approximation, in the same way planets are approximated by point particles when dealing with celestial mechanics, and therefore results in approximate solutions. Consequently, assumption of the continuum hypothesis can lead to results which are not of desired accuracy. That said, under the right circumstances, the continuum hypothesis produces extremely accurate results.
Those problems for which the continuum hypothesis does not allow solutions of desired accuracy are solved using statistical mechanics. To determine whether or not to use conventional fluid dynamics or statistical mechanics, the Knudsen number is evaluated for the problem. The Knudsen number is defined as the ratio of the molecular mean free path length to a certain representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. (More simply, the Knudsen number is how many times its own diameter a particle will travel on average before hitting another particle). Problems with Knudsen numbers at or above unity are best evaluated using statistical mechanics for reliable solutions.
[edit] Navier–Stokes equations
Main article: Navier–Stokes equations
The Navier–Stokes equations (named after Claude-Louis Navier and George Gabriel Stokes) are the set of equations that describe the motion of fluid substances such as liquids and gases. These equations state that changes in momentum (force) of fluid particles depend only on the external pressure and internal viscous forces (similar to friction) acting on the fluid. Thus, the Navier–Stokes equations describe the balance of forces acting at any given region of the fluid.
The Navier–Stokes equations are differential equations which describe the motion of a fluid. Such equations establish relations among the rates of change of the variables of interest. For example, the Navier–Stokes equations for an ideal fluid with zero viscosity states that acceleration (the rate of change of velocity) is proportional to the derivative of internal pressure.
This means that solutions of the Navier–Stokes equations for a given physical problem must be sought with the help of calculus. In practical terms only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow (flow does not change with time) in which the Reynolds number is small.
For more complex situations, such as global weather systems like El Niño or lift in a wing, solutions of the Navier–Stokes equations can currently only be found with the help of computers. This is a field of sciences by its own called computational fluid dynamics.
[edit] General form of the equation
The general form of the Navier–Stokes equations for the conservation of momentum is:

where
is the fluid density,
is the substantive derivative (also called the material derivative),
is the velocity vector,
is the body force vector, and
is a tensor that represents the surface forces applied on a fluid particle (the comoving stress tensor).
Unless the fluid is made up of spinning degrees of freedom like vortices, is a symmetric tensor. In general, (in three dimensions) has the form:

where
are normal stresses,
are tangential stresses (shear stresses).
The above is actually a set of three equations, one per dimension. By themselves, these aren't sufficient to produce a solution. However, adding conservation of mass and appropriate boundary conditions to the system of equations produces a solvable set of equations.
[edit] Newtonian versus non-Newtonian fluids
A Newtonian fluid (named after Isaac Newton) is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means regardless of the forces acting on a fluid, it continues to flow. For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. (Compare friction). Important fluids, like water as well as most gases, behave — to good approximation — as a Newtonian fluid under normal conditions on Earth.[2]
By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time – this behaviour is seen in materials such as pudding, oobleck, or sand (although sand isn't strictly a fluid). Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" (this is seen in non-drip paints). There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property — for example, most fluids with long molecular chains can react in a non-Newtonian manner.[2]
[edit] Equations for a Newtonian fluid
Main article: Newtonian fluid
The constant of proportionality between the shear stress and the velocity gradient is known as the viscosity. A simple equation to describe Newtonian fluid behaviour is

where
τ is the shear stress exerted by the fluid ("drag")
μ is the fluid viscosity – a constant of proportionality
is the velocity gradient perpendicular to the direction of shear.
For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure, not on the forces acting upon it. If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress (in Cartesian coordinates) is

where
τij is the shear stress on the ith face of a fluid element in the jth direction
vi is the velocity in the ith direction
xj is the jth direction coordinate.
If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types.
Among fluids, two rough broad divisions can be made: ideal and non-ideal fluids. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. An Ideal fluid is non viscous- offers no resistance whatsoever to a shearing force.
One can group real fluids into Newtonian and non-Newtonian. Newtonian fluids agree with Newton's law of viscosity. Non-Newtonian fluids can be either plastic, bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelatic.
[edit] See also

Physics portal
Wikibooks has more on the topic of
Fluid mechanics
Applied mechanics
Secondary flow
Bernoulli's principle
Communicating vessels

Is It More Expensive To Be Single?

2010-09-07T11:02:00.002-07:00

Have you ever considered how much it costs to be single versus the cost of being in a relationship? It may seem strange, but being single can actually cost you more money than being with someone.

You always hear stories about the guy spending a ton of money on the girl. So it is natural to think that there is no way being in a relationship can be cheaper. At a quick glance, this seems to be very true. Looking around you, there are couples going on dates all of the time, buying gifts, and every little thing adds up.

These are important but you need to consider other aspects of the relationship. If you share an apartment or a loft, the cost of the apartment is much cheaper. It is cut in half if you share the same sized place. You can easily share a bedroom, so a 1 bedroom apartment would cost half what you would originally pay. This amount adds up to a lot over time.
More savings comes from travel too. You can do and share more things that you could not do if you were single. Sharing rooms, again is very easy. It is not entirely essential to have a whole room to yourself for the whole day even if you are traveling alone. Significant savings are made if you share with a partner.

Sharing food also saves a lot of money. Aside from the fact that you can share food, you can also cook at home. Couples are more likely to cook at home than single people are. Eating out costs a lot more money and hurts savings possibilities couples would have at home.

DESIGN

2010-09-07T11:02:00.001-07:00

No generally-accepted definition of “design” exists[1], and the term has different connotations in different fields (see design disciplines below). Informally, “a design” (noun) refers to a plan for the construction of an object (as in architectural blueprints, circuit diagrams and sewing patterns) and “to design” (verb) refers to making this plan[2]. However, one can also design by directly constructing an object (as in pottery, cowboy coding and graphic design).
More formally, design has been defined as follows.
(noun) a specification of an object, manifested by an agent, intended to accomplish goals, in a particular environment, using a set of primitive components, satisfying a set of requirements, subject to constraints;
(verb, transitive) to create a design, in an environment (where the designer operates)[3]
Here, a "specification" can be manifested as either a plan or a finished product and "primitives" are the elements from which the design object is composed.
With such a broad denotation, there is no universal language or unifying institution for designers of all disciplines. This allows for many differing philosophies and approaches toward the subject (see Philosophies and studies of design, below).
The person designing is called a designer, which is also a term used for people who work professionally in one of the various design areas, usually also specifying which area is being dealt with (such as a fashion designer, concept designer or web designer). A designer’s sequence of activities is called a design process[4]. The scientific study of design is called design science [5].
Designing often necessitates considering the aesthetic, functional, economic and sociopolitical dimensions of both the design object and design process. It may involve considerable research, thought, modeling, interactive adjustment, and re-design. Meanwhile, diverse kinds of objects may be designed, including clothing, graphical user interfaces, skyscrapers, corporate identities, business processes and even methods of designing[6].
Contents
1 Design as a process
1.1 Typical steps
2 Philosophies and studies of design
2.1 Philosophies for guiding design
2.2 Approaches to design
2.3 Methods of designing
2.4 Philosophies for the purpose of designs
3 Terminology
3.1 Design and art
3.2 Design and engineering
3.3 Design and production
3.4 Process design
4 See also
4.1 Design disciplines
4.2 Design approaches and methods
4.3 Other design related topics
5 External links
6 Footnotes
//
[edit] Design as a process
Design, as a process, can take many forms depending on the object being designed and the individual(s) participating. A simple definition is that design is the process of giving form to an idea. "Form" could be a plan of action or a description of a physical thing.
[edit] Typical steps
A design process may include a series of steps followed by designers. Depending on the product or service, some of these stages may be irrelevant, ignored in real-world situations in order to save time, reduce cost, or because they may be redundant in the situation.
Typical stages of the design process include:
Pre-production design
Design brief or Parti – an early (often the beginning) statement of design goals
Analysis – analysis of current design goals
Research – investigating similar design solutions in the field or related topics
Specification – specifying requirements of a design solution for a product (product design specification [7]) or service.
Problem solving – conceptualizing and documenting design solutions
Presentation – presenting design solutions
Design during production
Development – continuation and improvement of a designed solution
Testing – in situ testing a designed solution
Post-production design feedback for future designs
Implementation – introducing the designed solution into the environment
Evaluation and conclusion – summary of process and results, including constructive criticism and suggestions for future improvements
Redesign – any or all stages in the design process repeated (with corrections made) at any time before, during, or after production.
These stages are not universally accepted but do relate typical design process activities. For each activity there are many best practices for completing them.[8]
[edit] Philosophies and studies of design
There are countless philosophies for guiding design as the design values and its accompanying aspects within modern design vary, both between different schools of thought and among practicing designers.[9] Design philosophies are usually for determining design goals. A design goal may range from solving the least significant individual problem of the smallest element, to the most holistic influential utopian goals. Design goals are usually for guiding design. However, conflicts over immediate and minor goals may lead to questioning the purpose of design, perhaps to set better long term or ultimate goals.

A 1938 Bugatti Type 57SC Atlantic from the Ralph Lauren collection. "Form follows function" can be an aesthetic point of view that a design can heighten, as often seen in the work of the Bugattis, Ettore, Rembrandt, and Jean.
[edit] Philosophies for guiding design
A design philosophy is a guide to help make choices when designing such as ergonomics, costs, economics, functionality and methods of re-design. An example of a design philosophy is “dynamic change” to achieve the elegant or stylish look you need.
[edit] Approaches to design
A design approach is a general philosophy that may or may not include a guide for specific methods. Some are to guide the overall goal of the design. Other approaches are to guide the tendencies of the designer. A combination of approaches may be used if they don't conflict.
Some popular approaches include:
KISS principle, (Keep it Simple Stupid, etc.), which strives to eliminate unnecessary complications.
There is more than one way to do it (TIMTOWTDI), a philosophy to allow multiple methods of doing the same thing.
Use-centered design, which focuses on the goals and tasks associated with the use of the artifact, rather than focusing on the end user.
User-centered design, which focuses on the needs, wants, and limitations of the end user of the designed artifact.
[edit] Methods of designing
Main article: Design methods
Design Methods is a broad area that focuses on:
Exploring possibilities and constraints by focusing critical thinking skills to research and define problem spaces for existing products or services—or the creation of new categories; (see also Brainstorming)
Redefining the specifications of design solutions which can lead to better guidelines for traditional design activities (graphic, industrial, architectural, etc.);
Managing the process of exploring, defining, creating artifacts continually over time
Prototyping possible scenarios, or solutions that incrementally or significantly improve the inherited situation
Trendspotting; understanding the trend process.
[edit] Philosophies for the purpose of designs
In philosophy, the abstract noun "design" refers to a pattern with a purpose. Design is thus contrasted with purposelessness, randomness, or lack of complexity.
To study the purpose of designs, beyond individual goals (e.g. marketing, technology, education, entertainment, hobbies), is to question the controversial politics, morals, ethics and needs such as Maslow's hierarchy of needs. "Purpose" may also lead to existential questions such as religious morals and teleology. These philosophies for the "purpose of" designs are in contrast to philosophies for guiding design or methodology.
Often a designer (especially in commercial situations) is not in a position to define purpose. Whether a designer is, is not, or should be concerned with purpose or intended use beyond what they are expressly hired to influence, is debatable, depending on the situation. In society, not understanding or disinterest in the wider role of design might also be attributed to the commissioning agent or client, rather than the designer.
In structuration theory, achieving consensus and fulfillment of purpose is as continuous as society. Raised levels of achievement often lead to raised expectations. Design is both medium and outcome, generating a Janus-like face, with every ending marking a new beginning.
[edit] Terminology
Look up design in Wiktionary, the free dictionary.
The word "design" is often considered ambiguous depending on the application.

The new terminal at Barajas airport in Madrid, Spain
[edit] Design and art
Design is often viewed as a more rigorous form of art, or art with a clearly defined purpose. The distinction is usually made when someone other than the artist is defining the purpose. In graphic arts the distinction is often made between fine art and commercial art. Applied art and decorative arts are other terms, the latter mostly used for objects from the past.
In the realm of the arts, design is more relevant to the "applied" arts, such as architecture and industrial design. In fact today the term design is widely associated to modern industrial product design as initiated by Raymond Loewy and teachings at the Bauhaus and Ulm School of Design (HfG Ulm) in Germany during the 20th Century.
Design implies a conscious effort to create something that is both functional and aesthetically pleasing. For example, a graphic artist may design an advertisement poster. This person's job is to communicate the advertisement message (functional aspect) and to make it look good (aesthetically pleasing).
The distinction between pure and applied arts is not completely clear, but one may consider Jackson Pollock's (often criticized as "splatter") paintings as an example of pure art. One may assume his art does not convey a message based on the obvious differences between an advertisement poster and the mere possibility of an abstract message of a Jackson Pollock painting. One may speculate that Pollock, when painting, worked more intuitively than would a graphic artist, when consciously designing a poster. However, Mark Getlein suggests the principles of design are "almost instinctive", "built-in", "natural", and part of "our sense of 'rightness'."[10] Pollock, as a trained artist, may have utilized design whether conscious or not.

A drawing for a booster engine for steam locomotives. Engineering is applied to design, with emphasis on function and the utilization of mathematics and science.
[edit] Design and engineering
Engineering is often viewed as a more rigorous form of design. Contrary views suggest that design is a component of engineering aside from production and other operations which utilize engineering. A neutral view may suggest that design and engineering simply overlap, depending on the discipline of design. The American Heritage Dictionary defines design as: "To conceive or fashion in the mind; invent," and "To formulate a plan", and defines engineering as: "The application of scientific and mathematical principles to practical ends such as the design, manufacture, and operation of efficient and economical structures, machines, processes, and systems.".[11][12] Both are forms of problem-solving with a defined distinction being the application of "scientific and mathematical principles". How much science is applied in a design is a question of what is considered "science". Along with the question of what is considered science, there is social science versus natural science. Scientists at Xerox PARC made the distinction of design versus engineering at "moving minds" versus "moving atoms".

Jonathan Ive has received several awards for his design of Apple Inc. products like this laptop. In some design fields, personal computers are also used for both design and production
[edit] Design and production
The relationship between design and production is one of planning and executing. In theory, the plan should anticipate and compensate for potential problems in the execution process. Design involves problem-solving and creativity. In contrast, production involves a routine or pre-planned process. A design may also be a mere plan that does not include a production or engineering process, although a working knowledge of such processes is usually expected of designers. In some cases, it may be unnecessary and/or impractical to expect a designer with a broad multidisciplinary knowledge required for such designs to also have a detailed specialized knowledge of how to produce the product.
Design and production are intertwined in many creative professional careers, meaning problem-solving is part of execution and the reverse. As the cost of rearrangement increases, the need for separating design from production increases as well. For example, a high-budget project, such as a skyscraper, requires separating (design) architecture from (production) construction. A Low-budget project, such as a locally printed office party invitation flyer, can be rearranged and printed dozens of times at the low cost of a few sheets of paper, a few drops of ink, and less than one hour's pay of a desktop publisher.
This is not to say that production never involves problem-solving or creativity, nor that design always involves creativity. Designs are rarely perfect and are sometimes repetitive. The imperfection of a design may task a production position (e.g. production artist, construction worker) with utilizing creativity or problem-solving skills to compensate for what was overlooked in the design process. Likewise, a design may be a simple repetition (copy) of a known preexisting solution, requiring minimal, if any, creativity or problem-solving skills from the designer.

An example of a business workflow process using Business Process Modeling Notation.
[edit] Process design
"Process design" (in contrast to "design process" mentioned above) refers to the planning of routine steps of a process aside from the expected result. Processes (in general) are treated as a product of design, not the method of design. The term originated with the industrial designing of chemical processes. With the increasing complexities of the information age, consultants and executives have found the term useful to describe the design of business processes as well as manufacturing processes.
[edit] See also

Design portal
Philosophy of design
[edit] Design disciplines
Commerce
Business design
New product development
Packaging design
Product design
Service design
Process Design
Applications
Experience design
Game design
Interaction design [13]
Sonic interaction design
Software design
Software development
Software engineering
System design
User experience design
User interface design
Web accessibility
Web design
Communications
Book design
Communication design
Content design
Exhibition design
Graphic design
Information design
Instructional design
Motion graphic design
News design
Production design
Sound design
Theatrical design
Typeface design
Typography
Visual communication
Scientific and mathematical
Combinatorial design [14]
Design of experiments
Physical
Architectural design
Architectural engineering
Automotive design
Cellular manufacturing
Ceramic and glass design
Design engineer
Environmental design
Fashion design
Floral design
Furniture design
Garden design
Geometric design
Industrial design
Interior design/redesign
Landscape architecture
Mechanical engineering
Sustainable design
Urban design
[edit] Design approaches and methods
Co-Design
Creative problem solving
Creativity techniques
C-K theory
Design for X
Design leadership
Design management
Design-build
Design patterns
Design strategy
Design thinking
Engineering design process
Error-tolerant design
Fault tolerant design
Functional design
Metadesign
Mind mapping
Open design
Participatory design [15]
Reliable system design
Theory of Constraints
Transformation design
TRIZ
Universal design
User innovation
[edit] Other design related topics
Design organizations
Chartered Society of Designers
The Design Association
AIGA
The Design Society
Interaction Design Association
Design Awards
European Design Awards
IF product design award
James Dyson Award
German Design Award
Design tools
Computer-aided design [16]
Graphic organizers
Design as intellectual property
Design patent (US patent law)
Industrial design rights
Industrial design rights in the European Union
Impact of design
Creative industries
Design classic
Design Museums and Education Centres
Design Exchange
Studying design
Critical design
Design education
Design research
Wicked problems [17]
Designs for the future
Concept design
Futurology

A Surefire Way to Make Any Guy Fall in Love

2010-09-07T10:54:00.000-07:00

Have you been trying to win the love of a really hot guy, but nothing is working and you don't know what to do anymore? Are you a regular on the singles scene and you now want to become one half of a great couple? Is it hard switching over from single thought process to relationship building thought process?

Some women get stuck in that mold of wild and fancy free dating and think that it will carry over well as they seek out a serious contender for a stable relationship. For the most part, the guys who are hanging out in single's hang outs aren't really looking to hook up for real. And if you're maintaining your wild and sexy attitude, the one guy who may have strayed in hoping to find love will most likely look right past you.
Beyond Sexuality

We've been trained, if not completely brainwashed to believe that sex is all there is. So naturally when we try to hook up with a guy it's our first line of defense. Sex draws them in, keeps them looking and keeps them interested.
But for how long?

For a real relationship to grow you need to move beyond this and fast. If a guy is quick to assess that all you're good for is a fun lay, whatever more you may have to offer is not going to interest him. Try switching things around and work to create a great bond with him first.
Don't jump into bed, but have this great conversation with him. Get to know him and let him see that you truly are a fabulous woman with lots to offer.
Keep Pressure Out

If things are going along nicely, but you're feeling that strong desire to move things more quickly, resist. This isn't something you really want to push a guy into. Let his emotions build on their own. Let him realize the gem he's found in you.
The more you try to push him into a relationship the harder time you'll have. Hold back, be patient and let the love grow. Without pressure, he'll fall in love with you a lot sooner.

CALCULUS

2010-09-07T10:53:00.000-07:00

From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article is about the branch of mathematics. For other uses, see Calculus (disambiguation).

It has been suggested that infinitesimal calculus be merged into this article or section. (Discuss)
Topics in Calculus
Fundamental theorem Limits of functions Continuity Mean value theorem
Differential calculus
Derivative Change of variables Implicit differentiation Taylor's theorem Related rates IdentitiesRules:
Power rule, Product rule, Quotient rule, Chain rule
Integral calculus
Integral
Lists of integrals Improper integralsIntegration by:parts, disks, cylindricalshells, substitution,trigonometric substitution,partial fractions, changing order
Vector calculus
Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem
Multivariable calculus
Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian
Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change[1], in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, and join calculus.
Contents
1 History
1.1 Ancient
1.2 Medieval
1.3 Modern
1.4 Significance
1.5 Foundations
2 Principles
2.1 Limits and infinitesimals
2.2 Differential calculus
2.3 Leibniz notation
2.4 Integral calculus
2.5 Fundamental theorem
3 Applications
4 See also
4.1 Lists
4.2 Related topics
5 References
5.1 Notes
5.2 Books
6 Other resources
6.1 Further reading
6.2 Online books
6.3 External links
//
[edit] History
Main article: History of calculus
[edit] Ancient

Isaac Newton is one of the most famous contributors to the development of calculus, with, among other things, the use of calculus in his laws of motion and gravitation.
The ancient period introduced some of the ideas of integral calculus, but does not seem to have developed these ideas in a rigorous or systematic way. Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1820 BC), in which an Egyptian successfully calculated the volume of a pyramidal frustum.[2][3] From the school of Greek mathematics, Eudoxus (c. 408−355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes while Archimedes (c. 287−212 BC) developed this idea further, inventing heuristics which resemble integral calculus.[4] The method of exhaustion was later reinvented in China by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th century AD, Zu Chongzhi established a method which would later be called Cavalieri's principle to find the volume of a sphere.[3]
[edit] Medieval

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Around AD 1000, the Islamic mathematician Ibn al-Haytham (Alhacen) was the first to derive the formula for the sum of the fourth powers of an arithmetic progression, using a method that is readily generalizable to finding the formula for the sum of any higher integral powers, which he used to perform an integration.[5] In the 11th century, the Chinese polymath Shen Kuo developed 'packing' equations that dealt with integration. In the 12th century, the Indian mathematician, Bhāskara II, developed an early derivative representing infinitesimal change, and he described an early form of Rolle's theorem.[6] Also in the 12th century, the Persian mathematician Sharaf al-Dīn al-Tūsī discovered the derivative of cubic polynomials, an important result in differential calculus.[7] In the 14th century, Indian mathematician Madhava of Sangamagrama, along with other mathematician-astronomers of the Kerala school of astronomy and mathematics, described special cases of Taylor series,[8] which are treated in the text Yuktibhasa.[9][10][11]
[edit] Modern
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In Europe, the foundational work was a treatise due to Bonaventura Cavalieri, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimal thin cross-sections. The ideas were similar to Archimedes' in The Method, but this treatise was lost until the early part of the twentieth century. Cavalieri's work was not well respected since his methods can lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first.
The formal study of calculus combined Cavalieri's infinitesimals with the calculus of finite differences developed in Europe at around the same time. The combination was achieved by John Wallis, Isaac Barrow, and James Gregory, the latter two proving the second fundamental theorem of calculus around 1675.
The product rule and chain rule, the notion of higher derivatives, Taylor series, and analytical functions were introduced by Isaac Newton in an idiosyncratic notation which he used to solve problems of mathematical physics. In his publications, Newton rephrased his ideas to suit the mathematical idiom of the time, replacing calculations with infinitesimals by equivalent geometrical arguments which were considered beyond reproach. He used the methods of calculus to solve the problem of planetary motion, the shape of the surface of a rotating fluid, the oblateness of the earth, the motion of a weight sliding on a cycloid, and many other problems discussed in his Principia Mathematica. In other work, he developed series expansions for functions, including fractional and irrational powers, and it was clear that he understood the principles of the Taylor series. He did not publish all these discoveries, and at this time infinitesimal methods were still considered disreputable.

Gottfried Wilhelm Leibniz was originally accused of plagiarizing Sir Isaac Newton's unpublished work (only in Britain, not in continental Europe), but is now regarded as an independent inventor of and contributor to calculus.
These ideas were systematized into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz, who was originally accused of plagiarism by Newton. He is now regarded as an independent inventor of and contributor to calculus. His contribution was to provide a clear set of rules for manipulating infinitesimal quantities, allowing the computation of second and higher derivatives, and providing the product rule and chain rule, in their differential and integral forms. Unlike Newton, Leibniz paid a lot of attention to the formalism—he often spent days determining appropriate symbols for concepts.
Leibniz and Newton are usually both credited with the invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today. The basic insights that both Newton and Leibniz provided were the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series. By Newton's time, the fundamental theorem of calculus was known.
When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit. Newton derived his results first, but Leibniz published first. Newton claimed Leibniz stole ideas from his unpublished notes, which Newton had shared with a few members of the Royal Society. This controversy divided English-speaking mathematicians from continental mathematicians for many years, to the detriment of English mathematics. A careful examination of the papers of Leibniz and Newton shows that they arrived at their results independently, with Leibniz starting first with integration and Newton with differentiation. Today, both Newton and Leibniz are given credit for developing calculus independently. It is Leibniz, however, who gave the new discipline its name. Newton called his calculus "the science of fluxions".
Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Cauchy, Riemann, and Weierstrass (see (ε, δ)-definition of limit). It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. Lebesgue generalized the notion of the integral so that virtually any function has an integral, while Laurent Schwartz extended differentiation in much the same way.
Calculus is a ubiquitous topic in most modern high schools and universities around the world.[12]
[edit] Significance
While some of the ideas of calculus were developed earlier in Egypt, Greece, China, India, Iraq, Persia, and Japan, the modern use of calculus began in Europe, during the 17th century, when Isaac Newton and Gottfried Wilhelm Leibniz built on the work of earlier mathematicians to introduce its basic principles. The development of calculus was built on earlier concepts of instantaneous motion and area underneath curves.
Applications of differential calculus include computations involving velocity and acceleration, the slope of a curve, and optimization. Applications of integral calculus include computations involving area, volume, arc length, center of mass, work, and pressure. More advanced applications include power series and Fourier series. Calculus can be used to compute the trajectory of a shuttle docking at a space station or the amount of snow in a driveway.
Calculus is also used to gain a more precise understanding of the nature of space, time, and motion. For centuries, mathematicians and philosophers wrestled with paradoxes involving division by zero or sums of infinitely many numbers. These questions arise in the study of motion and area. The ancient Greek philosopher Zeno gave several famous examples of such paradoxes. Calculus provides tools, especially the limit and the infinite series, which resolve the paradoxes.
[edit] Foundations
In mathematics, foundations refers to the rigorous development of a subject from precise axioms and definitions. Working out a rigorous foundation for calculus occupied mathematicians for much of the century following Newton and Leibniz and is still to some extent an active area of research today.
There is more than one rigorous approach to the foundation of calculus. The usual one today is via the concept of limits defined on the continuum of real numbers. An alternative is nonstandard analysis, in which the real number system is augmented with infinitesimal and infinite numbers, as in the original Newton-Leibniz conception. The foundations of calculus are included in the field of real analysis, which contains full definitions and proofs of the theorems of calculus as well as generalizations such as measure theory and distribution theory.
[edit] Principles
[edit] Limits and infinitesimals
Main articles: Limit of a function and Infinitesimal
Calculus is usually developed by manipulating very small quantities. Historically, the first method of doing so was by infinitesimals. These are objects which can be treated like numbers but which are, in some sense, "infinitely small". An infinitesimal number dx could be greater than 0, but less than any number in the sequence 1, 1/2, 1/3, ... and less than any positive real number. Any integer multiple of an infinitesimal is still infinitely small, i.e., infinitesimals do not satisfy the Archimedean property. From this point of view, calculus is a collection of techniques for manipulating infinitesimals. This approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals.
In the 19th century, infinitesimals were replaced by limits. Limits describe the value of a function at a certain input in terms of its values at nearby input. They capture small-scale behavior, just like infinitesimals, but use the ordinary real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits are the easiest way to provide rigorous foundations for calculus, and for this reason they are the standard approach.
[edit] Differential calculus
Main article: Differential calculus

Tangent line at (x, f(x)). The derivative f′(x) of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point.
Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a function and a point in the domain, the derivative at that point is a way of encoding the small-scale behavior of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called the derivative function or just the derivative of the original function. In mathematical jargon, the derivative is a linear operator which inputs a function and outputs a second function. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling function is given the input three, then it outputs six, and if the squaring function is given the input three, then it outputs nine. The derivative, however, can take the squaring function as an input. This means that the derivative takes all the information of the squaring function—such as that two is sent to four, three is sent to nine, four is sent to sixteen, and so on—and uses this information to produce another function. (The function it produces turns out to be the doubling function.)
The most common symbol for a derivative is an apostrophe-like mark called prime. Thus, the derivative of the function of f is f′, pronounced "f prime." For instance, if f(x) = x2 is the squaring function, then f′(x) = 2x is its derivative, the doubling function.
If the input of the function represents time, then the derivative represents change with respect to time. For example, if f is a function that takes a time as input and gives the position of a ball at that time as output, then the derivative of f is how the position is changing in time, that is, it is the velocity of the ball.
If a function is linear (that is, if the graph of the function is a straight line), then the function can be written y = mx + b, where:

This gives an exact value for the slope of a straight line. If the graph of the function is not a straight line, however, then the change in y divided by the change in x varies. Derivatives give an exact meaning to the notion of change in output with respect to change in input. To be concrete, let f be a function, and fix a point a in the domain of f. (a, f(a)) is a point on the graph of the function. If h is a number close to zero, then a + h is a number close to a. Therefore (a + h, f(a + h)) is close to (a, f(a)). The slope between these two points is

This expression is called a difference quotient. A line through two points on a curve is called a secant line, so m is the slope of the secant line between (a, f(a)) and (a + h, f(a + h)). The secant line is only an approximation to the behavior of the function at the point a because it does not account for what happens between a and a + h. It is not possible to discover the behavior at a by setting h to zero because this would require dividing by zero, which is impossible. The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero:

Geometrically, the derivative is the slope of the tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients. For this reason, the derivative is sometimes called the slope of the function f.
Here is a particular example, the derivative of the squaring function at the input 3. Let f(x) = x2 be the squaring function.

The derivative f′(x) of a curve at a point is the slope of the line tangent to that curve at that point. This slope is determined by considering the limiting value of the slopes of secant lines. Here the function involved (drawn in red) is f(x) = x3 − x. The tangent line (in green) which passes through the point (−3/2, −15/8) has a slope of 23/4. Note that the vertical and horizontal scales in this image are different.

The slope of tangent line to the squaring function at the point (3,9) is 6, that is to say, it is going up six times as fast as it is going to the right. The limit process just described can be performed for any point in the domain of the squaring function. This defines the derivative function of the squaring function, or just the derivative of the squaring function for short. A similar computation to the one above shows that the derivative of the squaring function is the doubling function.
[edit] Leibniz notation
Main article: Leibniz's notation
A common notation, introduced by Leibniz, for the derivative in the example above is

In an approach based on limits, the symbol dy/dx is to be interpreted not as the quotient of two numbers but as a shorthand for the limit computed above. Leibniz, however, did intend it to represent the quotient of two infinitesimally small numbers, dy being the infinitesimally small change in y caused by an infinitesimally small change dx applied to x. We can also think of d/dx as a differentiation operator, which takes a function as an input and gives another function, the derivative, as the output. For example:

In this usage, the dx in the denominator is read as "with respect to x". Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like dx and dy as if they were real numbers; although it is possible to avoid such manipulations, they are sometimes notationally convenient in expressing operations such as the total derivative.
[edit] Integral calculus
Main article: Integral
Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. In technical language, integral calculus studies two related linear operators.
The indefinite integral is the antiderivative, the inverse operation to the derivative. F is an indefinite integral of f when f is a derivative of F. (This use of upper- and lower-case letters for a function and its indefinite integral is common in calculus.)
The definite integral inputs a function and outputs a number, which gives the area between the graph of the input and the x-axis. The technical definition of the definite integral is the limit of a sum of areas of rectangles, called a Riemann sum.
A motivating example is the distances traveled in a given time.

If the speed is constant, only multiplication is needed, but if the speed changes, then we need a more powerful method of finding the distance. One such method is to approximate the distance traveled by breaking up the time into many short intervals of time, then multiplying the time elapsed in each interval by one of the speeds in that interval, and then taking the sum (a Riemann sum) of the approximate distance traveled in each interval. The basic idea is that if only a short time elapses, then the speed will stay more or less the same. However, a Riemann sum only gives an approximation of the distance traveled. We must take the limit of all such Riemann sums to find the exact distance traveled.

Integration can be thought of as measuring the area under a curve, defined by f(x), between two points (here a and b).
If f(x) in the diagram on the left represents speed as it varies over time, the distance traveled (between the times represented by a and b) is the area of the shaded region s.
To approximate that area, an intuitive method would be to divide up the distance between a and b into a number of equal segments, the length of each segment represented by the symbol Δx. For each small segment, we can choose one value of the function f(x). Call that value h. Then the area of the rectangle with base Δx and height h gives the distance (time Δx multiplied by speed h) traveled in that segment. Associated with each segment is the average value of the function above it, f(x)=h. The sum of all such rectangles gives an approximation of the area between the axis and the curve, which is an approximation of the total distance traveled. A smaller value for Δx will give more rectangles and in most cases a better approximation, but for an exact answer we need to take a limit as Δx approaches zero.
The symbol of integration is , an elongated S (the S stands for "sum"). The definite integral is written as:

and is read "the integral from a to b of f-of-x with respect to x." The Leibniz notation dx is intended to suggest dividing the area under the curve into an infinite number of rectangles, so that their width Δx becomes the infinitesimally small dx. In a formulation of the calculus based on limits, the notation

is to be understood as an operator that takes a function as an input and gives a number, the area, as an output; dx is not a number, and is not being multiplied by f(x).
The indefinite integral, or antiderivative, is written:

Functions differing by only a constant have the same derivative, and therefore the antiderivative of a given function is actually a family of functions differing only by a constant. Since the derivative of the function y = x² + C, where C is any constant, is y′ = 2x, the antiderivative of the latter is given by:

An undetermined constant like C in the antiderivative is known as a constant of integration.
[edit] Fundamental theorem
Main article: Fundamental theorem of calculus
The fundamental theorem of calculus states that differentiation and integration are inverse operations. More precisely, it relates the values of antiderivatives to definite integrals. Because it is usually easier to compute an antiderivative than to apply the definition of a definite integral, the Fundamental Theorem of Calculus provides a practical way of computing definite integrals. It can also be interpreted as a precise statement of the fact that differentiation is the inverse of integration.
The Fundamental Theorem of Calculus states: If a function f is continuous on the interval [a, b] and if F is a function whose derivative is f on the interval (a, b), then

Furthermore, for every x in the interval (a, b),

This realization, made by both Newton and Leibniz, who based their results on earlier work by Isaac Barrow, was key to the massive proliferation of analytic results after their work became known. The fundamental theorem provides an algebraic method of computing many definite integrals—without performing limit processes—by finding formulas for antiderivatives. It is also a prototype solution of a differential equation. Differential equations relate an unknown function to its derivatives, and are ubiquitous in the sciences.
[edit] Applications

The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus
Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other.
Physics makes particular use of calculus; all concepts in classical mechanics and electromagnetism are interrelated through calculus. The mass of an object of known density, the moment of inertia of objects, as well as the total energy of an object within a conservative field can be found by the use of calculus. An example of the use of calculus in mechanics is Newton's second law of motion: historically stated it expressly uses the term "rate of change" which refers to the derivative saying The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction. Commonly expressed today as Force = Mass × acceleration, it involves differential calculus because acceleration is the time derivative of velocity or second time derivative of trajectory or spatial position. Starting from knowing how an object is accelerating, we use calculus to derive its path.
Maxwell's theory of electromagnetism and Einstein's theory of general relativity are also expressed in the language of differential calculus. Chemistry also uses calculus in determining reaction rates and radioactive decay. In biology, population dynamics starts with reproduction and death rates to model population changes.
Calculus can be used in conjunction with other mathematical disciplines. For example, it can be used with linear algebra to find the "best fit" linear approximation for a set of points in a domain. Or it can be used in probability theory to determine the probability of a continuous random variable from an assumed density function. In analytic geometry, the study of graphs of functions, calculus is used to find high points and low points (maxima and minima), slope, concavity and inflection points.
Green's Theorem, which gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C, is applied in an instrument known as a planimeter which is used to calculate the area of a flat surface on a drawing. For example, it can be used to calculate the amount of area taken up by an irregularly shaped flower bed or swimming pool when designing the layout of a piece of property.
In the realm of medicine, calculus can be used to find the optimal branching angle of a blood vessel so as to maximize flow. From the decay laws for a particular drug's elimination from the body, it's used to derive dosing laws. In nuclear medicine, it's used to build models of radiation transport in targeted tumor therapies.
In economics, calculus allows for the determination of maximal profit by providing a way to easily calculate both marginal cost and marginal revenue.
Calculus is also used to find approximate solutions to equations; in practice it's the standard way to solve differential equations and do root finding in most applications. Examples are methods such as Newton's method, fixed point iteration, and linear approximation. For instance, spacecraft use a variation of the Euler method to approximate curved courses within zero gravity environments.
[edit] See also
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Main article: Outline of calculus
[edit] Lists
List of differentiation identities
List of calculus topics
Publications in calculus
Table of integrals
[edit] Related topics
Calculus of finite differences
Calculus with polynomials
Complex analysis
Differential equation
Differential geometry
Elementary calculus
Fourier series
Integral equation
Mathematical analysis
Mathematics
Multivariable calculus
Non-classical analysis
Non-standard analysis
Non-standard calculus
Precalculus (mathematical education)
Product Integrals
Stochastic calculus
Taylor series
Time-scale calculus

MATHEMATICS

2010-09-07T10:28:00.000-07:00

"Maths" and "Math" redirect here. For other uses of "Mathematics" or "Math", see Mathematics (disambiguation) and Math (disambiguation).

Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1]Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns,[2][3] formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.[4]

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".[5] Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, for example in China in 300 BC, in India in AD 100, and in the Muslim world in AD 800, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.[7]

Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.[8]

Contents
1 Etymology
2 History
3 Inspiration, pure and applied mathematics, and aesthetics
4 Notation, language, and rigor
5 Mathematics as science
6 Fields of mathematics
6.1 Quantity
6.2 Structure
6.3 Space
6.4 Change
6.5 Foundations and philosophy
6.6 Theoretical computer science
6.7 Applied mathematics
7 See also
8 Notes
9 References
10 External links

Etymology
The word "mathematics" comes from the Greek μάθημα (máthēma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study", even in Classical times.[9] Its adjective is μαθηματικός (mathēmatikós), related to learning, or studious, which likewise further came to mean mathematical. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), Latin: ars mathematica, meant the mathematical art.

The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle, and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek.[10] In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.

History
Main article: History of mathematics

Pythagoras (c.570-c.495 BC) has commonly been given credit for discovering the Pythagorean theorem. Well-known figures in Greek mathematics also include Euclid, Archimedes, and Thales.The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[11] was probably that of numbers: the realization that a collection of two apples and a collection two oranges (for example) have something in common, namely quantity of their members.

In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[12] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.

Since numeracy pre-dated writing, further steps were needed for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]

Mayan numeralsThe earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[13] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.[14]

Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[15]

Inspiration, pure and applied mathematics, and aesthetics
Main article: Mathematical beauty

Sir Isaac Newton (1643-1727), an inventor of infinitesimal calculus.Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.[16] Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics. However pure mathematics topics often turn out to have applications, e.g. number theory in cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics".[17] As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.[18] Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.

For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He identified criteria such as significance, unexpectedness, inevitability, and economy as factors that contribute to a mathematical aesthetic.[19] Mathematicians often strive to find proofs of theorems that are particularly elegant, a quest Paul Erdős often referred to as finding proofs from "The Book" in which God had written down his favorite proofs.[20][21] The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.

Notation, language, and rigor

Leonhard Euler, who created and popularized much of the mathematical notation used todayMain article: Mathematical notation
Most of the mathematical notation in use today was not invented until the 16th century.[22] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery.[23] Euler (1707–1783) was responsible for many of the notations in use today. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax (which to a limited extent varies from author to author and from discipline to discipline) and encodes information that would be difficult to write in any other way.

Mathematical language can also be hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Moreover, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".

The infinity symbol ∞ in several typefaces.Mathematical proof is fundamentally a matter of rigor. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[24] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[25]

Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[26]

Mathematics as science

Carl Friedrich Gauss, himself known as the "prince of mathematicians",[27] referred to mathematics as "the Queen of the Sciences".Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences".[28] In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]

Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.[29] However, in the 1930s important work in mathematical logic convinced many mathematicians that mathematics cannot be reduced to logic alone, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[30] Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.

An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.[31] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences. Experimental mathematics continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method.[citation needed] In his 2002 book A New Kind of Science, Stephen Wolfram argues that computational mathematics deserves to be explored empirically as a scientific field in its own right.

The opinions of mathematicians on this matter are varied. Many mathematicians[who?] feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts; others[who?] feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics.[citation needed]

Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal,[32][33] established in 1936 and now awarded every 4 years. It is often considered the equivalent of science's Nobel Prizes. The Wolf Prize in Mathematics, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize, was introduced in 2003. These are awarded for a particular body of work, which may be innovation, or resolution of an outstanding problem in an established field. A famous list of 23 such open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis) is duplicated in Hilbert's problems.

Fields of mathematics

An abacus, a simple calculating tool used since ancient times.Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.

Quantity
The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic. The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem. Number theory also holds two problems widely considered to be unsolved: the twin prime conjecture and Goldbach's conjecture.

As the number system is further developed, the integers are recognized as a subset of the rational numbers ("fractions"). These, in turn, are contained within the real numbers, which are used to represent continuous quantities. Real numbers are generalized to complex numbers. These are the first steps of a hierarchy of numbers that goes on to include quarternions and octonions. Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity". Another area of study is size, which leads to the cardinal numbers and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.

Natural numbers Integers Rational numbers Real numbers Complex numbers

Structure
Many mathematical objects, such as sets of numbers and functions, exhibit internal structure as a consequence of operations or relations that are defined on the set. Mathematics then studies properties of those sets that can be expressed in terms of that structure; for instance number theory studies properties of the set of integers that can be expressed in terms of arithmetic operations. Moreover, it frequently happens that different such structured sets (or structures) exhibit similar properties, which makes it possible, by a further step of abstraction, to state axioms for a class of structures, and then study at once the whole class of structures satisfying these axioms. Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra. By its great generality, abstract algebra can often be applied to seemingly unrelated problems; for instance a number of ancient problems concerning compass and straightedge constructions were finally solved using Galois theory, which involves field theory and group theory. Another example of an algebraic theory is linear algebra, which is the general study of vector spaces, whose elements called vectors have both quantity and direction, and can be used to model (relations between) points in space. This is one example of the phenomenon that the originally unrelated areas of geometry and algebra have very strong interactions in modern mathematics. Combinatorics studies ways of enumerating the number of objects that fit a given structure.

Combinatorics Number theory Group theory Graph theory Order theory

Space
The study of space originates with geometry – in particular, Euclidean geometry. Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions; it combines space and numbers, and encompasses the well-known Pythagorean theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Within differential geometry are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus. Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may have been the greatest growth area in 20th century mathematics; it includes point-set topology, set-theoretic topology, algebraic topology and differential topology. In particular, instances of modern day topology are metrizability theory, axiomatic set theory, homotopy theory, and Morse theory. Topology also includes the now solved Poincaré conjecture and the controversial four color theorem, whose only proof, by computer, has never been verified by a human.

Geometry Trigonometry Differential geometry Topology Fractal geometry Measure Theory

Change
Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a powerful tool to investigate it. Functions arise here, as a central concept describing a changing quantity. The rigorous study of real numbers and functions of a real variable is known as real analysis, with complex analysis the equivalent field for the complex numbers. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior.

Calculus Vector calculus Differential equations Dynamical systems Chaos theory Complex analysis

Foundations and philosophy
In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic includes the mathematical study of logic and the applications of formal logic to other areas of mathematics; set theory is the branch of mathematics that studies sets or collections of objects. Category theory, which deals in an abstract way with mathematical structures and relationships between them, is still in development. The phrase "crisis of foundations" describes the search for a rigorous foundation for mathematics that took place from approximately 1900 to 1930.[34] Some disagreement about the foundations of mathematics continues to present day. The crisis of foundations was stimulated by a number of controversies at the time, including the controversy over Cantor's set theory and the Brouwer-Hilbert controversy.

Mathematical logic is concerned with setting mathematics within a rigorous axiomatic framework, and studying the implications of such a framework. As such, it is home to Gödel's incompleteness theorems which (informally) imply that any formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proven are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Whatever finite collection of number-theoretical axioms is taken as a foundation, Gödel showed how to construct a formal statement that is a true number-theoretical fact, but which does not follow from those axioms. Therefore no formal system is a complete axiomatization of full number theory.[citation needed] Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science.

Mathematical logic Set theory Category theory

Theoretical computer science
Theoretical computer science includes computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most powerful known model – the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. A famous problem is the "P=NP?" problem, one of the Millennium Prize Problems.[35] Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.

Theory of computation Cryptography

Applied mathematics
Applied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas.

Applied mathematics has significant overlap with the discipline of statistics, whose theory is formulated mathematically, especially with probability theory. Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data be available). When reconsidering data from experiments and samples or when analyzing data from observational studies, statisticians "make sense of the data" using the art of modelling and the theory of inference – with model selection and estimation; the estimated models and consequential predictions should be tested on new data.[36]

Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using ideas of functional analysis and techniques of approximation theory; numerical analysis includes the study of approximation and discretization broadly with special concern for rounding errors. Other areas of computational mathematics include computer algebra and symbolic computation.

Mathematical physics
Fluid dynamics
Numerical analysis
Optimization

Probability theory
Statistics
Financial mathematics
Game theory

Mathematical biology
Mathematical chemistry
Mathematical economics
Control theory

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HEAT TRANSFER

2010-09-07T10:25:00.001-07:00

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Heat transfer, also known as heat flow, heat exchange, or transfer of thermal energy is the movement of heat from one place to another. When an object is at a different temperature from its surroundings, heat transfer occurs so that the body and the surroundings reach the same temperature (thermal equilibrium). Heat transfer always occurs from a higher-temperature region to a cooler-temperature one as described by the second law of thermodynamics or the Clausius statement.

Where there is a temperature difference between objects in proximity, heat transfer between them cannot be stopped although its rate can be controlled.

Contents
1 Overview
2 Heat transfer mechanisms
2.1 Conduction
2.2 Convection
2.3 Radiation
2.4 Mass Transfer
2.5 Convection vs. conduction
3 Heat transfer in phase changes
3.1 Boiling
3.2 Condensation
4 Modelling approaches
4.1 Heat equation
4.2 Computational methods
4.3 Lumped system analysis
5 Applications and techniques
5.1 Insulation and radiant barriers
5.1.1 Critical insulation thickness
5.2 Heat exchangers
5.3 Heat dissipation
5.3.1 Heat sinks
5.3.2 Buildings
5.4 Thermal energy storage
5.5 Evaporative cooling
5.6 Radiative cooling
5.7 Laser cooling
5.8 Magnetic cooling
5.9 Other
6 See also
7 References
8 Further reading
9 External links

[edit] Overview
See also: Heat and Thermodynamics
This article deals with specific methods by which heat transfer occurs.

Note that although the definition of "heat" implicitly means the movement of energy, the term "heat transfer" has acquired a traditional usage in engineering and other contexts (despite its literal redundancy).

Fundamental methods of heat transfer include conduction, convection, and radiation. Although separate physical laws have been discovered to describe the behaviour of each of these methods, real systems may exhibit a complicated combination. Various mathematical methods have been developed to solve or approximate the results of heat transfer in systems.

Heat transfer is a path function (process quantity), as opposed to a point function (state quantity).

Heat transfer is typically studied as part of a general chemical engineering or mechanical engineering curriculum. Typically, thermodynamics is a prerequisite to undertaking a course in heat transfer, as the laws of thermodynamics are essential in understanding the mechanism of heat transfer. Other courses related to heat transfer include energy conversion, thermofluids and mass transfer.

Heat transfer methodologies are used in the following disciplines, among others:

Automotive engineering
Thermal management of electronic devices and systems
HVAC
Insulation
Materials processing
Power plant engineering
There are some notable similarities in equations for heat, momentum, and mass transfer[1]. The molecular transfer equations of Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are very similar. A great deal of effort has been devoted to developing analogies among these three transport processes so as to allow prediction of one from any of the others.

[edit] Heat transfer mechanisms
There are a number of distinct, or fundamental, modes of heat transfer:

Conduction: Transfer of energy between objects in physical contact
Convection: Transfer of energy between an object and its environment, due to fluid motion
Radiation: Transfer of energy from or to a body by the emission or absorption of electromagnetic radiation
Mass transfer: Movement of physical objects represents a movement of their internal energy
[edit] Conduction

Fire test used to test the heat transfer through firestops and penetrants used in construction listing and approval use and compliance.Main article: Heat conduction
On a microscopic scale, conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring atoms. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from one atom to another. Conduction is the most significant means of heat transfer within a solid or between solid objects in contact. Fluids (and especially gases) are less conductive.

Steady state conduction is a form of conduction which happens when the temperature difference driving the conduction is constant so that after an equilibration time, the spatial distribution of temperatures in the conducting object does not change any further. In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out.

Transient conduction occurs when the temperature within an object changes as a function of time. Analysis of transient systems is more complex and often calls for the application of approximation theories, and/or numerical analysis by computer.

[edit] Convection
Main article: Convective heat transfer
Convection is the transfer of heat from one place to another by the movement of fluids. The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid.[2] Convection is usually the dominant form of heat transfer in liquids and gases. Although often discussed as a third method of heat transfer, convection actually describes the combined effects of conduction and fluid flow.

Free or natural convection occurs when the fluid motion is caused by buoyancy forces that result from the density variations due to variations of temperature in the fluid. Forced convection is when the fluid is forced to flow over the surface by external source such as fans, stirrers, and pumps, creating an artificially induced convection current.[3]

Convection is described by Newton's law of cooling, which states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings.

[edit] Radiation

A red-hot iron rod from which heat transfer to the surrounding environment will be primarily through radiation.Main article: Thermal radiation
Thermal radiation is the transfer of heat energy through empty space by electromagnetic waves. All objects with a temperature above absolute zero radiate energy. No medium is necessary for radiation to occur, for it is transferred by electromagnetic waves; radiation takes place even in and through a perfect vacuum. For instance, the energy from the Sun travels through the vacuum of space before warming the earth. Radiation is the only form of heat transfer that can occur in the absence of any form of medium (i.e., through a vacuum).

Thermal radiation is a direct result of the movements of atoms and molecules in a material. Since these atoms and molecules are composed of charged particles (protons and electrons), their movements result in the emission of electromagnetic radiation, which carries energy away from the surface. At the same time, the surface is constantly bombarded by radiation from the surroundings, resulting in the transfer of energy to the surface. Since the amount of emitted radiation increases with increasing temperature, a net transfer of energy from higher temperatures to lower temperatures results.

Unlike conductive and convective forms of heat transfer, thermal radiation can be concentrated in a tiny spot by using reflecting mirrors. Concentrating solar power takes advantage of this fact. For example, the sunlight reflected from mirrors heats the PS10 solar power tower, and during the day it can heat water to 285°C (558.15°K) or 545°F.

[edit] Mass Transfer
Please help improve this article by expanding it. Further information might be found on the talk page. (August 2010)

Main article: Mass transfer
It is possible to move heat by physical transfer of a hot or cold object from one place to another. This can be as simple as placing hot water in a bottle and heating your bed or the movement of an iceberg and changing ocean currents.

[edit] Convection vs. conduction
Consider a body of fluid where heat is produced or enters at its lower end and leaves at its upper end. Ignoring radiation, conduction and convection can be considered to "compete" for dominance. If heat conduction is too great, fluid moving down by convection will be heated by conduction so fast that its downward movement will be stopped due to its buoyancy, while fluid moving up by convection will be cooled by conduction so fast that its driving buoyancy will diminish. If, on the other hand, heat conduction is very low, a large temperature gradient will be formed and convection will be very strong.

The Rayleigh number (Ra) is a measure determining the result of this competition.

where

g is acceleration due to gravity
ρ is the density with Δρ being the density difference between the lower and upper ends
μ is the dynamic viscosity
α is the Thermal diffusivity
β is the volume thermal expansivity (sometimes denoted α elsewhere)
T is the temperature and ν is the kinematic viscosity.
The Rayleigh number can be understood as the ratio between the rate of heat transfer by convection to the rate of heat transfer by conduction, or, equivalently, the ratio between the corresponding timescales (i.e. conduction timescale divided by convection timescale), up to a numerical factor. This can be seen as follows, where all calculations are up to numerical factors depending on the geometry of the system.

The buoyancy force driving the convection is roughly gΔρL3 so the corresponding pressure is roughly gΔρL. In steady state, this is canceled by the shear stress due to viscosity and therefore roughly equals μV / L = μ / Tconv, where V is the typical fluid velocity due to convection and Tconv the order of its timescale. The conduction timescale, on the other hand, is of the order of Tcond = L2 / α.

Convection occurs when Rayleigh number is above 1000-2000. For example, the Earth's mantle, exhibiting non-stable convection, has Rayleigh number of the order of 103, and Tconv as calculated above is around 108 years.

[edit] Heat transfer in phase changes
Transfer of heat through a phase transition in the medium such as water-to-ice or water-to-steam or steam-to-water or ice-to-water involves significant energy and is exploited in many ways: steam engine, refrigerator etc. (see latent heat of fusion). For example, the Mason equation is an approximate analytical expression for the growth of a water droplet based on the effects of heat transport on evaporation and condensation.

[edit] Boiling
See also: boiling and critical heat flux
Heat transfer in boiling fluids is complex but of considerable technical importance. It is characterised by an s-shaped curve relating heat flux to surface temperature difference (see say Kay & Nedderman 'Fluid Mechanics & Transfer Processes', CUP, 1985, p. 529).

At low driving temperatures, no boiling occurs and the heat transfer rate is controlled by the usual single-phase mechanisms. As the surface temperature is increased, local boiling occurs and vapour bubbles nucleate, grow into the surrounding cooler fluid, and collapse. This is sub-cooled nucleate boiling and is a very efficient heat transfer mechanism. At high bubble generation rates the bubbles begin to interfere and the heat flux no longer increases rapidly with surface temperature (this is the departure from nucleate boiling DNB). At higher temperatures still, a maximum in the heat flux is reached (the critical heat flux). The regime of falling heat transfer which follows is not easy to study but is believed to be characterised by alternate periods of nucleate and film boiling. Nucleate boiling slowing the heat transfer due to gas phase {bubbles} creation on the heater surface, as mentioned, gas phase thermal conductivity is much lower than liquid phase thermal conductivity, so the outcome is a kind of "gas thermal barrier".

At higher temperatures still, the hydrodynamically quieter regime of film boiling is reached. Heat fluxes across the stable vapour layers are low, but rise slowly with temperature. Any contact between fluid and the surface which may be seen probably leads to the extremely rapid nucleation of a fresh vapour layer ('spontaneous nucleation').

[edit] Condensation
Condensation occurs when a vapor is cooled and changes its phase to a liquid. Condensation heat transfer, like boiling, is of great significance in industry. During condensation, the latent heat of vaporization must be released. The amount of the heat is the same as that absorbed during vaporization at the same fluid pressure.

There are several modes of condensation:

Homogeneous condensation (as during a formation of fog).
Condensation in direct contact with subcooled liquid.
Condensation on direct contact with a cooling wall of a heat exchanger-this is the most common mode used in industry:
Filmwise condensation (when a liquid film is formed on the subcooled surface, usually occurs when the liquid wets the surface).
Dropwise condensation (when liquid drops are formed on the subcooled surface, usually occurs when the liquid does not wet the surface). Dropwise condensation is difficult to sustain reliably; therefore, industrial equipment is normally designed to operate in filmwise condensation mode.
[edit] Modelling approaches
A number of approaches to modelling complex heat transfer phenomena have been developed.

[edit] Heat equation
Main article: Heat equation
The heat equation is an important partial differential equation which describes the distribution of heat (or variation in temperature) in a given region over time. In some cases, exact solutions of the equation are available; in other cases the equation must be solved numerically (see computational methods, below).

[edit] Computational methods
Please help improve this article by expanding it. Further information might be found on the talk page. (August 2010)

See also: Computational fluid dynamics
For example, simplified climate models may use Newtonian cooling instead of a full (and computationally expensive) radiation code to maintain atmospheric temperatures.

[edit] Lumped system analysis
Main article: Lumped capacitance model
See also: Biot number
Lumped system analysis is a common approximation in transient conduction which may be used whenever heat conduction within an object is much faster than heat conduction across the boundary of the object.

This is a method of approximation that reduces one aspect of the transient conduction system (that within the object) to an equivalent steady state system (that is, it is assumed that the temperature within the object is completely uniform, although its value may be changing in time).

In this method, a term known as the Biot number is calculated, which is defined as the ratio of the conductive heat resistance within the object to the convective heat transfer resistance across the object's boundary. For small Biot numbers, the approximation of spatially uniform temperature within the object can begin to be used, since it can be presumed that heat transferred into the object has time to uniformaly distribute itself, due to the lower resistance to doing so, as compared with the resistance to heat entering the object.

[edit] Applications and techniques
Heat transfer has broad application to the functioning of numerous devices and systems. Objectives of studying and applying heat transfer principles may be to preserve (i.e., insulate), increase, or decrease temperature in a wide variety of circumstances.

[edit] Insulation and radiant barriers
Main articles: Thermal insulation and radiant barrier

Heat exposure as part of a fire test for firestop products.Thermal insulators are materials specifically designed to reduce the flow of heat by limiting conduction, convection, or both. Radiant barriers are materials which reflect radiation and therefore reduce the flow of heat from radiation sources. Good insulators are not necessarily good radiant barriers, and vice versa. Metal, for instance, is an excellent reflector and poor insulator.

The effectiveness of an insulator is indicated by its R- (resistance) value. The R-value of a material is the inverse of the conduction coefficient (k) multiplied by the thickness (d) of the insulator. The units of resistance value are in SI units: (K·m²/W)

Rigid fiberglass, a common insulation material, has an R-value of 4 per inch, while poured concrete, a poor insulator, has an R-value of 0.08 per inch.[4]

The tog is a measure of thermal resistance, commonly used in the textile industry, and often seen quoted on, for example, duvets and carpet underlay.

The effectiveness of a radiant barrier is indicated by its reflectivity, which is the fraction of radiation reflected. A material with a high reflectivity (at a given wavelength) has a low emissivity (at that same wavelength), and vice versa (at any specific wavelength, reflectivity = 1 - emissivity). An ideal radiant barrier would have a reflectivity of 1 and would therefore reflect 100% of incoming radiation. Vacuum bottles (Dewars) are 'silvered' to approach this. In space vacuum, satellites use multi-layer insulation which consists of many layers of aluminized (shiny) mylar to greatly reduce radiation heat transfer and control satellite temperature.

[edit] Critical insulation thickness
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Low thermal conductivity (k) materials reduce heat fluxes. The smaller the k value, the larger the corresponding thermal resistance (R) value.
The units of thermal conductivity(k) are W·m−1·K−1 (watts per meter per kelvin), therefore increasing width of insulation (x meters) decreases the k term and as discussed increases resistance.

This follows logic as increased resistance would be created with increased conduction path (x).

However, adding this layer of insulation also has the potential of increasing the surface area and hence thermal convection area (A).

An obvious example is a cylindrical pipe:

As insulation gets thicker, outer radius increases and therefore surface area increases.
The point where the added resistance of increasing insulation width becomes overshadowed by the effects of surface area is called the critical insulation thickness. In simple cylindrical pipes:[5]

For a graph of this phenomenon in a cylidrical pipe example see: External Link: Critical Insulation Thickness diagram as at 26/03/09

[edit] Heat exchangers
Main article: Heat exchanger
A heat exchanger is a tool built for efficient heat transfer from one fluid to another, whether the fluids are separated by a solid wall so that they never mix, or the fluids are directly contacted. Heat exchangers are widely used in refrigeration, air conditioning, space heating, power generation, and chemical processing. One common example of a heat exchanger is the radiator in a car, in which the hot radiator fluid is cooled by the flow of air over the radiator surface.

Common types of heat exchanger flows include parallel flow, counter flow, and cross flow. In parallel flow, both fluids move in the same direction while transferring heat; in counter flow, the fluids move in opposite directions and in cross flow the fluids move at right angles to each other. The common constructions for heat exchanger include shell and tube, double pipe, extruded finned pipe, spiral fin pipe, u-tube, and stacked plate.

When engineers calculate the theoretical heat transfer in a heat exchanger, they must contend with the fact that the driving temperature difference between the two fluids varies with position. To account for this in simple systems, the log mean temperature difference (LMTD) is often used as an 'average' temperature. In more complex systems, direct knowledge of the LMTD is not available and the number of transfer units (NTU) method can be used instead.

[edit] Heat dissipation
[edit] Heat sinks
Main article: Heat sink
A heat sink is a term for a component that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems and the radiator (also a heat exchanger) in a car. Heat sinks also help to cool electronic and optoelectronic devices, such as CPUs, higher-power lasers, and light emitting diodes (LEDs). A heat sink uses its extended surfaces to increase the surface area in contact with the cooling fluid, the air for example.

[edit] Buildings
In cold climates, houses with their heating systems form dissipative systems. In spite of efforts to insulate such houses to reduce heat losses to their exteriors, considerable heat is lost which can make their interiors uncomfortably cool or cold. For the comfort of the inhabitants, the interiors must be maintained out of thermal equilibrium with the external surroundings. In effect, these domestic residences are oases of warmth in a sea of cold and the thermal gradient between the inside and outside is often quite steep. This can lead to problems such as condensation and uncomfortable draughts (drafts) which, if left unaddressed, can cause cosmetic or structural damage to the property. Such issues can be prevented by use of insulation techniques for reducing heat loss.

Thermal transmittance is the rate of transfer of heat through a structure divided by the difference in temperature across the structure. It is expressed in watts per square metre per kelvin, or W/m²K. Well-insulated parts of a building have a low thermal transmittance whereas poorly-insulated parts of a building have a high thermal transmittance.

A thermostat is a device capable of starting the heating system when the house's interior falls below a set temperature, and of stopping that same system when another (higher) set temperature has been achieved. Thus the thermostat controls the flow of energy into the house, that energy eventually being dissipated to the exterior.

[edit] Thermal energy storage
Main article: Thermal energy storage
Thermal energy storage refers to a number of technologies that store energy in a thermal reservoir for later use. They can be employed to balance energy demand between day time and night time. The thermal reservoir may be maintained at a temperature above (hotter) or below (colder) than that of the ambient environment. Applications include later use in space heating, domestic or process hot water, or to generate electricity. Most practical active solar heating systems have storage for a few hours to a day's worth of heat collected.

[edit] Evaporative cooling
Main article: Evaporative cooler
Evaporative cooling is a physical phenomenon in which evaporation of a liquid, typically into surrounding air, cools an object or a liquid in contact with it. Latent heat describes the amount of heat that is needed to evaporate the liquid; this heat comes from the liquid itself and the surrounding gas and surfaces. The greater the difference between the two temperatures, the greater the evaporative cooling effect. When the temperatures are the same, no net evaporation of water in air occurs, thus there is no cooling effect. A simple example of natural evaporative cooling is perspiration, or sweat, which the body secretes in order to cool itself. An evaporative cooler is a device that cools air through the simple evaporation of water.

[edit] Radiative cooling
Main article: Radiative cooling
Radiative cooling is the process by which a body loses heat by radiation and is an important effect in the Earth's atmosphere. In the case of the earth-atmosphere system it refers to the process by which long-wave (infra red) radiation is emitted to balance the absorption of short-wave (visible) energy from the sun. Convective transport of heat and evaporative transport of latent heat both remove heat from the surface and redistributes it in the atmosphere, making it available for radiative transport at higher altitudes.

[edit] Laser cooling
Main article: Laser cooling
Laser cooling refers to a number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields. The most common method of laser cooling is Doppler cooling. In Doppler cooling, the frequency of light is tuned slightly below an electronic transition in the atom. Thus the atoms would absorb more photons if they moved towards the light source, due to the Doppler effect. If an excited atom then emits a photon spontaneously, it will be accelerated. The result of the absorption and emission process is to reduce the speed of the atom. Eventually the mean velocity, and therefore the kinetic energy of the atoms will be reduced. Since the temperature of an ensemble of atoms is a measure of the random internal kinetic energy, this is equivalent to cooling the atoms.

Sympathetic cooling is a process in which particles of one type cool particles of another type. Typically, atomic ions that can be directly laser cooled are used to cool nearby ions or atoms. This technique allows cooling of ions and atoms that can't be cooled directly by laser cooling.

[edit] Magnetic cooling
Main article: Magnetic evaporative cooling
Magnetic evaporative cooling is a technique for lowering the temperature of a group of atoms. The process confines atoms using a magnetic field. Collisions mean that over time, individual atoms will become much more energetic than the others, and will escape, removing energy from the system and reducing the temperature of the remaining group. This process is similar to the familiar process by which standing water becomes water vapor.

[edit] Other
A heat pipe is a passive device that is constructed in such a way that it acts as though it has extremely high thermal conductivity. Heat pipes use latent heat and capillary action to move heat, and can carry many times as much heat as a similar-sized copper rod. Originally invented for use in satellites, they are starting to have applications in personal computers.

A thermocouple is a junction between two different metals that produces a voltage related to a temperature difference. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert heat into electric power.

A thermopile is an electronic device that converts thermal energy into electrical energy. It is composed of thermocouples. Thermopiles do not measure the absolute temperature, but generate an output voltage proportional to a temperature difference. Thermopiles are widely used, e.g., they are the key component of the infrared thermometers that are widely used to measure body temperature via the ear.

A thermal diode or thermal rectifier is a device that preferentially passes heat in one direction; a "one-way valve" for heat.

RUDOLF CLAUSIUS

2010-09-07T10:24:00.000-07:00

Rudolf Clausius
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"Clausius" redirects here. For the lunar crater, see Clausius (crater).
Rudolf Clausius

Born 2 January 1822(1822-01-02)

Died 24 August 1888 (aged 66)

Nationality Germany
Fields Physics
Known for Thermodynamics and
originator of the concept of entropy
Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb,[1] 2 January 1822 – 24 August 1888), was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics.[2] By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis. His most important paper, On the mechanical theory of heat, published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy.

Contents
1 Life
2 Work
2.1 Entropy
3 Tributes
4 Quotes
5 See also
6 References
7 External links

[edit] Life
Clausius was born in Köslin (now Koszalin) in the Province of Pomerania. He started his education at the school of his father. After a few years, he went to the Gymnasium in Stettin (now Szczecin). Clausius graduated from the University of Berlin in 1844 where he studied mathematics and physics with, among others, Heinrich Magnus, Johann Dirichlet and Jakob Steiner. He also studied history with Leopold von Ranke. During 1847, he got his doctorate from the University of Halle on optical effects in the Earth's atmosphere. He then became professor of physics at the Royal Artillery and Engineering School in Berlin and Privatdozent at the Berlin University. In 1855 he became professor at the ETH Zürich, the Swiss Federal Institute of Technology in Zürich, where he stayed until 1867. During that year, he moved to Würzburg and two years later, in 1869 to Bonn.

In 1870 Clausius organized an ambulance corps in the Franco-Prussian War. He was wounded in battle, leaving him with a lasting disability. He was awarded the Iron Cross for his services.

His wife, Adelheid Rimpham, died in childbirth in 1875, leaving him to raise their six children. He continued to teach, but had less time for research thereafter.

In 1886 he remarried Sophie Stack, and then had another child.

Two years later, on 24 August 1888, he died in Bonn, Germany.

[edit] Work
Clausius' PhD thesis concerning the refraction of light proposed that we see a blue sky during the day, and various shades of red at sunrise and sunset (among other phenomena) due to reflection and refraction of light. Later, Lord Rayleigh would show that it was in fact due to the scattering of light, but regardless, Clausius used a far more mathematical approach than some have used.

His most famous paper, "Über die bewegende Kraft der Wärme" ("On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom") [3] was published in 1850, and dealt with the mechanical theory of heat. In this paper, he showed that there was a contradiction between Carnot's principle and the concept of conservation of energy. Clausius restated the two laws of thermodynamics to overcome this contradiction (the third law was developed by Walther Nernst, during the years 1906–1912). This paper made him famous among scientists.

During 1857, Clausius contributed to the field of kinetic theory after refining August Krönig's very simple gas-kinetic model to include translational, rotational and vibrational molecular motions. In this same work he introduced the concept of 'Mean free path' of a particle. [4] [5] [6]

Clausius deduced the Clausius-Clapeyron relation from thermodynamics. This relation, which is a way of characterizing the phase transition between two states of matter such as solid and liquid, had originally been developed in 1834 by Émile Clapeyron.

[edit] Entropy
Main article: history of entropy
In 1865, Clausius gave the first mathematical version of the concept of entropy, and also gave it its name. He used the now abandoned unit 'Clausius' (symbol: Cl) for entropy. Clausius chose the word "entropy" because the meaning, from Greek, en+tropein, is "content transformative" or "transformation content" ("Verwandlungsinhalt"). [7] [8]

1 Cl = 1 cal/°C = 4.1868 joules per kelvin (J/K)
[edit] Tributes
He was elected a Fellow of the Royal Society of London in 1868 and received its Copley Medal in 1879.
He was elected a member of the Royal Swedish Academy of Sciences in 1878.
He received the Huygens Medal in 1870.
He received the Poncelet Prize in 1883.
He received an honorary doctorate from the University of Würzburg in 1882.
The crater Clausius on the Moon is named in his honor.
[edit] Quotes
The following are two famous quotes made by Clausius in 1865:

The energy of the universe is constant.

The entropy of the universe tends to a maximum.

Burning Waste to Produce Energy Has Great Potential As an Energy Source

2010-09-06T11:30:00.000-07:00

The human race has used wood to make fire for a very long time. It has been our main source of energy for most of our existence and we have used it to cook food and provide heating.

Use is dwindling but burning waste to produce energy has great potential as an energy source. This is particularly important when you consider the amount of waste produced in the modern world, the problems faced with disposal and the effort being put into recycling.

A Biomass Power Station works in a similar way to a coal fired power station. Waste is burned and used to heat water, the steam produced is used to turn turbines, the turbines turn generators and generate electricity. Any solid waste can be used including animal manure, woodchip, seaweed, rubbish and any other waste.

Bio-conversion is a related process where plant/animal waste is used to produce bio-fuels such as methanol or natural gas. These bio-fuels can be burned to produce power and vehicles have been developed powered by bio-fuels

Sugar can be used in a similar way because it can be fermented to make alcohol which can be burned. Alternatively, the left over sugar cane pulp can be burned and often a biomass power station provides energy for a sugar mill as well as the surrounding area.

A Biomass Power Station is planned for Portbury near Bristol which would produce 150 MW of power and this is enough to provide power for two hundred thousand homes. It will burn wood materials brought to the plant by ship from sustainable sources and will annually offset about four hundred thousand tones of carbon dioxide emissions.

Another Biomass Power Station is planned for Longannet in Scotland which will produce 20 MW from wood and waste derived fuel and provide electricity for about thirty three thousand homes. It will also offset one hundred and thirty tonnes of carbon dioxide emissions each year and prevent one hundred and thirty five tonnes of waste material being disposed in landfill sites.

Bio-fuels could help us reduce our reliance on fossil fuels and most particularly the oil used for transport which is obviously a good thing.

Some people claim that it will take a huge amount of land to grow the bio-fuels needed and this will affect our capacity to grow food. Bio-fuel powered vehicles produce similar carbon emissions to petrol driven vehicles but scientists argue that the plants growing the bio-fuel will take in the extra carbon emissions produced as they respire. Time will tell on this argument.

We should definitely take the opportunity to burn waste materials whenever we can. It is a very cheap source of fuel and would help reduce our dependence on fossil fuels. It also destroys waste and reduces the need to recycle. We collect waste anyway and have trouble with disposal.

However, growing bio-fuels could cause problems and some fuels may not always be available. Bio-fuels are burned and still produce greenhouse gases in the same way as fossil fuels

HOW to be SEDUCTIVE to ur BOYFRIEND!!!

2010-09-02T09:34:00.002-07:00

Even if you already have won your man's heart and already have him as your boyfriend, you should keep the fire burning and still seduce him. Here are some tips that will make your relationship as fiery as never before!

Have ample confidencE
Confidence is equal to sexiness. Guys will always find confident girls sexy and seductive. Being confident will also give you a smart look. If you accept and love yourself just the way you are, then he'll most likely feel the same way about you.

Look seductive.
From time to time, surprise your boyfriend with a seductive look. Curl up your hair then wear something low cut that would reveal some of your skin. If you're in a private area, you can let him see what's underneath your clothes, let him take a peek at your sexy lingerie. Also, add a spray of sexy scent and you're out to rock!

Bring up the teasing.
Look at him straight in the eye, pout you lips a bit then flip your hair. Be kinky without touching him, make him desire you visually first.

Naughty girl, nice girl.
Send your boyfriend caring messages one day and naughty ones the following day. Be spontaneous, though. You don't want to appear that everything was scripted and planned.

Set the mood
You can prepare a candle-lit dinner for two on your porch then play some sweet background music. After dinner, enjoy the music and dance together. Entice him further by putting on scented lavender in the room.

Work up on your creativity.
Never run out of surprises. Try to bake him a cake or some cupcakes then write "You're so hot" or "You're good enough to eat" on the cake box. Enjoy this dessert over a cup of coffee while watching a movie. It's a wholesome thing to do but the thought of it makes your boyfriend happy. And who knows what will happen after you enjoy the dessert?

Pose for a sexy photograph.
Shoot a sexy photo of yourself on your cell phone and send it to him or print the picture and put it inside his wallet or his bedroom where he can see it often.

There are so many ways to be sexy and seductive. All you have to do is be creative and spontaneous in what you do. Have fun and enjoy each moment with your boyfriend and you'll see that all your hard works will pay off in the end.

Pay Close Attention Here-

Now listen carefully! Take 2 minutes to read the next page and you'll discover a stunning trick which will show you- How to Captivate a Man, Make Him Fall in Love with You -- and Give You The World. There is a set of easy to follow psychological tricks which shows any woman how to be irresistible to men. I strongly urge you to read everything on the next page before it's too late and time runs out!

Why do Women get Excited by Bad Boys?

2010-09-02T09:08:00.000-07:00

The word "bad boy" has been thrown around in the seduction community like water. Pick-up gurus will say that in order to get the girl you must become a bad boy. What if you are not a bad boy? What if you are a good guy that doesn't want to play mind games with chicks or cheat on them with their best friend? What if you don't like to be in the lime light? What if you are so confused about being a bad boy or yourself that you wanna pull your hair out? It is true that some women love bad boys. It is also true that some women love the good guys. I was watching a video that a woman broke down the bad boy, the good guy, and the "nice" guy. She did a really good job that help clear a little confusion I had. But this article is not about the good guy, or even about the bad boy himself. This article is here to give you the "why" women loves these guys.

To be honest it's not the bad boy himself that she loves...it's something that she is lacking that she is trying to get from him. If a woman is bored with her life or her significant other, a man that is adventurous or bold excites her. If he doesn't try to stay on her good side (like most people do or like her boyfriend/husband does) then she finds him to be a challenge. You see, there is a good thing about the bad boy that women love...he says what he wants and does what he wants. Women love protection and a sense of security. The bad boy gives off a vibe that he doesn't take crap from anybody. If you don't take crap from anybody then the girl feels that no crap will come her way from other people. Women, just like men, love spontaneity. At any moment there may be some excitement that can come along. A road trip, an unplanned vacation, etc.--we can all agree that when something fun out of the blue happens, we get excited. The bad boy prides himself on being spontaneous.

Now as far as women like being treated like crap from these guys is a different story but as I write this I am coming to a better understanding in real time (funny how that happens sometimes) Let's use a beautiful woman and a guy that never dates at all. This man may have it in his head that he will do anything to be with this woman solely off of her looks. If she disrespects him he will take it. He will put up with her bull and try to stay on her good side. Women don't like this--only if they can use it to their advantage. As far as being with someone as a significant other, they don't respect it. What does the bad boy do? He checks her and lets her know that her looks are nothing and that she is nothing until she acts like she has some sense and can respect him. If she flakes on him then he will move on to another chick. He won't keep calling or begging her to go out with her. So being that this is the type of guy that she is looking for, she will be on her best behavior. Now the question about if women like being treated like crap. Just like the guy that has never dated, the woman may have never met a guy that has ever excited her like the bad boy. So she will tolerate a little disrespect her and there. A little cheating here and there. Why? Because she doesn't want to lose him! Just like men who don't date get desperate, women get desperate too. They get desperate to find a man that can excite them. If the man is "good-looking" she will lose her mind just to keep him.

What does this tell you? That you have to be a bad boy? No! Not even close. All you need is the qualities that attract women. The bad boy happens to have these qualities. He knows how to excite them. He knows how to keep them on their toes. You can too. You don't need to be over the top. You don't need to work extra hard. All you need to do fine tune your masculine confidence. That's right! That is the key--masculine confidence. The bad boy knows how to use his masculine confidence. Believe it or not but so does the good guy (think of your favorite heroes like superman and batman).

So you may be asking, "What do you mean 'masculine confidence'?" I mean that confidence that every masculine man has but has never really tapped into it. Most men think that you have to be a bad boy to get the girl, but miss the whole point.

Men are confused for obvious reasons. Women go for a certain type and the average man tries to be that type. When he becomes that type he may be losing his true self in the process. He doesn't understand that his success with women only requires him to strengthen his masculine confidence. Women can't resist men who are very masculine and strong. A man that can excite her to the point that she will lose her mind if she loses him. Be that man. Take action and learn how to become that man.

Why Do Women Get Excited By Bad Boys?

2010-09-02T07:46:00.001-07:00

ENGINEERING TECHNOLOGY: search box

2010-08-25T10:48:00.000-07:00

ENGINEERING TECHNOLOGY: search box: "<"

search box

2010-08-25T10:25:00.000-07:00

2010-08-25T10:17:00.000-07:00

Albert Einstein-Biography Profile

2010-08-24T10:11:00.000-07:00

Albert Einstein - Basic Information:
Nationality: German http://www.mechengee.blogspot.com
Born: March 14, 1879Death: April 18, 1955
Spouse:
Mileva Maric (1903 - 1919)
Elsa Lowenthal (1919 - 1936)
1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" (from the official Nobel Prize announcement)
Albert Einstein - Early Work:
In 1901, Albert Einstein received his diploma as a teacher of physics and mathematics. Unable to find a teaching position, he went to work for the Swiss Patent Office. He obtained his doctoral degree in 1905, the same year he published four significant papers, introducing the concepts of special relativity and the photon theory of light.
Albert Einstein & Scientific Revolution:
Albert Einstein's work in 1905 shook the world of physics. In his explanation of the photoelectric effect he introduced the photon theory of light. In his paper "On the Electrodynamics of Moving Bodies," he introduced the concepts of special relativity.
Einstein spent the rest of his life and career dealing with the consequences of these concepts, both by developing general relativity and by questioning the field of quantum physics on the principle that it was "spooky action at a distance."
Albert Einstein Moves to America:
In 1933, Albert Einstein renounced his German citizenship and moved to America, where he took a post at the Institute for Advanced Study in Princeton, New Jersey, as a Professor of Theoretical Physics. He gained American citizenship in 1940.
He was offered the first presidency of Israel, but he declined it, though he did help found the Hebrew University of Jerusalem.
Misconceptions About Albert Einstein:
The rumor began circulating even while Albert Einstein was alive that he had failed mathematics courses as a child. While it is true that Einstein began to talk late - at about age 4 according to his own accounts - he never failed in mathematics, nor did he do poorly in school in general. He did fairly well in his mathematics courses throughout his education and briefly considered becoming a mathematician. He recognized early on that his gift was not in pure mathematics, a fact he lamented throughout his career as he sought out more accomplished mathematicians to assist in the formal descriptions of his theories.
Other Articles on Albert Einstein:
Books about Albert Einstein & Relativity
Photographs of Albert Einstein
The Photoelectric Effect
Einstein's Theory of Special Relativity
Einstein's Theory of General Relativity
Film review - NOVA: Einstein's Big Idea
Film review - I.Q.
NobelPrize.org - Albert Einstein biography
Albert Einstein - Other Einstein Articles
Albert Einstein Photographs
Film Review - I.Q.
Books about Einstein & Relativity
Albert Einstein - Theory of Relativity
Einstein's Theory of Relativity
Special Relativity
General Relativity
Albert Einstein - Einstein's Photon Work
The Photoelectric Effect
What is a Photon?
Wave Particle Duality

!watch out 4 more, all Einstein's fans!

"DOCTORS are BAD for your HEALTH

2010-08-23T08:38:00.000-07:00

you may want to think twice before your next visit to the doctor's office. According to Dr. Barbara Starfield's now-famous study, iatrogenic deaths (those resulting from treatment by physicians or surgeons) are the third leading cause of mortality in the United States, resulting in the loss of 225,000 lives per year. Of that total, nosocomial (hospital-acquired) infections kill 80,000, physician errors claim 27,000, and unnecessary surgery results in 12,000 deaths.

But iatrogenic errors aren’t the only reason people should avoid hospitals, says physician and health care administrator Archelle Georgiou. She tells Big Think that relying on doctors may actually shorten your lifespan. Georgiou bases this idea on her studies of the earth’s so-called “blue zones,” isolated communities around the world whose inhabitants live longer and healthier lives than the greater populace.
In the Greek blue zone, the island of Ikaria, inhabitants are more than 4 times more likely to live to age 90 than Americans are—yet there is virtually no health care infrastructure. Georgiou tells us: “There are no hospitals or major surgery capabilities…. People needing emergency care are transported by helicopter to Samos (a neighboring island), and all elective surgery is done in Athens.”

A procedure like an arthroscopy or a hysterectomy that would take 3-5 days in the U.S. consumes 3-5 weeks for Ikarians, who must relocate to Athens for the procedure and convalescence. Therefore, "their threshold for elective surgery is significantly higher than ours," Georgiou says. The result is that people depend on themselves rather than doctors for non-life threatening ailments. And, knowing that health care is so inconvenient, Ikarians take greater care not to get sick—they eat a healthy diet rich in vegetables and exercise daOur greater access to health care (discounting, of course, the millions of uninsured Americans) might make us more likely to live unhealthfully. “U.S. culture is steeped with a 'find it and fix it' mentality,” Georgiou tells us. Rather than try to prevent illnesses, we rely on our doctor's ability to fix what ails us. And the result is that "we spend significantly more on health care than any other nation but without the benefit of improved outcomes or longevity.” In the U.S., our life expectancy is only 78, yet we spend 2.5 times more money per capita than Japan, the country with the highest life expectancy (82.6 years). One-half to one-third of the $2.2 trillion per year America spends on health care is simply unnecessary, says former AMA chairman Raymond Scalettar.ily.Our reliance on doctors may be tied to our faith, Georgiou believes. According to the World Values Survey, the U.S. ranks high on the traditional versus secular-rational values scale (in between Ireland and Northern Ireland). “Our nation’s traditional values make us more religious, more deferential to authority, more paternalistic,” she says. In other words, the impulse that causes us to listen to our pastors is the same one that makes us heed our physicians. “As a result, Americans have abdicated personal responsibili ty
Takeaway

One in every twenty patients contract potentially fatal infections in hospitals. In 2002 there were nearly 38 million hospital visits in the U.S., placing the number of hospital-acquired infections around 1.9 million per year. Weaning ourselves off our health care addiction would not only help reduce this number but also help rein in the nation’s ballooning health care costs. ty and delegated the responsibility for their health to their
doctor and to the health care system. We don’t ask questions, we just do what the doctor says."What is true on the tiny island of Ikaria, might not hold true in a country as big and diverse as the U.S. Dr. Steven Schroeder, a professor of health and health care at UCSF, says that poverty, rather than a over-reliance on doctors, is to blame for our poor showing in global health comparisons. Poor Americans are four times more likely to die an early death than the rich. It is safe to assume that many of these poor are among the 45 million uninsured in our country, meaning that their access to health care, like the Ikarians, is restricted to emergency room care (the most expensive kind of health care). To be sure, other behavioral aspects of their lives might be to blame for their lower life expectancy, but over-reliance on doctors is surely not the cause. And while it may be true that Americans generally should lead healthier lives, studies have shown that regularly visiting the doctor is a potent weapon against the second leading cause of death in the United States: cancer. Cancer screenings can catch the disease in its early stages, increasing a patient’s likelihood of long-term survival. And people who have routine check ups are more likely to undergo these screenings. According to the American Cancer Society, campaigns to increase usage of Pap testing and mammography have contributed to a 70% decrease in cervical cancer incidence rates since the introduction of the Pap test in the 1950s as well as a steady decline in breast cancer mortality rates since 1990. But more can still be done: the National Cancer Institute says that of the estimated 569,490 who will die of cancer in the U.S. in 2010, as much as 35% of these premature deaths could have been avoided through screening.

watch out for more reasons!