Continuum Definition and 131 Threads

Homework Statement The continuum element shown in Figure (a) deforms to figure (b) I'm looking to find the positions after deformation (x coordinates) by expressing them in terms of E coordinates. Homework Equations The Attempt at a Solution x1 = E1 + E2 x2 = E1 + E2 x3 = E3 The...

Homework Statement I am studying my lecturer's notes and in this part he uses a delta potential to illustrate a simple example of Fermi's golden rule, that the rate of excitation is ##\propto t##. Homework Equations The Attempt at a Solution I've managed to get the bound states, by solving...

Freidel "Continuum Limit and Renormalization" ILQGS 1/4/14 http://relativity.phys.lsu.edu/ilqgs/ Tomorrow Laurent Freidel gives the online International LQG Seminar talk, the topic being "Continuum Limit and Renormalization". It might be helpful to look over a Freidel paper ahead of time...

Homework Statement I am self-studying this note and I am stuck in the derivation of the normal shear stress. I can't see how the relations (23) and (24) come about, i.e. I don't understand \tau'_{xx} = \frac{\tau_{xx}+\tau_{yy}}{2}+\tau_{yx} and \tau'_{yy} =...

Homework Statement Hi I can't follow the derivaton in this link. It is the following equality they have in the beginning, which I don't understand: \nabla \cdot u = \frac{1}{\rho}\frac{d\rho}{dt} Following the very first equation on the page, I believe it should be \nabla \cdot u =...

Looking for a quantum-based explanation as to why solids, when heated, emit radiation as a continuum, rather than discretely. Gas will emit discrete spectral lines when heated. Somone already suggested to me that there may be many random purtubations to the discrete energy levels in a heated...

Hello^^ (I'm new here) I want to know the mathematical tools i need to study continuum mechanics. It would be great if someone give me a link that contains video lectures. Thanks for help .

Does entanglement means that space-time is not a continuum after all?

Let's define a set (collection) \mathcal{C} by the following conditions. X\in\mathcal{C} iff all following conditions hold: 1: X\subset [0,1]. 2: X is closed. 3: If x\in X and x<1, then there exists x'\in X such that x<x'. 4: For all x\in X there exists a \delta_x >0 such that...

Hi, All: I have heard all these claims thrown around that the sex/gender* of a person is not "binary" , i.e., it is not necessarily either male or female, but instead that it is a continuum with male and female at the ends. Is there something to this? If so, how can one test this; are there...

Hello all, Background I've been playing with computer simulations quite a bit recently, and wrote one that crudely simulates the formation of star systems. My first version was a conventional many body simulation with about 300 small bodies; it actually tends to come up with convincing star...

Are there any textbooks on something like this, a self consistent treatment of classical electromagnetism (relavistic is fine too) where the field equations are solved alongside with the matter fields.

Is there a way to know one way or another? If smallest possible scale is Planck scale, does it mean that space-time is discrete where smallest possible step is Planck's length (PL) and smallest possible time is Planck's time (PT)? If I move my hand from point A to point B, say 1m exactly in...

It is said that the space time continuum gives rise to space and time. So, is space time continuum a mixture of space and time or something totally different from space and time? Plz elaborate as per current scientific understanding only. No out and out philosophy please?

Homework Statement What do you understand by the following terms; (i) principal stretch (ii) an anisotropic material (iii) a dilatant deformation, (iv) a Lagrangian description of a deformation, and (v) a pure deformation. Homework Equations Am just trying to find descriptions for...

I was wondering if anyone knows of a good book on the mathematical theory of continuum mechanics. I have looked online, and the only ones I can seem to find are like your average physics or applied mathematics book. I want something with rigorous theoretical formulation of the subject. It...

Hi all, I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor). I have attached the specifics of the question in a attached photo. Ultimately, there comes a point...

Hi all, I'm currently trying to teach myself continuum mechanics (as I am enrolled in a course for which continuum mechanics is a pre requisite and have never taken such course) I have been reading a book by mase and mase "introduction to continuum mechanics for engineers" 2nd edition. I...

If someone were able to travel back in time and change an event in history which resulted in a divergent timeline from the one you came from would both timelines be part of the same space-time continuum? I suspected they could be because part of their timelines are shared and connected to...

What's being curved, when mass bends the "spacetime continuum?" Okay, I've read lots of books about Einstein's spacetime being curved by mass and all, but I've never read a really good hypothesis as to what, exactly, is being curved. You can't curved nothing (sounds like a double negative, but...

I have heard generally that it is possible to put different physical theories on a lattice and after renormalization get the same continuum theory. I mean, different lattice theories that lead to the same continuum theory. Is this true for, say, qcd, or other particle theories? Are there...

What's the difference between analytical and continuum mechanics?

I have never had an advanced classical mechanics class, only elementary level treatments using mostly Newtonian approaches, on very simple mechanical systems. I'm interested in learning about continuum mechanics, having in mind the applications in the applied field of seismology, which studies...

Continuum approximation of fluid mechanics (& relativistic fluids) I have a few 'foundational' questions on fluid mechanics which I haven't been able to find quick answers to, any help would be appreciated. At the start of any course on fluids, one is told of the continuum hypothesis...

Homework Statement http://img683.imageshack.us/img683/7060/selection001l.png Homework Equations \epsilon^{pl} = \epsilon - \epsilon^{el} \epsilon^{pl} = \epsilon - \frac{\bar{\sigma}}{E} r = \frac{\epsilon_w}{\epsilon_t}The Attempt at a Solution I'm stuck trying to calculate \bar{\sigma}...

Continuum Mechanics Books - help please Hi all.. Im almost done with this course in the current semester .. just academically .. I really haven't ' felt ' this subject .. haven't truly understood it ..so I'm re reading it these vacations . I need a v good book .. please suggest the best...

Homework Statement The components of stress in the x_i reference Cartesian system at a point of interested have been determined to be: \left[\begin{array}{ccc} 500 & 0 & 300 \\ 0 & 700 & 0 \\ 300 & 0 & -100 \end{array}\right] \mathrm{MPa} Determine the principal values and directions of...

I've looked at a few Physics programs and none seem to cover any time of fluids or continuum mechanics in general. It seems to be a very relevant subject to cover but it's only slightly addressed in one of the lower level classes. In these classes they usually only going over Bernoulli's...

Homework Statement http://imageshack.us/photo/my-images/513/selection027.png" http://imageshack.us/photo/my-images/513/selection027.png Homework Equations E_{ij}=\frac{1}{2} \left( \frac{\partial{u_i}}{\partial{X_j}} \frac{\partial{u_j}}{\partial{X_i}} - \delta_{ij}\right)...

Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.

Hello, I'm not sure if this is the right place to ask about Continuum Mechanics or if the right place would be the engineering forums, but since Continuum Mechanics is a branch of Classical Mechanics, I thought it might be the place. My question is about Stress. Why does the stresses on...

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Above reference describes the history of the continuum hypothesis. Among the items of interest is the development of axiom systems in which the continuum hypothesis is true.

Hello, I have problem with understanding the concept of energy of deformed body. As far as I know, Clapeyron's theorem states that elastic energy of deformed body is half the work done by external forces; this are surface and body forces which deform the body. Then, I wonder, where has...

Usually in statistical physics, when your system has a large number N of particles, you take the continuum limit -- you let N\rightarrow\infty, and convert sums to integrals (with an appropriate normalization factor). My understanding is that as a finite number tends to infinity, the infinity...

Homework Statement This is not so much a homework problem but a part of a project I'm working on. So in just a few words; what I have (at time t=0) is a discrete state (half simple harmonic oscillator) connected to a wire with continuous states. These states are coupled by a complex...

I consider an array of lattice points and construct a vector at each lattice points. How to convert this discrete system into a continuum one by using the Taylor series expansion by considering the lattice distance say \lambda? thanks in well advance?

Please explain how the Continuum Idealization allows us to treat properties as point functions and to assume that properties vary continually in space no jump continuity? Thanks

Suppose we assume that the Continuum Hypothesis is false. Then there must be a subset of the real numbers that has the cardinality of Aleph 1. What is an example of such a subset?

how easy does it become to learn general relativity after a good course in continuum mechanics?

First off, hi everyone! This is my first post because I just found these forums (by Googling "Physics forums" in hopes of finding a good forum to ask science questions, specifically physics!). Anyway, I received a text message from a friend who is a teacher in grade school and was not sure how...

Hello! I read somewhere about intro to continuum mechanics. There was a vector \vec{\mu} and displacement vector \delta\vec{\mu}. As vector \vec{\mu} move, it will get new position \vec{\mu}'=\vec{\mu}+\delta\vec{\mu} \vec{\mu}'=\vec{\mu}+\frac{\partial\vec{\mu}}{\partial x_i}\delta...

Hi I'm looking for a good, in depth book on continuum mechanics and classic gauge theory. Can you suggest something? What I know about the subject is the chapter in Goldstein's classical mechanics.

One the things which always bugged me about the definition of the integral is that limit of a Reimann sums consists of a countably infinite number of terms, yet it is supposed to be giving the under area under a curve which varies in a continuous manner. Has anyone else thought seriously about...

Hi, so I scanned an image of the problem statement and my attempt at the solution. I don't know if I am headed in the right direction and need some guidance. This is my first post ever and I hope I am doing this properly. Thank you for any help you guys can provide.

i am currently reading a book about continuum mechanics. they define derivatives of tensor valued functions of tensors in such way: http://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics ) it seems to be related covariant derivative, but i can not figure out its meaning in physics...

Did Paul Cohen "settle" the Continuum Hypothesis? Paul Cohen proved the Continuum Hypothesis is independent of ZFC and concluded that it's truth or falseness is undecidable (1963). Is this still the case today? These links suggest there is still interest in proving or disproving it...

the book "Introduction to tensor calculus and continuum mechanics" hi please help me ! i've try to find appendix d of this or solution that excersise anyone can help me ? any link or full version of this book thart have "appendix d" my english languge not good sorry thanks a lot bye

Hey, all. What would be some good books on continuum mechanics for undergraduates majoring in Physics? I'm familiar with Timoshenko's book that's used in Engineering, but I'm looking for something a Physics student may use. Thanks in advance.

R=2^\alepha 0 vs Continuum hypothesis! A result in "a taste of topology" A year ago or so I read a proof in A Taste Of Topology, Runde that the cardinality of the continuum equals the cardinality of the powerset of the natural numbers. But a few hours ago I found Hurkyl making that statement...

Due to several threads, recent thinking and book readings, suggesting the the concept of "symmetry" itself, as well as the concept of "continuum" are somehow related to a key problem. I asked myself the question about the original line of reasoning of the introduction of symmetry historically...