What is Continuum: Definition and 142 Discussions

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...

I have just started to work in a ultrafast spectroscopy lab. My topic that i will be starting on next week is supercontinuum pulse compression. I just graduated with my BS Physics and have only some experience with ultrafast optics. I know the general theory of how these things work and need a...

Homework Statement Mechanics of Deformable Media (Bhatia and Singh), 5.2: Consider a long rod of elastically isotropic material of L standing vertically in a vacuum in equilibrium under the gravitational field of the earth, then: (i) What are the boundary conditions for \sigma_{ij} on the...

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...

Homework Statement Consider a rubber band living in the plane and having a uniform density, whose endpoints are V1 and V2. The rubber band passes through a runner without mass, inside which it can slide in a frictionless manner. The runner can assume any arbitrary position E in the plane...

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...

example 3.30: Let the stress tensor components σij be derivable from the symmetric tensor field φij by the equation σij = εiqkεjpmφkm,qp. Show that, in the absence of body forces, the equilibrium equations are satisfied. I don't have any idea have to solve this problem. Can someone help...

Hey, I've picked up a book on continuum mechanics to do a bit of studying by my self. As this topic is somewhat odd (difficult) I wonder if anyone knows of a place where students of continuum mechanics meet for discussion? I'm not sure if there is a subforum here at physicsforums which deals...

Hi, In a few journals I've come across the term "centimeter continuum emission" - e.g. 21 cm continuum emission. What is meant by this? And how can it be continuum when it has a discrete cm value? Thanks, San

Mods: I wasn't sure if I should put this here or in DE's, if you think it would be better there, feel free to move it. Everyone: If I have a bunch of particles, which I'm modelling as a continuum, and I want to put periodic boundary conditions which reflect (completely specular reflection)...

Hi I am doing a beginners physics course and I am learning about free-free emissions and bound bound emissions. I understand that an electron can emit and absorb any amount of energy if its in the continuum and therefore free. But what about the proton? It it sits in the continuuem can it...

I need to learn optics, SR and continuum mechanics for my physics qual exam in June. Can anyone suggest some books that would be appropriate for self study?

I have the oppurtunity to take a class called continuum mechanics. Has anyone here taken the subject?, did you find it interesting and most importantly useful in your work? It sounds pretty fun, but I don't know if it is that useful for later. So could you be so kind as to tell me how it has...

I have a question about FEM applied to stress/strain type of problem, is this the right section to post it? -Thank you

"Independent Continuum" Can anybody please explain to me what this actually means. My understanding in very vague terms is that something is constant, with reference to Einstein's The Special and General Theory book, where he says that we often think of time (and space i think) as "independent...

I started reading a great textbook and thought I would share some of its finer points. It is a great introduction to mechanics of solids and liquids, although the title explicitly states Earth and Environmental Sciences. http://www.science.mcmaster.ca/~geo/faculty/emeriti/middleton/index.html...

I'm not usually a fan of "Causal Sets" QG, but this is a significant advance in that theory. http://arxiv.org/abs/gr-qc/0604124 On Recovering Continuum Topology from a Causal Set Seth Major, David Rideout, Sumati Surya 31 pages, 5 figs. Dedicated to our friend and teacher Rafael Sorkin, to...

Does the Continuum Hypothesis imply the General Continuum Hypothesis?

http://golem.ph.utexas.edu/~distler/blog/archives/000713.html" has a new post about CDT. He goes on about continuum limits and doesn't believe Reuter on the GR renormalization fixed point, suggesting (on no evidence that I could see) that the GR doesn't have the right kind for a good continuum...

what are the open and still not yet answered problems in continuum mechanics as of today? i reackon navier-stokes equations solutions is something that is related to the issue, right?

Here is a free and downloadable textbook on Tensor Calculus. http://www.math.odu.edu/~jhh/counter2.html Scroll to bottom of page to find pdf files.

The laws determinning the passage of light through varying densities of transparent material and through varying "acceleration" caused by a common field of gravity have similarities. I prefer to think of warping of the time space continuum as an increase in density. Light bends as it passes...

...I'm currently studying R. Aris, "Vectors, Tensors, and the Basic Eqns. of Fluid Mechanics." What are some of the other classic references for the mechanics of continuous media?

What is continuum mechanics. What does the word "continuum mean"? What is discrete?

Does anyone know good books on tensor analysis, especially need to learn it to understand continuum mechanics. Thank you.

Kind of trivial result, but thought it might be interesting. This is part of a wider development which will be described further, either here or in another thread. Statement: "A Point in Spacetime has the Cardinality of the Continuum" Justification: Time can play a really neat...

Hi tide, A while back I asked you about potential. And you said to consider the electrons as a continuum when we talk about a body having charge on its surface. Its clear that if you have any finite number of point charges, (the electrons), then there is no way you can arrange them so that the...

I need people's theory's on time and the space time continuum. I believe that time is made up of realities, and that the main reality is where we are now. When events happen, little branches come off. (Every person has their own reality that is linked into the whole.) When time travel happens...

Hi, this is just an idea for now, i guess. It's incomplete but does the best I can do up till this point. Maybe it combines all the forces, maybe it doesnt. All I know is that mathmatically it can be done. And this is my interpitation of it, and it makes observing life look so weird cause I...

Did Einstein meant by space-time continuous that time is just another dimension, like the other 3? If so, why are we experiencing this one that differently? (Should this have gone in the phylosophy section?)

If the standard for "consciousness" were -- for the purposes of this discussion -- reduced down to an "exchange of information", might then all things within the Universe have a "level of consciousness" based on the COMPLEXITY of the information being exchanged...

Can anyone describe the nature of the time continuum? How does it work?

light as a continuum We have an iron rod and it is connected to a power supply. One meter away there is a sheet of white paper hanging on a wall. Both the rod and the paper are unlit. Very slowly we increase the voltage passing through the iron rod. Very slowly the rod starts to...

p and q are real numbers. If p < q then [p,q] = {x : p <= x <= q} or (p,q] = {x : p < x <= q} or [p,q) = {x : p <= x < q} or (p,q) = {x : p < x < q} . A single-simultaneous-connection is any single real number included in p,q ( = D = Discreteness = a localized...

If we take any R member (with an infinitely many digits) which is being used as a set's boundary, we find this: A member with an infinitely many digits never reaches 0 by definition. It means that there is always an unclosed interval for some line's segment {0_____R member with...

Hi, To check a bijection between two sets, we have to look at the contents of the two examined sets as if they are discrete elements, otherwise we can't use the bijection method. |R| = Continuum, so my question is, how can we check if there is or there is not a bijection between |Q|...

How does one incorporate discontinuity into otherwise continuous probability? The game of blackjack comes to mind - one may win by accumulating card values more than an opponent, but only up to the cutoff of 21 points, beyond which one most precipitously and surely loses. Optimum play may be...