Finite Definition and 1000 Threads

I need help trying to set up this problem. I want to find the capacitance between a point charge and a finite plate (or disk) as the point moves from above the center of the plate to some distance off the plate. I have been able to simulate this problem using FEM, however, there should be a...

Hi, Physics forum! Just a little push of my doubts I hope somebody could help me with my confusion of one of our home works. I know that all boundary conditions are zero. My doubt is how do I interpret (x,y,0)=0.01 source in the figure? Where is it located in the grid. I am hoping someone...

<Moderation note: edited LaTex code> E.g. A rotation by a finite angle θ is constructed as n consecutive rotations by θ/n each and taking the limit n→∞. $$ \begin{pmatrix} x' \\ y' \\ \end{pmatrix} =\lim_{x \to \infty} (I + \frac{\theta}{n} L_z )^n \begin{pmatrix} x...

Hello guys, I was reading some models about the topology and size of the universe (always a controversial topic), then a question came to my mind. It is predicted that our universe will expand until it reaches heat death. Can a closed, finite universe also reach heat death and be described by...

Homework Statement Homework Equations I could really use a push on how to approach this problem. My primary problem is it asks for the heat flux into the page, which makes no sense to me as that is the z direction and this is in the x/y plane. If anyone could explain this problem and maybe...

I am using the Finite Difference Method to solve Poisson's equation \frac{\partial \phi}{\partial z^2} = \frac{\rho}{\epsilon} To do it is discretized according to the Finite Difference Approximation of the second order derivative yielding the following set of equations for each grid point...

Homework Statement Suppose that ##H## and ##K## are subgroups of finite index in the (possibly infinite) group ##G## with ##|G : H|m## and ##|G:K|=n##. Prove that ##lcm(m,n) \le |G : H \cap K | < mn##. Homework EquationsThe Attempt at a Solution I was able to get the upper bound on ##|G : H...

Hi guys, Based on what I know about the status of modern cosmology the question whether the universe is infinite or finite in extent is still open. Are there any plausible models in which the universe is finite and closed, despite the curvature being close to flat? Thanks in advance.

Homework Statement Give an example of each, or state that the request is impossible: 1) A finite set that contains its infimum, but not its supremum. 2) A bounded subset of ℚ that contains its supremum, but not its infimum. Homework EquationsThe Attempt at a Solution I either understand this...

Homework Statement I read somewhere that if ##\{A_i\}## is a collection of subsets in some topological space ##X## that is locally finite, then ##\overline{\bigcup A_i} = \bigcup \overline{A}_i##, but I am having difficulty showing this. Homework EquationsThe Attempt at a Solution I already...

I need to take a look at some references about QFT at finite density but I can't find anything, or at least I don't know where to look. I should emphasize that what I need is QFT at zero temperature and finite density so it seems to me QFT in finite temperature books may not be what I need or...

How would I design a non-trivial algebraic function of degree 4 containing a branch at the origin with the (finite) power expansion: ##w(z)=1+0.5 z-1/4 z^{1/2}+3/4 z^{1/4}##? having the form ## f(z,w)=a_0+a_1 w+a_2 w^2+a_3 w^3+a_4 w^4=0## with the ##a_i ## ( preferably not fractional)...

What does it mean when a limit is finite

Homework Statement Which algebraic expressions must be solved when you use finite difference approximation to solve the following Possion equation inside of the square : $$U_{xx} + U_{yy}=F(x,y)$$[/B] $$0<x<1$$ $$0<y<1$$ Boundary condition $$U(x,y)=G(x,y)$$ Homework Equations Central...

Homework Statement I'm currently working on a homework set for my intermediate QM class and for some reason I keep drawing a blank as to what to do on the first problem. I'm given three potentials, V(x), the first is of the form {A+Bexp(-Cx^2)}, the others I'll leave out. I'm asked to draw the...

Suppose $G$ is an infinite group and $H$ is an infinite subgroup of $G$. Let $g\in G$. Suppose $\forall h\in H\ \exists h'\in H$ such that $gh=h'g$. Can we conclude that $gH=Hg$? What if $G$ and $H$ are of finite orders?

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.2 ... ... Lemma 1.2 reads as follows: My questions related to the above proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with another aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: My questions regarding Bresar's proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...

Homework Statement An electron is enclosed in a potential well, whose walls are ##V_0 = 8.0eV## high. If the energy of the ground state is ##E = 0.50eV##, approximate the width of the well. Answer: ##0.72nm## Homework Equations For an electron in a potential well, whose energy is less than...

In my simulation I have a wire with a fixed current flowing, I observed if I change the diameter of the wire the magnetic field (B) in a fixed point of the space also changes, is it correct?

Hello I am trying to prove that $\mathbb{Q}$ is not a finite set. I proceed with path of proof by contradiction. Suppose that $\mathbb{Q}$ is a finite set. Then $\exists\; n \in \mathbb{N}$ such that $I_n \sim \mathbb{Q}$, where \[ I_n = \{i \in \mathbb{Z^{+}} |\; i \leq n\} \] This means that...

Suppose I want to solve the time-independent Schrödinger equation (ħ2/2m ∂2/∂x2 + V)ψ = Eψ using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...

I am trying to solve a system of equations and have a question regarding the validity of my approach when implementing a fifth-order Cash-Karp Runge-Kutta (CKRK) embedded method with the method of lines. To give the questions some context, let me state the problem I am attempting to solve: $$...

Hi, Is space finite? In my opinion, it is inconceivable that space is finite. If space is finite, what is exactly outside of this stuff we called as space? More space? What exactly surrounds the singularity before the Big Bang event started? If it is nothing that "surrounds" the singularity...

Okay, I'm following a series of video lectures on applications of finite element method to engineering, and the tutor started by demonstrating the mathematical background of FEM using a simple heat transfer problem. He derived the governing equation (in just one dimension): (1)...

I am solving the simple 2nd-order wave equation: $$ \frac {\partial ^2 E}{\partial t^2} = c^2 \frac {\partial ^2 E}{\partial z^2} $$ Over a domain of (in SI units): ## z = [0,L=10]##m, ##t = [0,t_{max} = 10]##s and boundary/initial conditions: $$ E(z=0) = E(z=L) = 0 $$ $$ E(t=0) =...

I searched for a proof of the statement in the title and found this document. But it just proves that for two norms ## \rho(x) ## and ## ||x|| ##, we have ## m\rho(x)\leq ||x|| \leq M \rho(x) ## for some m and M. But how does it imply that the two norms are equivalent? Thanks

[this thread was moved from the Quantum Physics subforum, hence no template] In this page : http://www.physicspages.com/2012/08/06/finite-square-barrier-scattering/ When the E<V The boundary condition tells us the equation (9) (10) and (11) (12). I tried to get the results from those equation...

Suppose I am given some 1D Hamiltonian: H = ħ2/2m d2/dx2 + V(x) (1) Which I want to solve on the interval [0,L]. I think most of you are familiar with the standard approach of discretizing the interval [0,L] in N pieces and using the finite difference formulas for V and the...

Question. Is it true that a finite extension $K:F$ is simple iff the purely inseprable closure is simple over $F$? I think have an argument to support the above. First we show the following: Lemma. Let $K:F$ be a finite extension and $S$ and $I$ be the separable and purely inseparable...

origin page : http://www.physicspages.com/2012/08/08/finite-step-potential-scattering/ No quite understand how the solution come from this equation

I found in Thompson "From Error-Correcting to Sphere Packing and Simple Groups" this on page 131 How do you compute m/n in a finite field? Take the equivalence class 5 given above. Why does 2/5 and 18/22 give 5? thanks

How can the universe be infinite and yet have a finite age?

How the symmetric and antisymmetric have results: A=0,G=H and B=0,G=-H in last picture ?[emoji53]

Does anyone know how to find the total mass matrix of two coupled element by using Finite Element Method?

Hello, First of all, this question does stem from graduate work, but it seems far too simple to tag "advanced". I am looking to write some code to simulate the force from a railgun. The first step in doing this (from a tutorial I found) is to find the magnetic field at any point within the...

Homework Statement d2T/dx2 = 5*(dT/dx) - 0.1*x = 0 T(0) = 50 T(10) = 400 (Δx) = 2I've figured out how to do these problems when Δx = 1, but when it equals any other number it goes wrong. I know you start by plugging in the algebraic approximations for the differential elements, I think maybe my...

speed? This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky. In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite...

The universe- from our understanding, is expanding, thus the regions (for lack of a better word) particles have not yet reached do not exist. How far our universe can/ will expand is unknown, it may be infinite, but we can conclude at this time, as it is still expanding, that it is finite. True...

I am assuming scientists say that the universe is 13.8 billion years old with respect to time on earth. If so, how come the infinite energy present at such a small scale didn't make gravitational time dilation infinite during the first stage? Wouldn't time dilation make the universe infinitely...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

I'm trying to numerically solve the time dependent Schrödinger equation and I've been told that the best approach is to numerically integrate using a finite difference method, however I don't understand why I couldn't just use ode45 to solve it?! Is the finite difference (interpolation) method...

I found this part of forum the most relevant to this theme so excuse me if I missed. This year I'm doing a high school summer project related to quantum mechanics. Anyway I'm using finite difference method to solve Schrodinger equation. Before starting to work on a project I decided to get some...

OK, so it's time to start a new thread. I heard many times that there exists only one black hole solution for a given mass and angular momentum, but I know already that this is not true. We all know that if we throw something into an existing black hole, its event horizon starts to ripple. So...

Homework Statement Comment how the energy and wave functions of the electron would change in the case of a finite dept quantum well with the same width. Homework EquationsThe Attempt at a Solution I feel completely clueless as how to approach! :( * The full question can be found in the...

I've calculated the eigenstates of the Hubbard Hamiltonian for two fermions. The ground state is (U2 - (U2 + 16t2)1/2)/2 For U = infty, I get 0. For U >> t, I should get the exchange energy J = -4t2/U How do I get from the ground state equation to J?

Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that...