Finite Definition and 1000 Threads

Hi, I am running a finite element on a cylinder with that converges at the bottom for a opening, which is symmetrical in both directions so i modeled one quarter but the problem is my stresses are the same with when i compare with a full model that i also done but the deflections are different...

What's the best way to explain why tidal forces for an observer free-falling through an event horizon are finite? My first thought was to say that "gravity isn't a force, it's a curved space-time". On further thought, however, it seems to me that consideration of the Rindler horizon shows...

Homework Statement Two parallel charged wires are in vacuum. Width of wires is equal to the distance between them. Calculate electric field in the middle (point A). Homework Equations Superposition The Attempt at a Solution Using superposition, y components on vector E are cancelled. I get...

I know that space is expanding, so the further away you go from my location, the faster space is expanding, asymptomatically approaching the speed of light. I also know that as relative velocities approach the speed of light, the length of space contracts. From this I come up with a limit for...

Hi PF! I'm using a finite differencing scheme to solve the following $$h_t = h h_{zz} + 2h_z^2$$ where the subscripts denote partial derivatives. The difficulty I'm facing is the boundary conditions are dynamic, and move with time ##t##. This makes choosing a ##\Delta z## very difficult and...

For particle in a box with the finite depth, is it traveling wave? or standing wave? I am confused with its ability to pass through the potential walls that is classically forbidden area which makes me think it is traveling wave. But for particle in a box with infinite potential, I understand...

If G is a finite set closed under an associative operation such that ax = ay forces x = y and ua = wa forces u = w, for every a, x, y, u, w ##\in## G, prove that G is a group. What I attempted: If we can prove that for every x ##\in## G, x##^{-1}## is also ##\in## G, then by the closure of the...

Hello, I am working on a solo project outside my domain of expertise (Physics PhD student). I am trying to analyze/replicate the wave phenomena shown in the following video: To summarize what I am doing: I need to analyze a simple (cylindrical) pool, say 17.5" wide, 4" deep Figure out how...

Hi PF! I am looking at finite differencing schemes and it seems we need more initial information to compute central finite differencing than forward finite differencing. Is this true, or am I understanding the process wrong? Thanks!

Just for fun, I tried enumerating the topologies on n points, for small n. I found that if the space X consists of 1 point, there is only one topology, and for n = 2, there are four topologies, although two are "isomorphic" in some sense. For n = 3, I I found 26 topologies, of 7 types. For n...

Homework Statement Prove that[/B] P(\cup_{i=1}^n E_i) \geq \max_i P(E_i) (1) for n≥1 Homework Equations I know that P(\cup_{i=1}^n E_i) \leq \sum_{i=1}^n P(E_i). The Attempt at a Solution I know when n=1, trivially P(E_1) \geq \max_1 P(E_1) =P(E_1). So I was hoping I could use induction to...

This is a rather simple question, so it has been rattling my brain recently. Consider a surjective map ## f : S \rightarrow T ## where both ## S ## and ## T ## are finite sets of equal cardinality. Then is ## f ## necessarily injective? I proved the converse, which turned out to be quite...

Homework Statement Let ##P## be a permutation matrix. Show that for some ##N>0## P^N := \underbrace{PP...P}_{N \ \text{times}} = I 2. Relevant definitions A permutation matrix is a ##n\times n## matrix containing only zeros and ones such that there is exactly one ##1## per row and per column...

This may appear like a homework question, but I am not asking for answers for the question, so please don't remove this post! This is a conceptual question, and I just want to show how I came to that question. The following question, " An electron and a proton of identical energy E encounter...

Hi All, Say we have a finite collection ## S_1,...,S_n ## of sets , which are not all pairwise disjoint , and we want to find the minimal collection of the ## S_j ## whose union is ## \cup S_j ## . Is there any theorem, result to this effect? I would imagine that making the ## S_j##...

I had these code in this forum but comes out error as below, any suggestion? Error 1 error C4430: missing type specifier - int assumed. Note: C++ does not support default-int c:\users\username\documents\visual studio 2010\projects\fdm 001\fdm 001\explicit 001.cpp 27 Error 2...

At the exact center of a finite wire (i.e. a distance, say $L/2$ from each end), why can I not apply Gauss's Law in integral form to find an EXACT solution for the electric field? At the center of the wire, $E$ is entirely radial, so it seems like I should be able to draw an infinitesimally...

Homework Statement Homework EquationsThe Attempt at a Solution for ##r \le a## and ##l = 0##, the radial equation is $$- \frac {\hbar^{2}}{2m} \frac {d^{2}u}{dr^{2}} - V_{0} = Eu $$ $$- \frac {\hbar^{2}}{2m} \frac {d^{2}u}{dr^{2}} - [V_{0} + E]u = 0$$ call ##k^{2} = \frac...

Greetings, I am working as a TA and I encountered a particular question which asks the student to use the Ampere's Law in order to get the magnetic field created by a semi-infinite wire. I know that there will be charge accumulation a time-dependent electric-field, hence a displacement current...

Can anyone show me how to solve the 3D diffusion equation which has been modeled into FDM by using matlab?

I am attempting to answer the attached question. I have completed parts 1-4 and am struggling with part 5. 5. Prove that if a^{l_0}b_1^{l_1}...b_n^{l_n}=e then a^{l_0}=b_1^{l_1}=...=b_n^{l_n}=e If |a|>|b1|>|b2|>...>|bn| then I could raise both sides of a^{l_0}b_1^{l_1}...b_n^{l_n}=e to the...

Whenever I attempt to research this question, my search results yield "Is the Universe Infinite" where the question ALWAYS refers to the volume of the universe. This question is usually answered along the lines of: "If the universe is closed, than it's volume, aka it's 3D surface area in...

hi dear i have a question. i have equation (1/α ) dT/dt =d2T/dr2 +1/r dT/dr +d2T/dz T=T(r,z) T(Ri,z)=Ti T(Ro,z)=To T(r,0)=To dT(r,L)/dz =0 by finite difference method O(h^3) and this question's MATLAB program. is there anyone who can do it ? it is very important for me tnx

Homework Statement I just noticed that whenever I'm doing a problem involving Gauss Law, it always involves an infinite line/plate. I can't seem to figure out why it must be infinite large/long. Here is an explanation I read, but don't quite understand...

I google searched finite math after reading the course description in my community college course catalog. I am a math major and is fine math work learning or should I use my time wisely and learn other branches of math. Ie ode, pde, proof writing etc. Will my future classes cover some of the...

Homework Statement Show that any finite graph contains two vertices lying on the same number of edges. Homework Equations None The Attempt at a Solution I am confused how my book proved this. Let G be a graph with n vertices ##v_1, ..., v_n.## Place ##v_i## in a pigeonhole labelled...

Homework Statement Purcell 2.10 [/B][not the problem I'm asking about, but needed for Purcell 2.11 which I am asking about] A thin rod extends along the z axis from z = -d to z = d. The rod carries a charge uniformly distributed along its length with linear charge density \lambda. By...

Brocard's problem is a problem in mathematics that asks to find integer values of n for which $$x^{2}-1=n!$$ http://en.wikipedia.org/wiki/Brocard's_problem. According to Brocard's problem ##x^{2}-1=n!=5!*(5+1)(5+2)...(5+s)## here,##(5+1)(5+2)...(5+s)=\mathcal{O}(5^{r}),5!=k##. So, ##x^{2}-1=k...

Homework Statement Problem: Let A_1 , A_2 , . . . be a countable number of finite sets. Prove that the union S = ⋃_i A_i is countable. Solution: Included in the TheProblemAndSolution.jpg file. Homework Equations Set-theoretic algebra. The Attempt at a Solution Unless I missed something, it...

I mean the photoelectric effect of the hydrogen atom. It is weird. By the Fermi golden rule, the transition or absorption rate is proportional to the density of the final states. At threshold, the electron has zero momentum and thus zero density of state. Therefore, the absorption coefficient...

Homework Statement Let ## x_j = \begin{Bmatrix} {1, 0 \leq j \leq N-1} \\ {0, else} \\ \end{Bmatrix} ## Show that ##\hat{x}(\phi) = \frac{e^{-i\frac{N-1}{2}\phi}sin(\frac{N}{2}\phi)}{sin(\frac{1}{2}\phi)}##Homework Equations [/B] ##\hat{x}(\phi) := \sum_{j = -\infty}^{\infty} x_j...

I was reading a section in my book discussing the commutativity of infinitesimal and finite rotations. In the book the authors try to set up a scenario to explain why finite rotations are not commutative. The following is an excerpt from the book regarding this language: "The impossibility of...

Homework Statement In the figure below, there is a linear rectilinear uniform wire with charge density of ## \lambda ##. It its located at the Z axis, where z1 = a and z2 = b, (b> a) The point O is the origin of the coordinates. "R" is the cylindrical polar radial coordinate. a) Find the...

Hi evryone, the system i am working on, is composed of two relatied non-linear equations that I discretised using finite volume method with fully implicit scheme, the difficulty is that the two unknonw appear in both equations and i don't know how to solve it. Any propositions? Thank you.

i want to solve a nonlinear PDE with finite difference method ,but using just discretization like in linear PDE , it will lead to nowhere , what's the right way to use FDM to solve nonlinear PDE or could someone provide me with book's titles or articles that can help me solving a nonlinear pdf...

Homework Statement A point source emits visible light isotropically. Its luminous flux is 0.11 lumen. Find the flux whithin the cone that has half angle of 30 degree from the light source. Homework Equations luminous flux = luminous intensity * solid anlge The Attempt at a Solution I tried...

One of my friend has answered this question in this way. Angular displacement can't be a vector because addition is not commutative. Say we are looking at the Earth with North America facing us and the North Pole facing up:if we rotate the Earth so that we move 90 degrees north, now the NP is...

x^2=n!+1⇒ (x+1)(x-1)=n! where (x+1)/2 and (x-1)/2 are consecutive integers and have consecutive primes as factor ,let ,y and z (respectively) so it can be written y-1=z. Consider prime counting function π(z),π(2z-1) that count primes less than the variable or argument. It can be seen that f(z)...

Homework Statement Suppose I am undertaking an experiment using a scanning electron microscope in which there is a positively charged plate underneath the target sample. I want to find the change in energy of the electron due to a positive voltage on this plate from the point it leaves the...

Homework Statement Consider the transverse field Ising model, with $$H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$$ I have to calculate the magnetization $$\langle\sigma_z\rangle$$ at finite temperature. Homework EquationsThe Attempt at a Solution I have to say, I'm a bit lost.

Hello, in Griffith's section on the Finite Square Well, ##\psi(x)## (what is the name of this anyway?, I know ##\Psi(x,t)## is called the wave function but how do I call just ##\psi(x)##?) Anyways, The solution is For x < a and x > a, the terms that are infinite as x approaches infinity are...

Hi all, I have a simple question as follows: f is a function from X to Y where X=[0,1]; and Y is finite, i.e. \vert Y\vert <\infty then is f Borel measurable? Thank you for your help in advance.

hi guys i need some help with the iteration made in a numerical solution for the eigenstates in a finite square well potential using the effective length approximation First, i find the eigenstate for a infinite square well, then i define the related alpha and i use it to define an effective...

Homework Statement There's not a particular problem, per se, just that I seem to be missing something with my understanding of how to evaluate a string against a non-deterministic finite automaton with epsilon transitions. But one I've been working with is shown below Homework Equations NA...

Why do they asume that the big bang is the origin of the universe? While the big bang might have occurred, it is not the "origin" of the universe. It at most is the origin of the expansion of matter through the universe. Think about the universe as a huge infinite vacuum that contains matter...

Homework Statement Hi all, I need to find the potential of a positively charged rod with charge Q. Assuming to the right as positive,the center of the rod is on the origin, and it extends to -L/2 in the negative x direction, and L/2 in the positive x direction. There is a point at distance x...

The formula for Helmholtz coil is given by mu*(0.8^1.5)*nI/R, where I is the current, n is te number of coil and R is the radius of the coil. Now assume the bunch of coils have a small 'thickness' w (so it looks like a hollow cylinder with a very small height), and the the two coils are...

i know the rules of finite expansion but i just want to know why do we need it and what does it mean ?

I have big problem with finite difference schemes (DS) on Matlab. I need write DS on Matlab, example: u_x=(u_(i+1,j)-u_(i-1,j))/2, we choose step is 1. On Matlab: u_x=(u( :,[2:n,n])-u( :,[1,1:n-1]))/2 And I can write u_y, u_xx, u_yy, u_xy. But now, I need to write for higher order, example...

Hello! (Wave) I want to show that if $A$ is a finite set of finite sets then the set $\bigcup A$ is finite. The set $A$ is finite. That means that there is a natural number $n \in \omega$ such that $A \sim n$, i.e. there is a bijective function $f$ such that $f: A...