Conditions Definition and 1000 Threads

Homework Statement Derive the boundary conditions for the B field imposed by divB=0I'm lost with this question, I don't really understand how boundary conditions work. D.J. Griffiths only really mentions how to arrive at the conclusion that: B_{1}\bot-B_{2}\bot=0 but doesn't outline the method...

If only some stars become black holes what sets them apart from other stars, is it just size?

Homework Statement Solve the heat equation ut=uxx on the interval 0 < x < 1 with no-flux boundary conditions. Use the initial condition u(x,0)=cos ∏x Homework Equations We eventually get u(x,t)= B0 + ƩBncos(n∏x/L)exp(-n2∏2σ2t/L2) where L=1 and σ=1 in our case. B0 is...

Homework Statement Homework Equations An overtdetermined system - If m > n, then the linear system Ax = b is inconsistent for at least one vector b in ℝ^n. The Attempt at a Solution If m > n (more rows than columns), in which case the column vectors of A cannot span ℝ^m (fewer vectors...

Hi All I have an exam tomorrow morning, I've almost completed my study guide but there are a few questions I have no idea how to answer. If someone here could give me a few pointers, or tell me how to solve it, or maybe you already know how to solve it; I can study off your solutions. Any...

Hello, I was wondering if anyone can help me with my FEA approach. I want to check that my boundary conditions for a simple quarter torus (representing a section of a helical spring) are correct. I'm neglecting the helical angle at this stage. I have fixed one end in all axes, and applied...

So, that is the question: Under what conditions does L=Iw hold? Where L,I,w are all scalars. Some specifics perhaps: 1) Supose a fixed axis of rotation, with accel, does is hold? 2) Suppose de axis of rot is not a ppal axis 3) Suppose there is fixed axis of rot, but I choose neither x nor y...

Homework Statement The PDE: ∂n/∂t + G∂n/∂L=0 The initial condition: n(0,L)=ns The boundary condition: n(t,0)=B/G The parameter B and G above are dependent upon process conditions and change at each time. They can be calculated with adequate experimental data. Homework Equations...

Homework Statement Solve: y'' - λy = 0 where y(0)=y(1)=0, y=y(t) Homework Equations The Attempt at a Solution Hi everyone, This is part of a PDE question, I just need to solve this particular ODE. I know how to do it in the case for y'' + λy = 0, where you get the...

Homework Statement Here's the question: Use laplace transforms to find X(t), Y(t) and Z(t) given that: X'+Y'=Y+Z Y'+Z'=X+Z X'+Z'=X+Y subject to the boundary conditions X(0)=2, Y(0)=-3,Z(0)=1. Now I have learned the basics of laplace transforms, but have not seen a question in...

If we place an infinite conducting sheet in free space, and fix its potential to \varphi_0, how do we solve solve for the potential on either side of the sheet? Since the potential blows up at infinity, it seems impossible to define boundary conditions.

Hi, I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model. I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N? I.e...

Homework Statement Let X be a metric space and A a subset of X. Prove that the following are equivalent: i. A is dense in X ii. The only closed set containing A is X iii. The only open set disjoint from A is the empty set Homework Equations N/A The Attempt at a Solution I can...

First off, I've never taken a differential equations class. This is for my Math Methods for Physicists class, and we are on the topic of DE. Unfortunately, we didn't cover this much, so most of what I am about to show you comes from the professor giving me tips and my own common sense. I'd...

Homework Statement Consider the following optimization problem: min f(x) s.t. g(x) ≥ 0 h(x) ≤ 0 q(x) = 0  Let xbar satisfy g(x) = h(x) = q(x) = 0. a)State and prove a set of necessary and sufficient conditions for x to be a local minimum. b)How would the conditions...

A double delta potential is given by V(x) = c_+ \delta (x + \frac{L}{2}) + c_- \delta (x - \frac{L}{2}). Use the discontinuity relation to find the boundary conditions in x = \pm \frac{L}{2} . The general solutions are: \psi(x) = \begin{cases} Ae^{ikx} + Be^{-ikx} & x < -\frac{L}{2}...

Homework Statement Find the solution to the heat equation for the following conditions: Homework Equations The Attempt at a Solution Not sure. I've only encountered the following scenarios: temperatures of both ends are arbitrary values both ends are insulated (so the first...

I need to apply D'Lembert's method but in this case I don't know how. How to proceed? Determine the solution of the wave equation on a semi-infinite interval $u_{tt}=c^2u_{xx},$ $0<x<\infty,$ $t>0,$ where $u(0,t)=0$ and the initial conditions: $\begin{aligned} & u(x,0)=\left\{ \begin{align}...

Homework Statement Solve Laplace's equation u_{xx} + u_{yy} = 0 on the semi-infinite domain -∞ < x < ∞, y > 0, subject to the boundary condition that u_y = (1/2)x u on y=0, with u(0,0) = 1. Note that separation of variables will not work, but a suitable transform can be applied...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}}+1+x,\text{ }0<x<1,\text{ }t>0 \\ & u(x,0)=\frac{1}{6}{{x}^{3}}-\frac{1}{2}{{x}^{2}}+\frac{1}{3},\text{ }{{u}_{t}}(x,0)=0,\text{ }0<x<1, \\ & {{u}_{x}}(0,t)=0=u(1,t),\text{ }t>0. \end{aligned} $ Here's something new for me, the boundary...

When I am studying the Rayleigh-Taylor instability, I saw this equation: \frac{\partial \eta}{\partial t} + u' \frac{\partial \eta}{\partial x} = \omega ' (\eta) I do not quite understand the meaning of this equation. Can some one provide me with some instructions and information...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x\in [0,1],\text{ }t>0, \\ & u(x,0)=f(x), \\ & {{u}_{t}}(x,0)=0,\text{ }u(0,t)=u(1,t)=0 \\ \end{aligned} $ where $f(x)$ is defined by $f(x)=x$ if $0\le x\le \dfrac12$ and $f(x)=1-x$ if $\dfrac12\le x\le1.$ I'm not sure how to...

Hello, whenever I come to the derivation of the Fresnel equations I get stuck on the boundary condition for the component of the E-Field that is parallel to the surface. I know for the parallel components Maxwell dictates that: E_{1t} = E_{2t}. For the parallel incoming light field...

user meopemuk mentioned this: In the case of a crystal model with periodic boundary conditions, basis translation vectors e1 and e2 are very large (presumably infinite), which means that basis vectors of the reciprocal lattice k1 and k2 are very small, so the distribution of k-points is very...

Well as the topics says I need a clarification why do we need the so called boundary conditions? I have seen it in electostatics, magnetostatics etc. I tried in many ways to get that stuff into my head, but its just only banging my head not getting into.. I really wana know what is that and...

What's the difference between standard conditions and standard state? I noticed in my thermodynamics chapter that in standard state, the reaction quotient is 1 because all activities are equal to 1 (if I remember correctly). Standard conditions is about standard temperature and pressure...

Nowadays people usually consider PDEs in weak formulations only, so I have a hard time finding statements about the existence of classical solutions of the Poisson equation with mixed Dirichlet-Neumann boundary conditions. Maybe someone here can help me and point to a book or article where I...

Homework Statement A ball falls from rest at a height H above a lake. Let y = 0 at the surface of the lake. As the ball falls, it experiences a gravitational force -mg. When it enters the water, it experiences a buoyant force B so the net force in the water is B - mg. a) Write an...

ansys -- Boundary conditions for 2 cylinders and fluid i want to do a analysis in ansys in which a cylinder will rotate about a axis which is out side of the cylinder and this cylinder is also rotating about its own axis. cylinder is half filled with liduid. i want to do the stress analysis or...

Find the necessary and sufficient conditions on the real numbers a,b,c for the matrix: \begin{bmatrix} 1 & a & b\\ 0 & 1 & c \\ 0 & 0 & 2 \end{bmatrix} to be diagonalizable. Attempt: Now for this one I also solved for the eigenvlues which were: λ1 = 1, λ2 = 1, λ3 = 2 So the problematic...

I'm having a ton of trouble understanding how to solve diff eqs by using Fourier or laplace transforms to solve for the green's function, with boundary conditions included. I can understand the basics of green's function solutions, especially if transforms are not needed, but my textbook seems...

Homework Statement 4y'' - 4y' + y = 0 y(1) = -4 y'(1) = 0 Homework Equations getting the coeff's gets messier and messier.. am i doing something wrong? The Attempt at a Solution 4y'' - 4y' + y = 0 y'' - y' - (1/4)y = 0 r_1 = r_2 = 1/2 general soln: y(t) = c_1e^(t/2) +...

I would like to do some monitoring of power line conditions. To start with, I just want to monitor and record the voltage wave form on the two split phases. I would dedicate a small computer to the purpose. The idea is to reduce the voltage from the power line in a safe way and feed that...

1) Transform the problem so that boundary conditions turn to homogeneous ones assuming that $g_0$ and $g_1$ are differentiable. $\begin{align} &{{u}_{t}}=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\ &{{u}_{x}}(0,t)={{g}_{0}}(t),\text{ }{{u}_{x}}(L,t)={{g}_{1}}(t),\text{ for }t>0, \\...

Homework Statement Because q(x,t) = A*exp[-(x-ct)2/σ2] is a function of x-ct, it is a solution to the wave equation (on an infinite domain). (a) What are the initial conditions [a(x) and b(x)] that give rise to this form of q(x,t)? (b) if f(x) is constant, then Eq. (2) shows that solution is...

1) Solve $\begin{aligned} {{u}_{t}}&=K{{u}_{xx}},\text{ }0<x<L,\text{ }t>0, \\ {{u}_{x}}(0,t)&=0,\text{ }{{u}_{x}}(L,t)=0,\text{ for }t>0, \\ u(x,0)&=6+\sin \frac{3\pi x}{L} \end{aligned}$ 2) Transform the problem so that the boundary conditions get homogeneous: $\begin{aligned}...

Homework Statement Here is the original thing: (x^{2}+1)y'+4x(y-1)=0, y(0)=4 Homework Equations The Attempt at a Solution I thought I knew the procedure.. but I got it wrong. Can someone let me know where I went wrong? First I rearrange the equation to get the following...

I think my book is giving me the wrong answer...The problem is to find solution of following: r'(t) = t2\hat{i} + 5t\hat{j} + \hat{k} The initial condition is: r(1) = \hat{j} + 2\hat{k} My solution: r(t) = < (1/3)t3 + c1 , (5/2)t2 + c2 , t+c3 > r(1) = < 0 , 1 , 2 > r(1) = <...

Explain me please how to show that C.R conditions are holds. $$f(z)=\left\{\begin{matrix}e^{-\frac{1}{z^4}}\ \ \ \text{if z not 0 }\\ 0 \ \ \ \ \ \ \ \text{if z not 0 }\end{matrix}\right.$$Thank you.

Hey, before you read this over I'll mention that I've checked the general solution and it works. So if you don't feel like following my steps to get the general solution just jump down to the end of my attempt, because the real problem for me is figuring out what to do with the side conditions...

Homework Statement Write a Matlab function that takes as input three integers n, a and b, and outputs the number of positive integers less than n that are divisible by a or b. For example, with n = 1000, a = 3 and b = 5, the output should be 466. Homework Equations MATLAB's use of...

Homework Statement Consider the transfer function H(s)=\cfrac{1}{a_{2}s^{2}+a_{1}s+a_{0}} where real-valued coefficients a_{2},a_{1}, a_{0} are arbitrary except that a_{2} is nonzero. Verify that the system is stable iff the coefficients a_{2},a_{1}, a_{0} have the same sign. Homework...

Hi, I have two questions that come from a unique example of magnetism. Here is the scenario: a thin and long piece of iron is placed in between a magnet and the north pole faces the outing sheet and some iron tacks. The iron tack do not get attracted to the iron even though a south pole is...

Homework Statement Using f(z) = f(re^iθ) = R(r,θ)e^iΩ(r,θ), show that the Cauchy-Riemann conditions in polar coordinates become ∂R/∂r = (R/r)∂Ω/∂θ Homework Equations Cauchy-Riemann in polar coordinates Hint: Set up the derivative first with dz radial and then with dz tangential...

I am currently reading through Griffiths Quantum Mechanics textbook, and on page 14, Griffiths proves that \frac{d}{dt}\int_{-\infty}^{\infty} |\Psi(x,t)|^2 \, dx = \left.\frac{i \hbar}{2m}\left( \Psi^* \frac{\partial \Psi}{\partial x} - \frac{\partial \Psi^*}{\partial x} \Psi \right)...

I'm trying to solve a non-linear time-dependent diffusion equation to find R(x,t). To do so, I'm positing that : R(x,t)=\sum^{J}_{1}X_{i}(x)T_{i}(t) which allows me to arrive at something that looks like : dT_{i}/dt=A_{i}T_{i}(t)-B*T_{i}(t)^{2} The problem I'm having, through sheer...

Eq u'(x)+p(x)u=f(x) with initial condition u(0)=0 It's homogenous solution is u_h=Ce^{-\int^x_0 p(s)ds} Complete solution u(x)=e^{-\int^x_0 p(s)ds}\int^x_0f(s)e^{\int^s_0 p(z)dz}ds=\int^x_0 f(s)g(x,s)ds where g(x,s)=e^{-\int^{x}_s p(\xi)d \xi } I didn't see that last...

Homework Statement From a previous exercise (https://www.physicsforums.com/showthread.php?t=564520), I obtained u(r,\phi) = \frac{1}{2}A_{0} + \sum_{k = 1}^{\infty} r^{k}(A_{k}cos(k\phi) + B_{k}sin(k\phi)) which is the general form of the solution to Laplace equation in a disk of radius a. I...

Homework Statement An electrostatic point charge of 1 Coulomb (C) placed symmetrically between two infinitely/perfectly conducting parallel plates. These two infinitely large conducting plates are parallel to the yz plane.The region between the two plates is designated as “Region A.” Starting...

Hi, I was wondering if someone could point me to a textbook or easy to read paper (or website) that briefly describes/proves the differences here. What I mean is if I do classical (continuous energies) statistical mechanics where my initial state is a volume (greater than or equal to h-bar)...