Boundary Definition and 900 Threads

Homework Statement n is given by: ∂2Θ/∂x2=1/α2 ∂Θ/∂t , where Θ(x, t) is the temperature as a function of time and position, and α2 is a constant characteristic for the material through which the heat is flowing. We have a plate of infinite area and thickness d that has a uniform...

Something has been bugging as of late: usually, derivatives (ordinary and partial) are defined for interior points. However, I often come across statements in which they seem to also be defined for boundary points. For example, Leibniz' rule of integration, as usually stated, assumes some...

I am trying to solve the following heat equation ODE: d^2T/dr^2+1/r*dT/dr=0 (steady state) or dT/dt=d^2T/dr^2+1/r*dT/dr (transient state) The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2. I have searched the analytical solution for this kind of ODEs in polar coordinate...

Hi I am studying magnetic vector potential from Griffiths book. The eq 5.76 in his book gives the boundary condition for the magnetic vector potential. \frac{\partial \vec{A_2} }{\partial n}- \frac{\partial \vec{A_1} }{\partial n}=-\mu_o \vec{K} where n is the vector perpendicular to the...

Homework Statement True or false: Let S be any set in R2. The boundary of S is the set of points contained in S which are not in the interior of S. Homework Equations The Attempt at a Solution Common sense tells me true. I don't really understand it though, if S is an open set...

Homework Statement Hi guys, I'm having trouble understanding the finite potential well, in particular the boundary conditions The well under scrutiny has potential V(x)= 0 for |x|<a and V(x)=V_0 for >a Homework Equations \frac{d^2\psi}{dx^2}=-\sqrt{\frac{2mE}{\hbar^2}}\psi=-\alpha^2\psi...

I am disappointed. This take on determinism comes from the Stanford Encyclopedia: "Determinism: The world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law. The...

Okay, so I've read Max Born's book twice and believe I now have a reasonable, high-level understanding of general relativity. The thing I'm now trying to tease out is Mach's principle. One thought experiment that I've been falling asleep thinking about is how the presence of distant masses...

This is an example shown in "Introduction to Electrodynamics" by Griffiths. Page 226 example 5.8. Given a sheet of current K on the xy-plane where current traveling in +ve x direction. Find the magnetic field. I am confused on the way the book justify the z direction of B is zero. The...

Can't seem to work this out, any solutions would be greatly appreciated! Thanks in advance! Solve the boundary-value problem Uxx + Uyy + U = 0 , 0<x<1,0<y<1 U(0,y) = 0 , Ux(a,y)= f(y) U(x,0) = 0 , Uy(x,1)= sin(3*pi*x)

Homework Statement Consider \frac{\partial u}{\partial t} = k\frac{\partial^2u}{\partial x^2} subject to u(0,t) = A(t),\ u(L,t) = 0,\ u(x,0) = g(x). Assume that u(x,t) has a Fourier sine series. Determine a differential equation for the Fourier coefficients (assume appropriate continuity)...

So, I do not think I did this properly, but if f(-x)=-f(x), then u(-x,0)=-u(x,0), and if g(-x)=-g(x), then ut(-x,0)=-ut(x,0). According to D`Alambert`s formula, u(x,t)=[f(x+t)+f(x-t)]/2 + 0.5∫g(s)ds (from x-t to x+t) so, u(0,t)=[f(t)+f(-t)]/2 + 0.5∫g(s)ds (from -t to t) f is odd, and so is...

I am sometimes just not sure how to go about solving magnetics problems and applying the right boundary conditions. I was hoping for a little advice. For example in an infinitely long cylinder (along z-axis) with radius a, and a permanent magnetization given by: \vec{M} =...

Hello, I'm having trouble getting started on this problem. Here's the question: [PLAIN]http://img810.imageshack.us/img810/2464/ee323assn3q3.jpg My issue is in setting up the governing partial differential equation in 3 dimensions. What I've tried so far is setting du/dt equal to the...

I understand application of Snell's law for transition from one medium to another but I have a question regarding this model. When an electromagnetic wave transitions from air into a conductive medium does the wavelength change instantaneously as the theory seems to imply or is there a boundary...

Hi there, I have completed my analysis in BEM. The results gives me velocity potential in form of 37954305E-04 +1.58625295E-06 +2.10275811E-07 +... I have real scattering values, imaginary and absolute scattering values in this form. I am new to the method and from a different...

Homework Statement A sphere under uniform rotation R, in a simple shear flow, given at infinity by ui = G(x2 + c)deltai1 The centre of sphere is fixed at x2 Boundary conditions are ui = EijkRjxk on sphere, and ui = G(x2 + c) at...

Homework Statement Find the solution of the equation v''- 4v'+5v=0,such that v=-1 and v'=1 when x=pi=3.14159Homework Equations ... The Attempt at a Solution I treat it as a polynomial=>r^2+4r+5=0 =>delta=-4=>r1=2+2i and r2=2-2i v=e^[x+2](A*cos[2]+B*i*sin[2]) v=-1=e^[pi+2](A*cos[2]+B*i*sin[2])...

Boundary conditions & time domain electromagnetic waves: does classical model fit? Consider two propagating media: a lossy dielectric medium and a lossless dielectric medium. Thus, the interface that separates them has two tangential components of electric field, one for each medium. One of...

I don't seem to grasp the meaning of boundary conditions for Laplace's equation. Consider the Lagendre expansion of the potential at x due to a unit charge 1/|x-x'|, where x' is the position of the unit point charge. To do the expansion, we need to consider a volume in space where the...

Homework Statement Solve the given boundary value problem or else show that it has no solutions: y'' + 4y = cos x, y'(0) = 0, y'(pi) = 0. Homework Equations N/A The Attempt at a Solution So I made it all the way through the problem I think, but I am not getting the correct answer...

When solving Schrodinger's eqn for a quantum ring, what would be the boundary conditions? The solution (polar) should be Ψ(Φ) = A exp(ikΦ) + B exp(-ikΦ) And I believe the boundary conditions are Ψ(0) = Ψ(2pi) Ψ(0) = A + B Ψ(2pi) = A exp(ik*2π) + B exp(ik*2π) and I suppose I can...

Hi, I am trying to work this problem out but I don't know how to solve the boundary value. here is the problem statement thanks in advance

For a parallel polarization EM hitting the conductor boundary in an oblique angle. z axis is perpendicular to the boundary and point into the conductor. y-axis it out of the page which give x pointing up. Let the boundary surface by xy plane. With this: The direction of the incident is...

If a PDE has no boundary conditions specified, how does one go about providing a solution--even if this is a general solution? I'm stuck looking at the separation of variables and other methods which all seem to heavily rely on those boundary conditions and initial conditions. If anyone...

Homework Statement A cantilever beam has uniform load w over a length of L as described by the eq. EI y'''' = -w y(0) = y'(0) = 0 y''(L) = y'''(L) = 0 EI are constants find y(x) Homework Equations L[y^4] = S^4*Y(s) - S^3*Y(0) - S^2*Y'(0) - s*Y''(0) - Y'''(0) The...

I'm playing with the PDE toolbox in Matlab and solving Laplace's equation, ∇2V = 0, for various electrostatic geometries. I say 'playing' because I started in the wrong end (or right end, depending on how you look at it) by simple trial and error until the solutions looked like something...

Klein–Gordon equation with time dependent boundary conditions. Suppose we look for solutions to the Klein–Gordon equation with the following time dependent boundary conditions, psi(r,theta,phi,t) = 0 zero at infinity psi(on surface of small ball, B_1,t) = C*exp[i*omega*t] psi(on...

Say we consider the time independent Klein–Gordon equation, see: http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation Lets impose the following boundary conditions, the function is zero at infinity and on some small ball of radius R centered on some origin the function is some...

Homework Statement Find the area of the surface that is the boundary of the region enclosed by the surfaces x^{2}+y^{2}=9 and y+z=5 and z=0 Homework Equations A(S)=\int\int_{D}\left|r_{u}\times r_{v}\right| \; dA The Attempt at a Solution I am really confused as to what he...

Homework Statement Find the closure, interior, boundary and limit points of the set [0,1) Homework Equations The Attempt at a Solution I think that the closure is [0,1]. I believe the interior is (0,1) and the boundary are the points 0 and 1. I think the limit point may also be...

No, the boundary operator is not relative--sorry, Einstein . I mean, the boundary operator in relative homology. I have seen it defined in two different ways , which I do not believe are equivalent to each other: Given a pair (X,A), A<X, and Del is the Bdry. operator on...

The greatest problem of thermoelectrics is the need to maintain very low thermal conductivity. How is it possible that pyroelectrics do not have this limitation and do not need temperature differences to produce electricity from heat?If we will heat all pyroelectric body uniformly it will still...

Homework Statement I am trying to solve the Laplacian Equation with mixed boundary conditions on a rectangular square that is 1m x 1m. Homework Equations \nabla2T=0 .....T=500K ....________ ....|@@@@| T=500K...|@@@@|...T=500K ....|@@@@| ....|______.| ....Convection ....dT...

I understand \vec J_{free} only exist on boundary surface of perfect conductors. Copper is close enough and have surface current. Also copper is paramagnetic material which implies \mu_{cu} = \mu_0 or very very close. In order to find the exact angle of the of the magnetic field inside the...

Homework Statement I have to study the limit of a sequence which is defined as follows. I'm not looking for an answer, just a method of how to do it, or even what this notation means. An = { (\frac{n^{2}}{3n^{3}+1}, \frac{4n^{2}}{n^{2}+1} ] n even An = { (\frac{n^{2}}{6n^{2}-4}...

Why does the grain boundary cut directly through a particle, instead of looping around the particle's surface?

boundary conditions for pressurized cylinder in fem?

My understanding of: \int_S \nabla X \vec{H} \cdot d\vec{S} = \int_C \vec{H} \cdot d \vec{l} = I Means the current I creates the magnetic field in the form of \nabla X \vec{H} instead of magnetic field creates the current I. But in the boundary condition, it claims the tangential...

Thant helped. thank you!

Suppose I want to integrate f(z)(z-a)^{-1} where |a|=1 over the circle |a|=1, why is it that: f(a)=\frac{1}{\pi i}\int_{|z|=1}\frac{f(z)}{z-a}dz instead of: f(a)=\frac{1}{2\pi i}\int_{|z|=1}\frac{f(z)}{z-a}dz

Homework Statement Use a Green's function to solve: u" + 2u' + u = e-x with u(0) = 0 and u(1) = 1 on 0\leqx\leq1 Homework Equations This from the lecture notes in my course: The Attempt at a Solution Solving for the homogeneous equation first: u" + 2u' + u = 0...

i think jordan wigner transform, when applied to open boundary system, can simplify a spin 1/2 system to a free fermion system but there is a difficulty in the case of periodic boundary condition in this case, we have to deal with terms like S_N^+S_1^-=(-)^{\sum_{k=1}^{N-1}n_k}...

Homework Statement A point charge Q is at the boundary plane of two infinite, homogeneous dielectrics with dielectric constants \epsilon_1 and \epsilon_2. Calculate the electric potential, the electric field and the displacement vector at any point in space. Homework Equations...

Homework Statement S = Set of rational numbers Boundary(interior(S)) = ? The Attempt at a Solution I have no Idea how to do this, I don't know what interior of the rational numbers are. Maybe you guys could give an example of like the interior of the natural numbers or the boundary of the...

Let E be a subset of R2 that is non-empty, compact, and connected. Suppose furthermore that E is the union of a countably infinite number of almost disjoint closed cubes {Ri} with non-zero volume. Is there anything interesting about this set, particularly its boundary? Can it have infinite...

Homework Statement http://img843.imageshack.us/img843/3515/11193469.png Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://img801.imageshack.us/img801/4829/scan0001i.jpg An upload of my attempt to solve the problem. Not sure to interpret the results. A = B...

Homework Statement http://img685.imageshack.us/img685/5585/63862334.png Homework Equations -The Attempt at a Solution y_1(0,t)=y_2(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} = \frac{C}{A} y_1_x(0,t)=y_2_x(0,t) \longrightarrow 1+\frac{B}{A}e^{2i \omega t} =\frac{k_2}{k_1}...

Hello, I am facing a diffusion equation.. \frac{du(x,t)}{dt} = D \frac{d^2u}{dx^2} .. with slightly exotic boundary conditions: u(0,t) = 0 \frac{d^2u(a,t)}{dx^2}+ \alpha \frac{du(a,t)}{dx} = 0 I expected the solution to be relatively easy to find, since separation of variables quickly...

what is the real boundary(or difference) between discrete&continous(as the title)? my major is physics and i find that scientists are dealing with the different treatment to these two kinds of phenomenons, but what is the real boundary? by this i mean what they actually are and how they ARE...