Boundary Definition and 1000 Threads

Though this question arose in quantum mechanics, i think it should be posted here. Consider a particle in a well with infinite walls: $i i \frac{\partial \Psi}{\partial t} = -\frac12 \frac{\partial^2 \Psi}{ \partial x^2},\:0<x<a$ but the wall start to squeeze :devil: $\Psi(x=0,t) \equiv...

O.K, please let me see if I got it right: Let M be an orientable m-manifold with non-empty boundary B. Let p be a point in B , and let {del/delX^1,...,del/delX^(m-1) }_p be a basis for T_pB for every p in a boundary component . Let N be a unit normal field on B . Now, this is the...

Can you help me with this? I have a function with domain and range in R^2. What conditions it must have so that a point in the boundary of the domain will have its image in the boundary of the range? Thanks.

Homework Statement Formally solve the following boundary value problem using Fourier Transforms. Homework Equations (\partial^{2}u/\partialx^{2})+(\partial^{2}u/\partialy^{2}) = 0 (-\infty<x<\infty,0<y<1) u(x,0)= exp^{-2|x|} (-\infty<x<\infty) u(x,1)=0...

Because of boundary points, I can sort of see intuitively why Euclidean half-space, i.e. {(x_1, ... , x_n) : x_n >= 0} is not a manifold, but is there a simple rigorous argument for why Euclidean half-space is not homeomorphic to an open set of R^n. I do not know too much topology and the...

Homework Statement Homework Equations N/A The Attempt at a Solution Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either. Help appreciated.

Homework Statement Homework Equations N/A The Attempt at a Solution The problem and attempt are as above, I'm not sure where to go from here though. I'm not sure what to do with the boundary condition of dx/dt=-2 and t=0. Any help appreciated.

hi, I'm a chemical engineering student with a little problem with Comsol multiphysics; in practice, i have to solve a problem of diffusion in a solid sphere. after drawing the domain, i have to set a boundary condition on sphere's surfaces. this condition, for my problem, is FLUX=Kc(Cb-C) and...

what do boundary conditions mean wid respect to transmission lines??

the universe is supposedly isotropic. it is also supposedly finite. if i were on a galaxy farthest from the earth, i would experience nonIsotropy (forgive the made up word). because if i look in the direction of the Earth i would see a appropriately populated neighborhood with galaxies moving...

This exercise deal with the temperature u(x,y,t) in a homogeneous and thin plate. We assume that the top and bottom of the plate are insulated and the material has diffusivity k. Write the BVP . Problem: The plate is triangular , picture this as a right triangle with this coordinates, (0,0) ...

Hi guys. I'm apprently stuck on the basics of the analysis. On the proof that Q lacks least upper boundary property to be precise. The example I have uses a set A (p in Q | p > 0, p^2 < 2) then q is defined as p - \frac{p^{2} - 2}{p + 2} . Then they show that if p is in A then q is in A too...

Is this true? V\subset\mathbb{R}^n\;\textrm{open}\quad\implies\quad m_n(\partial V)=0

Homework Statement Hi all. I have the following expression, which relates the incoming amplitude with the reflected amplitude at a point x = L in a coaxial cable: A_{\text{reflected}} = \frac{R-Z_0}{R+Z_0}A_{\text{incoming}}. Here R is the resistance at the point x = L and Z0 is the...

See the link, please http://camoo.freeshell.org/quest1.pdf" Laura

Please can anyone tell me how to set this up? I know how to do the required settings in the Physics/Period Conditions. However, to fully implement it, I'm also required to choose boundary conditions in the 2D incompressible navier stokes solver (e.g. wall, inlet, outflow, open boundary...

Please, I would like sugestions on how to calculate that. It seems a very common topic on higgs experimental search, and I would like to understand that. Thanks!

Homework Statement One half of the region between the plates of a spherical capacitor of inner and outer radii a and b is filled with a linear isotropic dielectric of permittivity \epsilon_1 and the other half has permittivity \epsilon_2, as shown in the figure. If the inner plate has total...

On the boundary (surface) of two regions, the tangential components of electric fields on above and below surface are continuous. I wonder if it is also true for displacement \vec{D} and polarization \vec{P}? That is, can I say: the tangential component of \vec{D} or \vec{P} on above and below...

Reference: http://en.wikipedia.org/wiki/Holographic_Principle The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that...

Hi there, I'm using comsol for the first time, and I think I've got everything working, except that I need to write a boundary condition that is dependent upon the gradient of a variable. How do I tell Comsol to take the gradient? I suppose I can define my own function, but I don't even know...

Homework Statement solve the BVP: y'' -2y' + 2y = 0 ... (1) reduction y(0) = 1 y(pi) = 1 Homework Equations y= emx The Attempt at a Solution substitution y=emx & its derivatives in (1) we get: m2 -2m +2 = 0 = (1+i)(1-i) then y = e(c1 sinx + c2 cosx) using the...

Homework Statement A pair of infinite, parallel planes are equipotential surfaces. The plane at z = 0 has an electric potential of 0 and the plane at z = b also has a potential of zero. The electric field at b is 0 at time t at which there is a constant, positive charge density between the...

Hi, I have been given a differential equation to use in order to solve for the Hydrogen wavefunction in the ground state using Euler's method. d^2u_nl/dr^2 -(l(l+1)/r^2)*u_nl + 2k*(E_nl-V(r))*u_nl = 0 V(r) = -a/r where a = 1/137.04 I have been given initial conditions u_nl(0) = 0 an...

1. 1D heat conduction problem: Two rods, the first of length a , the second of length L-a with respective cross sectional areas A_1 , A_2 and heat conductivities k_1 , k_2 , are joined at one end. There are some boundary conditions on the other ends of the rods, but my question is only...

Homework Statement Solve \left(\frac{\partial^{2}}{\partial z^{2}}- \frac{1}{\kappa} \frac{\partial}{\partial t}\right) T=0 with boundary conditions (i) T(0,t)=T_{0}+T_{1} Sin[\omega t] (ii) T is finite as z\rightarrow\inftyHomework Equations Separation of Variables gives: T =...

Trying to solve the following boundary value problems. y'' + 4y = cos x; y(0) = 0, y(pi) = 0 y'' + 4y = sin x; y(0) = 0, y(pi) = 0 The answer key says that there's no solution to the first part, but there is a solution to the 2nd part. I'm really lost and am not sure how to go...

Let S be any subset of M, where (M, g_ab) is a spacetime. Can you guys help me kind of visualize why the boundary of the chronological future of S is an achronal, 3 dimensional embedded manifold? I am just having a hard time seeing why this is so. I'm picturing a sphere, and then having...

I am trying to solve an ode of the form u"(x)=a(x) where a(x) is some known function and the domain is from -inf to +inf. I am required to use Green's function. The boundary condition is u(0) = Integral[u(x),{x,0,1}] = 0 My Green's function has the form G(x,y) = A(y)*x+B(y) x<y G(x,y)...

Hi guys, I have a question in using comsol software, particularly on heat transfer. Its a 2D geometry. A rectangle whereby heat is applied on the top surface at the particular point and the 3 sides are thermally insulated. As more heat is applied over time, a hole will be created. A...

Homework Statement The Problem is mentioned in the attachment. Homework Equations substitute C2 in terms of C1. Can we use the identity that trace of rate of strain tensor equals 0 in an incompressible flow? The Attempt at a Solution I arrived at the following equation V...

Homework Statement Let X be a space. A\subseteqX and U, V, W \in topolgy(X). If W\subseteq U\cup V and U\cap V\neq emptyset, Prove bd(W) = bd(W\capU) \cup bd (W\cap V) Homework Equations bd(W) is the boundary of W... I think I have the "\supseteq" part, but I am having trouble with...

Homework Statement Calculate potential function and the electric field for the region between two concentric cylinders, where V ( inner cylinder) = 0 at r = 0.015 m and V(outer cylinder) = 100 for r = 0.025 Homework Equations \Delta (square ) V = 0 The Attempt at a Solution so...

Hi. You know that B_{1n} = B_{2n} as one of the boundary condition when magnetic field is go across from material 1 to material 2, n means direction perpendicular to the boundary surface. I wander this theorem is right in non-uniform field which is function of space variable r...

Homework Statement A problem with odd harmonics only. Show that the solution of the heat equation du/dt=c2*(d2u)/(dx2), subject to boundary conditions u(0,t)=0 and ux(L,t)=0, and the initial condition u(x,0)=f(x) , is u(x,t)= \sum Bnsin[(\pi/2L)(2n+1)x]e-((c*\pi/2L)*(2n+1))^2 where n...

Hello everyone, if an electric field in a medium with permittivity eps_1 moves at an angle into a material with eps_2, there is refraction. The field in the second medium changes angle. we can see that the tangential component is not changed but the one normal to the surface of separation...

Urgent: Boundary Condition querries. Homework Statement Question given: A dielectric interface is described by 4y+3z=12. The side including the origin is free space and its electric flux density, D=ax+3ay+2az (micro) C/m2. On the other side, (Epsilon)r2 = 2. Find D2. Homework Equations...

Firstly I really feel so lucky to find this forum. Since I don't have a strong physics background but now dealing with many problems directly related to physics. I'm now doing some simulation in comsol and need to solve some PDEs. I'm using this PDE coefficient form in comsol. The equations...

Homework Statement Hi all. I am given the following differential equation: X'' - k*X=0. I am told that k = -m^2, so the general solution is given by: X = a*cos(m*x)+b*sin(m*x), where a and b are constants. I am also given boundary conditions: 1) X(-Pi) = X(Pi) 2) X'(-Pi) =...

Tripping the boundary layer...why?? I don't understand why we have these "vortex generators" to trip the boundary layer into becoming turbulent...i've seen this a lot on F1 cars. On a regular car you can trip the boundary layer in front of your windshield...does the boundary layer somehow...

Homework Statement Solve Laplace's equation inside the rectangle 0 \le x \le L, 0 \le y \le H with the following boundary conditions u(0,y) = g(y)\text{, } u(L,y) = 0\text{, } u_y(x,0) = 0\text{, and } u(x,H) = 0 Homework Equations The Attempt at a Solution I know that with...

Free Electron Model: Why periodic boundary conditions and what is "L"? Right, hello! The quantum free electron model for electrons in solids (in One dimension) says we need to use periodic boundary conditions such that if Y(x) is the wavefunction, then Y(x) = Y(x+L). Where L seems to be...

Homework Statement I have the solution to the differential equation : Phi = A*sin(x) + B*cos(x) and need to apply the boundary conditions Phi(-a/2) = Phi(a/2) = 0. Homework Equations The Attempt at a Solution I am confused. If I plug these in, then I get A*sin(-ka/2) = -...

Hi everyone, I have a uniform electric field in which I place an object. I have read that the electric potential inside my object, \Phi_{in}, and the one on the outside, \Phi_{out} must be equal at the boundary. (ie. \Phi_{in}=\Phi_{out} on the boundary) I don't understand why this is...

Homework Statement Hi all. Please take a look at this: \int_{ - \infty }^\infty {x \cdot \exp } \left( { - \left| x \right|} \right){\rm{d}}x = \left. {\left( { - \exp \left( { - \left| x \right|} \right) \cdot x} \right)} \right|_{ - \infty }^\infty + \int_{ - \infty }^\infty {\exp...

As we know,the codifferential \delta is the adjoint of the exterior derivative,and the boundary operator \partial is also the adjoint of exterior derivative according to stokes' theorem, then what is the relation between codifferential and boundary operator?

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)...

Hey folks, I'm trying to find the Green function for the equation -\partial_\mu \partial^\mu \phi = K where K is some source term. Its a 2D problem with the wave confined to a rectangular cavity where the cavity is located at z = 0 and z=a. This tells me that G|_0= G|_a=0 I've pretty...

Hi there, I am solving laplace equation in a code i made in C. I am using Finite Difference Method in order to simulate the current pattern. I used the stream function to do that...

I've done searching on the topic, and I really don't know where else to turn, so here it goes. I hope somebody can point me in the right direction. I've been working on using a shooting method to solve the steady-state spherically symmetric fluid equations for an accreting plasma. Basically, it...