Boundary conditions Definition and 364 Threads

Homework Statement Example Question: an electron with mass m is confined in a thin wire, with periodic boundary conditions applied in the x direction and harmonic potentials in the y and z direction. Write an expression for the wave functions in the ground state. Write down all the energy eigen...

As i understand, the purpose of laplaces/poissons equation is to recast the question from a geometrical one to a differential equation. im trying to figure out what are the appropriate boundary conditions for poissons equation: http://www.sciweavers.org/upload/Tex2Img_1418842096/render.png...

Homework Statement Let a slab 0 \le x \le c be subject to surface heat transfer, according to Newtons's law of cooling, at its faces x = 0 and x = c , the furface conductance H being the same on each face. Show that if the medium x\le0 has temperature zero and medium x=c has the...

I am currently reading Zwiebach and intend on reading Becker and Polchonski afterwoods. In chapter 4 he slves a partial differential equation with the Dirichlet and Neumann BC. My question is what the difference is between the two BC.(BC=Boundary conditions). Thanks for any help.

Hi All, This is my first post on these forums. I am not looking for a solution to this problem but more interested in seeing if someone can point me to a resource that can explain the following. Thanks in advance for any help. I'm trying to solve a pde which gives a temperature profile. We...

I have the following 2D Poisson equation (which can also be transformed to Laplace) defined on a triangular region (refer to plot): \begin{equation} \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation} with the following three boundary conditions...

Homework Statement I am trying to calculate the transmission and reflection coefficients for rectangular finite potential barrier between (-a, a) for a particle of mass m with energy equal to the height of the barrier (E = V0 > 0). Homework Equations...

Dear experts, I´m trying to model in ANSYS Mechanical (v14.5) the linear buckling behavior of a cylinder made of BEAM4 elements under combined loading (axial compression and bending moment) applied at the ends. How should I set up the boundary conditions of a cylinder to keep rigid the ends...

All, I recently completed a project where transient thermal boundary conditions are rotated around a cylinder for a general number of revolutions. In reality, the cylinder rotated but it was much easier to rotate the thermal conditions around the model in the ANSYS environment. I used 360...

Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?

Homework Statement I have a hollow, grounded, conducting sphere of radius R, inside of which is a point charge q lying distance a from the center, such that a<R. The problem claims, "There are no other charges besides q and what is needed on the sphere to satisfy the boundary condition". I...

Homework Statement I have an infinite plate of which two electrodes are attached at a distance ##2a## and the electric potential between them is ##U##. Now I have to find a function ##\phi (x,y)## that satisfies Laplace's equation ##\nabla ^2 \phi =0## and is equal to ##0## at all possible...

Hi, I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth. For example for...

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

Hi there Can anyone tell what is the meaning of boundary conditions for temperature distribution in a flowing viscous fluid in a pipe ? for example I need some one explane for me this: T = T1 at r = R, x<0 T = T0 at x = 0, r<R where T1 is a temperature of well and T0 is a temperature...

Hi, Can anybody help me withg the following problem: A rectangular plate with points starting from top left corner and going clockwise:: A B C D. Sides CD and DA are simply supported, and a point force F is applied anywhere on the surface. I am looking for the bending stress distribution...

hi pf! i was reading a sample problem in a text on ode's and came across a boundary condition that didnt really make sense to me. the physical scenario is: a liquid ##L## measured in moles/cubic meter (##mol / m^3##) is injected into a stream of water. ##L## is being injected at a rate...

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that is not grounded, then there will be (as long as I am dealing with static problems) no electric...

Homework Statement Part (a): List the boundary conditions Part (b): Show the relation for potential is: Part (c): Find Potential everywhere. Part (d): With a surface charge, where does the Electric field disappear? Homework Equations The Attempt at a Solution Part (a) Boundary conditions...

I don't really understand boundary conditions and I've been trying to research it for ages now but to no real avail. I understand what boundary conditions are, I think. You need them along with the initial conditions of a wire/string in order to describe the shape of motion of the string. I...

Homework Statement A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by y(x, t). It is attached to a boundary at x = 0. The condition at the boundary is y+\alpha \frac{\partial y}{\partial x} =0 where \alpha is a constant. Write the...

Homework Statement I have been given a complex function I have been given a complex function \widetilde{U}(x,t)=X(x)e(i\omega t) Where X(x) may be complex I have also been told that it obeys the heat equation...

Homework Statement Hello, I have to demonstrate that multiplying a differential equation: -d/dx[a(x)*d/dx{u(x)}]=f(x), 0<x<1 subject to u(0)=0 and u(1)=0. by some function v(x) and integrating over an interval [0,1], I get a new equation that can be used in an optimisation problem, that...

This is my first post so I hope this in the right place. I am fairly sure this is quite a straight forward question but I having trouble working out the details of it. "State the boundary conditions for an inviscid fluid at an impermeable fixed boundary x_3-h(x_1,x_3)=0 where we do...

Hi, it is easy solving these PDEs with the idealized homogeneous BCs they throw out in class, but I am having some difficulty solving the transient problem posed in the images below. I have tried working through it, but I don't have confidence in the result. I overlook the solution when the...

Homework Statement Find the volume of an object bounded by x2 + y2 ≤ 1, x2 + z2 ≤ 1 and y2 + z2 ≤ 1. Homework Equations The Attempt at a Solution This stuff is very new to me (multiple integrals to find volume) so I am not entirely familiar with it. My first thought was to put...

I'm working on a student design project building a multirotor UAV to host a sensor array. The airframe supports arm beams with motors producing thrust at the end, a battery, a flight controller, payload, ESC's and needs to be custom made so that it is of a size that can support large blades and...

Hello, I am looking to solve the 3D equation in spherical coordinates \nabla \cdot \vec{J} = 0 using the Ohm's law \vec{J} = \sigma \cdot (\vec{E} + \vec{U} \times \vec{B}) where \sigma is a given 3x3 nonsymmetric conductivity matrix and U,B are given vector fields. I desire the...

Hi, I have to use a wide 5 point stencil to solve a problem to fourth order accuracy. In particular, the one I'm using is: u'' = -f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) / 12h2 or when discretized u'' = -Uj-2 + 16Uj-1 -30Uj + 16Uj+1 -Uj+2 / 12h2 In addition to...

Hello! I have a nifty set of problems (or rather one problem, gradually building itself to be a great problem) that I like to collectively call "The final problem" as it is the last thing I need before I can take the exam in Numerical Methods.Information There is given a Laplace equation...

In Griffith's section about electrostatic boundary conditions, he says that given a surface with charge density \sigma , and take a wafer-thin Gaussian pillbox extending over the top and bottom of the surface, Gauss's law states that: \oint_{S} \mathbf{E} \cdot d \mathbf{a} =...

Homework Statement Consider a charged particle, of mass m and charge q, confined in a device called a Penning Trap. In this device, there is a quadrupole electric field described in cartesian coordinates by the potential Phi[x,y,z] = U0 (2z^2 - x^2 - y^2) / (r0^2 + 2z0^2) Where U0 is...

In linearized gravity we can one sets $$(1) \ \ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}$$ where h is taken to be a small perturbation about the flat space metric. One common decomposition of h is to write the spatial part as $$ h_{i j} = 2 s_{ij} - 2\psi \delta_{ij} \ h_{0i} \equiv...

Homework Statement Just need some quick confirmation. For a beam which has a load applied to it, will its free end always have a shear force, bending moment and curvature of zero?

Homework Statement Determining two sets of boundary conditions for a double integral problem in the polar coordinate system. Is the below correct? Homework Equations The Attempt at a Solution There are two sets of boundary conditions that you can use to solve this problem in the polar...

What is the answer of this differential equation. ((d^2) r)/((ds)^2) +(m/(r^2)) -(nr/3)=0 the boundary conditions (i) r=a when s=0 and (ii) dr/ds =0 when r=b. m and n are constants.

Homework Statement Ignore the text in German. You just need to see the picture. 2 conductors both with potential 0 are given. \alpha is the angle between the conductors. (r, \varphi) are polar coordinates pointing to a point in the plane. Homework Equations What we need to do is...

Homework Statement solve the heat equation over the interval [0,1] with the following initial data and mixed boundary conditions.Homework Equations \partial _{t}u=2\partial _{x}^{2}u u(0,t)=0, \frac{\partial u}{\partial x}(1,t)=0 with B.C u(x,0)=f(x) where f is piecewise with values: 0...

What are the boundary conditions of the universe?

Homework Statement If utt - uxx= 1-x for 0<x<1, t>0 u(x,0) = x2(1-x) for 0≤x≤1 ut(x,)=0 for 0≤x≤1 ux(x,)=0 u(1,t)=0 find u(1/4,2) Homework Equations The Attempt at a Solution I was thinking to make a judicious change of variables that not only converts the PDE to a homogenous PDE, but also...

Hey! Speaking electrodynamics, I can't seem to get mathematically or even physically convinced that the solution with Dirichlet or Neumann boundary conditions is UNIQUE. Can someone explain it? Thanks.

Hi all, Say I am solving a PDE as \frac{\partial y^2}{\partial^2 x}+\frac{\partial y}{\partial x}=f, with the boundary condition y(\pm L)=A. I can understand for the second order differential term, there two boundary conditions are well suited. But what about the first order differential term...

Hi All, I would like to know why in the infinite well problem, after having solved the time independent SE, we are not supposed to equal to zero the x derivative of the spatial part of the wave function at -L and L (2L being the total width). We only have to make it zero at the boundary...

As learning laser fundumentals, I've just reviewed the boundary conditions for electromagnetic waves. However, I came back to a point that confused me in the past and want to get it clear now :) One of the boundary conditions, regarding the magnetic fields parallel to the medium-interface...

Homework Statement I'm trying to find the boundary conditions for the beam shown in the figure. Homework Equations Notation: V= Shear force M= Bending momentThe Attempt at a Solution at x=0 V=R1, M=0 at x=9 V=R3, M=0 In the solution provided at x=9 V=-R2. I don't understand why it's...

Homework Statement I am solving an inclined flow problem, and am stuck. The problem is to find the volumetric flow rate of inclined flow in a square channel. Once I have the velocity profile, I can just integrate over that to get the flow rate. 2. The attempt at a solution Letting the...

Hi everyone, I'm attempting to create a computer program to solve the transient 3d heat equation using the Crank Nicolson method. I would like to model the boundaries of my domain as losing heat via convection and radiation due to the temperature difference between the boundary and the air in...

I've been trying to get my head arround this problem for several days now, and while I deemed it relatively simple at first it turns out that I can't figure out the BCs on a conductor, to which we apply a potential U. In the simplified version of the problem, there is a rectangular conductor...

Hi, I shall show (using Fourier transform) that the solution to \frac{\partial^2 u(x,t)}{\partial t^2} = \frac{\partial^2 u(x,t)}{\partial x^2}\\ u(x,0) = f(x) \\ u_t(x,0) = 0 is u(x,t) = (f(x+t) + f(x-t))/2 I got it almost: Taking the Fourier transform in the variable x...

Suppose we have the following IBVP: PDE: u_{t}=α^{2}u_{xx} 0<x<1 0<t<∞ BCs: u(0,t)=0, u_{x}(1,t)=1 0<t<∞ IC: u(x,0)=sin(πx) 0≤x≤1 It appears as though the BCs and the IC do not match. The derivative of temperature with respect to x at position x=1 is a constant 1...