Boundary condition Definition and 117 Threads

  1. P

    The boundary condition for ##\delta## function

    Beginning with the Schrodinger equation for N particles in one dimension interacting via a δ-function potential ##(-\sum_{1}^{N}\frac{\partial^2}{\partial x_i^2}+2c\sum_{<i,j>}\delta(x_i-x_j))\psi=E\psi## The boundary condition equivalent to the ##\delta## function potential is...
  2. J

    Reflection of wave at open end (boundary condition)

    Hello! I need to understand one seemingly simple thing in wave mechanics, so any help is much appreciated! When a pulse travels to the right toward an open end(like a massless ring that is free to oscillate only in the vertical direction), then when the wave reaches the end it gets reflected and...
  3. genxium

    What is the general boundary condition of wave-guides?

    By wave-guides I refer to the device with (perfectly) conducting walls that enclose EM wave inside. I'm reading this tutorial here http://farside.ph.utexas.edu/teaching/em/lectures/node105.html and found this interesting boundary condition for wave-guides: ##E_{\parallel} = 0## -- (1)...
  4. Y

    Fluid mechanics question--slip boundary condition for gas?

    In solving the Navier Stokes equation, the typical boundary condition imposed on the tangential velocity at a solid surface is that of no-slip. However, it is known that for gaseous flow there always exists a non-zero velocity near the wall, especially at relatively big Knudsen number. Is there...
  5. baby_1

    Unit vector in Magnetic boundary condition

    Hello I'm getting confused when I want to use magnetic boundary equation could you tell me how we define the unit vector(an) in this equation? for example you assume that we have two different region (A in red and B in yellow) which vector (1,2,3,4) is right for equation and which is right...
  6. O

    How to numerically solve a PDE with delta function boundary condition?

    I have a PDE of the following form: f_t(t,x,y) = k f + g(x,y) f_x(t,x,y) + h(x,y) f_y(t,x,y) + c f_{yy}(t,x,y) \\ \lim_{t\to s^+} f(t,x,y) = \delta (x-y) Here k and c are real numbers and g, h are (infinitely) smooth real-valued functions. I have been trying to learn how to do this...
  7. Y

    Boundary condition between conductor and free-space

    For an imperfect conductor, when there is current, an electric field is set up inside the wire along the direction of the current flow, and is parallel to the wire. If this is true, then what I don't understand is boundary condition tells me the tangential E-field is always continuous, if...
  8. M

    How to apply boundary condition in generalized eigenvalue problem?

    Hi all, Generally boundary condition (Dirichlet and Neumann) are applied on the Load Vector, in FEM formulation. The equation i solved, is Generalized eigenvalue equation for Scalar Helmholtz equation in homogeneous wave guide with perfectly conducting wall ( Kψ =λMψ ), and found, doesn't...
  9. T

    Normal stress boundary condition at fluid/vacuum interface

    Homework Statement Stuck on two similar problems: "State the normal stress boundary condition at an interface x_3-h(x_1,x_2,t)=0between an invisicid incompressible fluid and a vacuum. You may assume that the interface has a constant tension." The second question in the same but the fluid is...
  10. X

    Beam deflection boundary condition calculation

    Homework Statement Find the deflection at x=L/4 and x=L/2 for the beam Homework Equations See attached pic. The Attempt at a Solution So I have the solution derived in class. Only 0<x<L/2 is derived because since the load on the beam is at L/2, the equation is valid for the...
  11. S

    Transforming Non-Homogeneous Boundary Conditions in 2D PDEs

    Homework Statement now I have a PDE $$u_{xx}+u_{yy}=0,for 0<x,y<1$$ $$u(x,0)=x,u(0,y)=y^2,u(x,1)=0,u(1,y)=y$$ Then I want to know whether there are some method to make the PDE become homogeneous boundary condition. $$i.e. u|_{\partialΩ}=0$$
  12. us40

    No Boundary Condition Universe: Stephen Hawking

    Hello, According to Stephen Hawking no boundary condition universe does not have any boundary in space time.If it is so then it is like earth.You can not go north to north pole.Earth does not have any edge or boundary.So universe is like closed structure like earth.Means after some times it...
  13. M

    Why boundary condition in steady electric current?

    when we electric field between two conductors in certain direction the current density should pass in its direction why current density direction change at boundary although the direction of electric field is the same for both conductors
  14. J

    Specification of the boundary condition in high order PDE

    Hi all, I'm asking a question about the number of the boundary conditions in high-order PDE. Say, we are solving the nonlinear Burger's equation \frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\nu \frac{\partial^2 u}{\partial x^2} subject to the initial condition u(x,0)=g(x)...
  15. D

    Derivative discretization with fixed boundary condition

    Hi all, It may be a trivial question. But, if I have a PDE of variable u(x,t) -------------------------------- \dot{u} = f(u,\partial_x{u},..) with boundary condition : u(0,t) = u(L,t) =0. -------------------------------- Now I need to calculate \partial_x{u} for that can I define the...
  16. M

    NH Modified Helmholtz Equation with Robin Boundary Condition

    Hi, I am working on a quite difficult, though seemingly simple, non-homogeneous differential equation in cylindrical coordinates. The main equation is the non homogeneous modified Helmholtz Equation \nabla^{2}\psi - k^{2}\psi =...
  17. fluidistic

    Understanding a boundary condition on the density of probability

    The book states that ##P(x|y,t)## represents the probability density that the potential has a value x at time t, knowing that it had the value y at t=0. I understand this, the words are very clear. However I'd find much more intuitive the notation ##P(x,t|y,0)##, but I guess that's just me...
  18. W

    How to solve eigenvalue problems with mixed boundary condition?

    suppose function f is define on the interval [0,1] it satisfies the eigenvalue equation f'' + E f=0, and it satisfies the boundary conditions f'(0)+ f(0)=0, f(1)=0. How to solve this eigenvalue problem numerically? the mixed boundary condition at x=0 really makes it difficult
  19. andyrk

    Why Is Tension Zero at the Free End of a Rotating Rope?

    A rope is tied at one end then rotated in a vertical circle. Why do we take the tension at the free end of the rope as 0(Boundary Condition)?
  20. A

    Dielectric Boundary Condition Question

    Hi, I have a question regarding the boundary condition present for a dielectric immersed in a static field. I hope one of you physics guru's can shed some light on this. Suppose we have a dielectric in space subjected to some external static electric field. I have read (without explanation)...
  21. Z

    Wavefunction boundary condition solve for k

    Homework Statement A wave function is given by: \Psi (x) = a cos(2\pi x) + b sin (2\pi x) for\: x<0 \\ and\\ \Psi (x) = Ce^{-kx} for\: x>0 \\ Determine the constant k in terms of a, b and c using the boundary conditions and discuss the case a >> b. Homework Equations...
  22. E

    Surface impedance - Boundary condition

    Hello! Let a plane wave propagate towards the -y direction. It is normally incident upon the plane (x,z) (whose normal unit vector is the y-direction unit vector, \mathbf{\hat{u}}_y): the plane represents the interface between the free space (in y > 0) and a general lossy medium (in y < 0). We...
  23. G

    Applying boundary condition on heat equation

    Homework Statement hey, i have a heat equation question which asks to solve for u(x,t) given that u(0,t)=Q_0 + ΔQsin(ωt).Homework Equations d_xx u = k d_t u u(0,t)=Q_0 + ΔQsin(ωt) The Attempt at a Solution so you can solve the equation pretty easily with separation of variables, i.e...
  24. B

    Compatibilty of the Dirichlet boundary condition

    Hi, I am trying to solve a Poisson equation \nabla^2 \phi = f in \Omega, with Dirichlet boundary condition \phi = 0 on \partial \Omega. My problem is that I am trying to understand the condition under which a solution exists. All the text I consulted says that the problem is solvable. However...
  25. M

    Criteria of periodic boundary condition

    We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.
  26. J

    PDE with variable boundary condition

    Homework Statement I am trying to solve this PDE with variable boundary condition, and I want to use combination method. But I have problem with the second boundary condition, which is not transformed to the new variable. Can you please give me some advise? Homework Equations (∂^2 T)/(∂x^2...
  27. E

    How to set up Neumann boundary condition for a PDE in a coordinate-invariant form?

    I'm having trouble finding out how to set up Neumann (or, rather, "Robin") boundary conditions for a diffusion-type PDE. More specifically, I have a scalar function f(\boldsymbol{x}, t) where \boldsymbol{x} is n-dimensional vector space with some boundary region defined by A(\boldsymbol{x})=0...
  28. H

    What does this boundary condition mean?

    One of the boundary conditions for a homogeneous uniform waveguide is \frac{\partial H_z}{\partial n}=0. What does this mean physically?
  29. B

    Boundary condition problem for diffusion equation

    BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length...
  30. B

    Boundary condition problem for diffusion equation

    Homework Statement BOUNDARY CONDITION PROBLEM I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation: δc/δt=D*((δ^2c)/(δx^2))-kc assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is...
  31. H

    Boundary condition for a charged surface

    Hi, I am looking at a problem where I have two electrically conducting fluids where charge accrues on the interface, I know that one of the equations that I have to use comes straight from the usual boundary conditions for the normal component of the electric field, the other one apparent comes...
  32. Z

    Solving for C1 and C2: A Wave Function Boundary Condition

    Homework Statement A one-dimensional wave function associated with a localized particle can be written as \varphi (x) = \begin{cases} 1- \frac{x^2}{8}, & \text{if } 0<x<4, \\ C_1 - \frac{C_2}{x^2}, & \text{if} \,x \geq 4. \end{cases} Determine C_1 and C_2 for which this wave...
  33. E

    Electromagnetic boundary condition

    in electromagnetics , considering boundary conditions of dielectric and perfect conductor , inside conductor E = 0. So, there should not be any time varying magnetic field. But in many books i have seen that inside conductor normal component of B is 0 because there is no time varying magnetic...
  34. A

    Laplace equation with boundary condition

    Good afternoon, I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that: ∇2\phi=0 \phix=1 when x=-A and x=A \phiy=0 when y=-B and y=B \phiz=0 when z=Ztop and z=Zbot I have tried...
  35. Z

    Boundary Condition for deflection of Beam

    I have a problem how to select the boundary condition when i answer this deflection of beam. for example: the boundary condition is [x=o,y=0],[x=l,y=0],[x=o,dy/dx=o] and [x=L,dy/dx=0] given that EIdy/dx= Ax+wx^2/2 EIy= Ax^2/2+wx^3/6 anybody can tell me how to select this?
  36. T

    Numerical Solutions for Mixed Boundary Condition

    Hi All, I was reading this paper the other day and I've been trying to find the numerical techniques its mentions but have been thus far unsuccessful. The authors simply state that is well know and straightforward, and they believe this so much that they don't even include a reference. Ok...
  37. B

    Diffusion through membrane, which boundary condition to implement?

    Hi, I am solving the diffusion equation using explicit finite difference to model the diffusion of an analyte through a membrane. I am interested in the concentration of the analyte on the other side vs time elapsed. On one side of the membrane is an initial concentration, which I am...
  38. R

    Third-order nonlinear ODE with boundary condition

    I'm trying to solve a third-order nonlinear ordinary differential equation. I couldn't get the answer even using Mathematica. The equation is: u'''(t) + u/2 u''(t) = 0 with conditions u(0)=0, u'(0)=0, u(10)=1. I need to get both analytic solution and numerical solution. For the...
  39. B

    Should I Scale My Boundary Condition Values for Problem Where I Scaled Interior?

    Hello all: I would very much appreciate advice on setting up a problem. Apologies in advance... This is probably a silly question--I'm more of a chemist than an engineer/math person! I have written a code for calculating changes in concentration/mass within a domain over time, as new...
  40. L

    Is There a Solution to the Boundary Condition Problem for y-2y'+2y=0?

    I'm asked to determine if for the solution y=c_{1}e^{x}cos(x)+c_{2}e^{x}sin(x) for: y"-2y'+2y=0 whether a member of the family can be found that satisfies the boundary conditions: y(0)=1, y'(\pi)=0 Not quite sure what to do here. The examples in my book give boundary conditions for the same...
  41. U

    What do you call a more general boundary condition?

    Is there a term to describe something like a boundary condition but which can be applied within the domain, not just on the boundaries? For example in a heat transfer problem you might specify a constant rate of heat generation in some region. Is that still called a boundary condition...
  42. S

    Flux boundary condition on a face of a cube

    Lets us say I have a cube and I apply to a face of the cube a heat flux of 100 watt/m^2. Lets us say i divide the face of the cube into say 10 elements (area of each face of the element is 1 m^2). What will be the flux on each element , will it also be 100 watt/m^2? Sorry for a...
  43. C

    What Are Natural Boundary Conditions?

    Hi, I was reading Lemon's Perfect Form and it talked about "natural boundary conditions". But I don't understand exactly how one determines them. It seems to me that one imposes some random condition then deduce stuff from it...?! Advanced thanks for any enlightenment!
  44. I

    Boundary condition for magnetic vector potential

    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...
  45. Y

    Question on an example relating to magnetic boundary condition.

    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...
  46. G

    Physical meaning of Neumann boundary condition

    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...
  47. Y

    Question about magnetostatic boundary condition.

    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...
  48. W

    Jordan wigner transform and periodic boundary condition

    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}...
  49. P

    Boundary condition for Maxwell equations

    It's obvious that if Maxwell equations are fulfilled by some E(x,y,z,t) and B(x,y,z,t), they are also fullfiled by E(x,y,z,t)+ E_0 and B(x,y,z,t)+B_0, where E_0 and B_0 are constants. This freedom has physical significance as it changes the Lorentz force which act on a charge. It...
  50. P

    Magnetostatics - boundary condition

    Let's consider two media with magnetic permeability \mu_1, \mu_2 . What's the condition for magnetostatic vector potential \vec{A} on the boundary. Is it true that its tangent component should be continuous. Thanks for replay.
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