Boundary Definition and 1000 Threads

I am solving the Laplace equation in 3D: \nabla^{2}V=0 I am considering azumuthal symmetry, so using the usual co-ordinates V=V(r,\theta). Now suppose I have two boundary conditions for [V, which are: V(R(t)+\varepsilon f(t,\theta),\theta)=1,\quad V\rightarrow 0\quad\textrm{as}\quad...

Hi at all, I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions: ##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}## ##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}## For eigenvalues, the text I'm following says that I have to consider that the...

Hello, I am trying to find a Magnetostatic(3D) solution for my design. My design consist of a coil embedded in Ceramic material developed by LTCC technology. I am below queries: 1. Is it important to define a material"Insulating"? How it will affect the Inductance of the system and the...

Hello PF community, I am currently self-studying electrodynamics from Griffiths textbook, and I'm at a point where the book discusses electrostatic boundary conditions. If someone can please check if my reasoning is right. So, as I am approaching an infinite, uniformly charged plane (let the...

I am unsure how to choose the boundary conditions for a system of PDEs or for a single PDE for that matter. The situation I am stuck with involves a system of 4 PDEs describing plasma in a cylinder. The dependent variables being used are Vr, Vt, Vz, ni, and the independent variables are Rr...

Homework Statement [/B] Determine the Green's functions for the two-point boundary value problem u''(x) = f(x) on 0 < x < 1 with a Neumann boundary condition at x = 0 and a Dirichlet condition at x = 1, i.e, find the function G(x; x) solving u''(x) = delta(x - xbar) (the Dirac delta...

There are few thing I'm not sure of and be happy for clarifications. In general: at steady state, what are the electric-field,potential, and current boundary conditions between a conductor and a dielectric medium? more specific: a) When dealing with a perfect conductor there exist a surface...

Homework Statement I have an infinitely long cylinder of a dielectric material, surrounded by another dielectric material and coated with graphene which has surface conductivity \sigma, implying it has a superficial current. The sheet of graphene is very thin, and the dielectrics are asumed to...

Homework Statement I'm trying to do all the calculations for the attached paper, and I'm having trouble with the boundary conditions for P polarization. My question is, how can I arrive to those conditions? The problem is 2D, an infinite dielectric cylinder coated with a layer of graphene...

Homework Statement Homework EquationsThe Attempt at a Solution The energy eigen - value of a particle in a box is given by ## E_n = \frac { n^2 h^2}{8mL^2} ## . Now, applying classical mechanics , ## \frac { p^2}{2m} = \frac { n^2 h^2}{8mL^2} ## . ## p \propto \frac { 1} L ## , So...

Homework Statement I am having an issue, not with the maths but with the boundary conditions for this question. A bar 10 cm long with insulated sides, is initially at ##100 ^\circ##. Starting at ##t=0## Find the temperature distribution in the bar at time t. The heat flow equation is...

Homework Statement I'm trying to find the boundary conditions for the following problem: A plate with length 2L is placed on supports at x = L/2 and x = - L/2. The plate is deforming elastically under its own weight (maximum displacement bowing up at x = 0). Both ends of the plate are free...

Can someone help me to understand what the boundary operator on a p-chain is doing exactly? Or boundary operators in general? I really need to develop a better intuition on the matter.

I am studying online course notes from University of Waterloo on 'Analytical mathematics in geology' in which the author describes a 'modified Fourier transform' which can be used to incorporate 3rd kind of boundary conditions. The formula is ## \Gamma \small[ f(x) \small] = \bar{f}(a) =...

How does low ambient pressure effect on the thickness of the boundary layer for given flow conditions of gas? In absolute vacuum the thickness of the boundary layer is 0 of course, but it seems that all the boundary layer thickness correlations use the Reynolds number, which doesn’t change much...

Hi, I am interested in simulating the vacuum field equations, but solving a full boundary value problem rather than the initial value problem. i.e. I might have boundary conditions in all spatial and temporal extents/extremes, rather than just an initial 3D surface. Does anyone know any free...

Hi PF! Given a fluid/fluid interface ##F(t,x,y,z) = 0## the kinematic boundary condition states ##DF/Dt = 0##. Given ##y=F## the text states ##v = \partial_tF+u\partial_xF+w\partial_zF##. How is this possible? I thought ##DF/Dt = 0 = \partial_tF+u\partial_xF+v\partial_yF+w\partial_zF## and...

Homework Statement I'm trying to keep the post brief and will post more info if needed. But I am trying to understand how the value of two "A" constants were found. This is from Griffiths Electrodynamics. In this part of the problem, I am given a boundary condition that is a function of theta...

Homework Statement So I have an equation V = Ae(kx)+Be(-kx) And boundary conditons V= V0 when x=0 and V= 0 when x=b 2. Homework Equations I have solved ones where v=0 at x=0 where it nicely simplifies as the exponentials =1 and the Coeffecients A=-B which leads to a sinh function and I...

I used Newtons method and taylor approximations to solve this equation $$f'''+\frac{m+1}{2}ff''+m(1-f^{'2})=0$$ It solves for velocity of air over a flat plate. The velocity is a constant ##u_e## everywhere except in a boundary layer over the plate, where the velocity is a function of distance...

Homework Statement I have to calculate the stationary field inside a room. Homework EquationsThe Attempt at a Solution I used the diffusion equation to calculate the temperature, which is T(x,y)=(Eeknx+Fe-knx)cos(kny), k=(n*pi/a), a is the length of the room. Now i have to satisfy boundary...

Homework Statement Find E1, E3, and ps2 Homework Equations boundary conditions The Attempt at a Solution (these are class notes)[/B] I understand how to find E1, but I am a bit confused about the reasoning behind finding E3... Why do we leave the 2x(hat) for E3...? I though that only...

Hello, My question is very simple but I do not have a lot of experience with simulation. I want to write some code to simulate a lattice with boundary conditions and then I will perform calculations with the Hubbard model to find different kinds of properties of interest. I would like to know...

Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## Homework Equations Radial equation \begin{equation}...

The question is basically find the boundary conditions when ##l=0##, for energies minor than 0. Homework Equations $$V(r)=\begin{cases} & 0\text{ $r<a_0$}\\ &V_0\text{ $a_0<r<a_1$}\\ & 0\text{ $r>a_1$}\\ \end{cases} $$ $$...

1. Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. How is the general form for the eigenfunctions? What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## 2...

It's understandable that finding absolute extremum is impossible for a function with restricted boundary conditions. But why does the derivative of similar functions is not zero when the extremum is on the end points? To be precisely short with my question, why does the derivative gives only...

I have a (somewhat) strange energy equation which has the following form: KE = A + B W + C \exp(-D W), where A,B,D are known constant, C is an unknown constant to be determined and kinetic and potential energy are given by KE and W respectively with W\equiv W(r) i.e. is a function of...

Homework Statement ## y''+\lambda y = 0 ; y(0) = 0, y(\pi)-y'(\pi) = 0## Homework EquationsThe Attempt at a Solution So, we have to test when lambda is equal to, less than and greater than 0. Let ## \lambda = 0## thus, the ODE becomes ## y'' = 0 ## which implies solutions of the form ## y(t) =...

Homework Statement Find the eigenvalues and eigenfunctions of the following boundary-value problem. ## y''+\lambda y = 0 ; y(0) = 0, y'(L) = 0 ## Homework EquationsThe Attempt at a Solution So, we have to test when lambda is equal to, less than and greater than 0. Let ## \lambda = 0## thus...

Hello gents, Q:/ what is the reason for letting the inner boundary condition = (-1) when solving the radial flow of infinite form of diffusivity equation, and i would like to know what will happened if i didn't equate it with (-1). as in the attached pic: https://i.imgur.com/AVesmHM.png

The following lines of codes implements 1D diffusion equation on 10 m long rod with fixed temperature at right boundary and right boundary temperature varying with time. xsize = 10; % Model size, m xnum = 10; % Number of nodes xstp =...

I have a simple but technical problem: How to calculate the extrinsic curvature of boundary of AdS_2? I am not very familiar with this kind of calculation. The boundary of AdS2metric $$ds^2=\frac{dt^2+dz^2}{z^2}$$ is given by (t(u),z(u)). The induced metric on the boundary is...

I've been playing around with Maxima and it's ctensor library for tensor manipulation. I decided to have a crack at deriving Schwarzschild's solution for the interior of a constant-density sphere. I've managed to derive a static, spherically symmetric solution, but am struggling a bit with the...

Q) A conducting sphere of radius R floats half submerged in a liquid dielectric medium of permittivity e1. The region above the liquid is a gas of permittivity e2. The total free charge on the sphere is Q. Find a radial inverse-square electric field satisfying all boundary conditions and...

This question is based on page 71 of Thomas Hartman's notes on Quantum Gravity and Black Holes (http://www.hartmanhep.net/topics2015/gravity-lectures.pdf). The Euclidean Schwarzschild black hole $$ds^{2} = \left(1-\frac{2M}{r}\right)d\tau^{2} + \frac{dr^{2}}{1-\frac{2M}{r}} +...

Hi, I need to solve Laplace equation ##\nabla ^2 \Phi(z,r)=0## in cylindrical coordinates in the domain ##r_1<r<r_2##, ##0<z<L##. The boundary conditions are: ## \left\{ \begin{aligned} &\Phi(0,r)=V_B \\ &\Phi(L,r)=V_P \\ & -{C^{'}}_{ox} \Phi(x,r_2)=C_0 \frac{\partial \Phi(x,r)}{\partial...

Homework Statement [/B] Inside a sperical dielectric mass there is a electric dipole on the center of the sphere. The sphere has radius a. This dieletric sphere is inside and on the center of a conductive spherical shell of radius b. The problem asks to find the potentials and then the...

hi guys, i am new user on ansys i have task from my lecturer. it is about static test for seat bus. i try simulate the seat bus on ansys statical structural. you can see my model on attachment (untitle1.png). at that picture, there are 2 bars will push the seat back. the stiffness beahvior of...

I'm currently trying to solve the following two-point boundary problem by means of the shooting method: To clarify, I'm investigating the optimal route of aerial/marine vehicles from one point to another point, considering a flow field. * The starting and ending locations are set as x0, y0...

The 2-sphere ##\mathbb{S}^2## can be expressed as the product ##\mathbb{S}^1 \times \mathbb{S}^1## Now can we express ##\mathbb{S}^1## as ##\mathbb{S}^1 \subset (-a,a)##, where ##(-a,a)## is some open interval of ##\mathbb{R}##? If so, then (I think) ##\mathbb{S}^1## is homeomorphic to...

Homework Statement http://imgur.com/7FKgeYs[/B] Here is the link to the problem I am stuck on. I don't know what question b) means by solve for the boundary values? Are these the same as boundary conditions or are boundary values explicit values? Homework Equations NA The Attempt at a...

Any open subset of ##\mathbb{R}^{n}##; The n-Sphere, ##\mathbb{S}^n##; The Klein Bottle. I guess they don't have a boundary, as a neighborhood of any point of them is homeomorphic to ##\mathbb{R}^n##. I'd like to know whether my guess is correct and whether the reason I'm giving for them not to...

We can ignore the boundary contribution, namely the term that arises when we solve $$\int d^{4}x \sqrt{-g}g^{ab} \delta R_{ab}$$ when varying the action. According to Wikipedia it's appropriate to do so only when the underlying manifold is both without boundary and compact. That condition seems...

Homework Statement Consider a plane monochromatic wave incident on a flat conducting surface. The incidence angle is ##θ##. The wave is polarized perpendicular to the plane of incidence. Find the radiation pressure (time-averaged force per unit area) exerted on the surface. Homework Equations...

Homework Statement a) [/B]There is a piston-cylinder arrangement; initial pressure is 200 kPa, initial volume is 0.04m^3. Volume of the gas increases to 0.1 m3 while the pressure remains constant, ie a constant pressure process. Calculate the work. b) There is a piston-cylinder arrangement...

So I have this problem, taken from Kraus's heat transfer book. So deriving the computational molecule, the conditions for (3.251a), (3.251b) is a bit of a no brainer. The issue I am having is about the boundaries for (3.251c) and (3.251d). This is actually the first time I have seen this...

Hi. Been a while since I logged in here, I missed this place. Anyway, I have a question (title). Is that even possible? Say for example I have the standard heat equation (PDE) subject to the boundary conditions: T(0,t) = To T(∞,t) = Ti And the initial condition: T(0,t) = Ti I am aware of how...

(Mentor note: moved here from noon homework thread hence no template) I was studying vibration of a one-dimensional monatomic chain and the textbook used periodic boundary condition (PBC). I wanted to justify the use of PBC, so I came up with this: atoms deep inside the crystal sees an...

Hi, I'm working on a project using LAMMPS. I am very new to the software and find the documentation doesn't always answer the fundamental questions I have. I noted previous LAMMPS queries were posted on this forum, although I am from a mechanical/materials engineering background. I am trying...