Boundary Definition and 900 Threads

I have the following PDE I wish to solve: \frac{\partial u}{\partial t}=D\frac{\partial^{2}u}{\partial x^{2}} With the following boundary conditions: \frac{\partial u}{\partial x}(t,1)+u(t,1)=f(t),\quad u(t,0)=0 Now, I wish to do this via the Crank-Nicholson method and I would naively...

I have been reading Sean Carroll's recent book called Something Deeply Hidden where he advocates a Many Worlds Interpretation of Quantum Mechanics. I was thinking that the most important question in all of Physics might be is everything quantum or is there a quantum/classical boundary. If we...

I understand the idea of the method of images, and its clever use of uniqueness to determine V(x,y,z) for non-trivial systems. My question now is simply about guidance for obtaining the effective "image" of this system, as it is clearly more complicated than the 2-plane analogue (in which there...

Consider the following linear first-order PDE, Find the solution φ(x,y) by choosing a suitable boundary condition for the case f(x,y)=y and g(x,y)=x. --------------------------------------------------------------------------- The equation above is the PDE I have to solve and I denoted the...

Pardon the very naive question, but why does the atmosphere in these gas giants seem to have, from a distance, a very clear, sharp and distinctive boundary? When one looks at Earth's atmosphere from space, it seems to have a fuzzy bluish boundary, gracefully vanishing into the black. I read...

PS: This is not an assignment, this is more of a brain exercise. I intend to apply a general derivative boundary condition f(x,y). While I know that the boxed formulation is correct, I have no idea how to acquire the same formulation if I come from the general natural boundary condition...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am reading Chapter 6: Topology ... ... and am currently focused on Section 6.1 Topological Spaces ... I need some help in order to fully understand a statement by Browder in Section 6.1 ... ... The...

Hello! In several of the derivations I read so far in my QFT books (M. Schawarz, Peskin and Schroeder) they use the fact that "we can safely assume that the fields die off at ##x=\pm \infty##" in order to drop boundary terms. I am not sure I understand this statement in terms of QFT. A field in...

Premise: everything that follows is done in the frequency domain. Boundary conditions If there are superficial currents (electric and magnetic) impressed on the boundary between two media, we have these discontinuities for the tangential components of the fields...

I'm not quite sure if my problem is considered a calculus problem or a statistics problem, but I believe it to be a statistics related problem. Below is a screenshot of what I'm dealing with. For a) I expressed f(t) in terms of parameters p and u, and I got: $$f(t)=\frac{-u \cdot a + u \cdot...

hi, all great brains, I have a question about BVP, which confused me a while, maybe someone can help to clarify it. For a point source with Dirichlet boundary in a 2D domain, the response at any coordinate except the source point is dependent on the surface of the source, for example, heat...

Hi, I'd like to be clarified regarding the general natural/Neumann boundary condition for a PDE. 1. The natural boundary condition is generally defined as: (1) and can be expressed as, according to this resource: (2) But apparently, according to...

Hi everyone, in the attached file I tried to find the transmitted and the reflected coefficients. I ran into trouble applying the boundary conditions to the linear components of the electric field. Check the outlined boxes and see if they make sense. Thanks

What is the difference between the two? Also, as another question, for enthalpy, is it correct to define it to be the sum of internal energy and flow energy or is there another understanding for it? Thanks in advance

Homework Statement I want to find the solution to the following problem: $$\begin{cases} \nabla^2 B=c^2 B &\text{ on the half plane } x>0 \\ B=B_0 \hat{z} & \text{ for } x<0 \end{cases}$$ in the ##xz## plane. ##c, B_0 \in \mathbb{R}## Homework Equations I am not really sure what would be...

Homework Statement [/B] I have a metal disc adhesively bonded at its edges to a piezoelectric ring. The piezoelectric ring vibrates radially which leads to the plate vibrating transversely. I am looking to work out the resonant frequency of the metal disc which I believe will depend on the...

Hi everyone, I'm working through the boundary conditions and I could not figure out what to do with the last boundary condition (when z=L) I know that the values for K are: How so? 1. Homework Statement A hollow right angle cylinder of radius a and length l. The sides and bottom are...

I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...

Homework Statement I am trying to fill in the gaps of a calculation (computing the deflection potential ##\psi##) in this paper: http://adsabs.harvard.edu/abs/1994A%26A...284..285K We have the Poisson equation: ##\frac{1}{x}\frac{\partial}{\partial x} \left( x \frac{\partial \psi}{\partial...

Hi everyone! I have to solve a problem using Poisson's equation. There are two parallel infinite conductor planes in vacuum. The distance between them is d and they are both kept at a potential V=0. Between them there is a uniform volume density charge \rho_0>0 infinite along the directions...

Homework Statement I try to integral as picture 1. The result that is found by me, it doesn't satisfy Green's function for boundary value problem. Homework EquationsThe Attempt at a Solution show in picture 2 & picture 3.

If you have a particle in a 1-d box with a finite potential when ##0 < x < L ## and an infinite potential outside this region, then the normalised wavefunction used to describe said particle is ## \psi (x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L})##. However, if you had say instead a finite...

Homework Statement Consider a plug flow (slippery walls) with a uniform velocity ##U## in a circular pipe of diameter,##d## and length ##L##. The fluid is a supersaturated solution with a concentration ##c##. At the pipe wall, precipitation of solute happens at a net reaction rate per unit area...

Hi! I have a question related to boundary condition in a one dimensional beam subject to compression and traction efforts. In my class notes I have the following: If we consider a 1D beam of length L which is fixed at x=0 and subject to an effort F at x=0 we have the following boundary...

In the textbook (attached image) it says that the boundary condition is V=0 at r=R. This creates a correlation that ##B_l=-A_l R^{2l+1}## but the potential at any boundary is continuous so when we take this account, we get. ##B_l=A_l R^{2l+1}## These two clearly contradict each other. I'd...

Hello, If I have a homgeneous linear differential equation like this one (or any other eq): $$y''(x)-y'(x)=0$$ And they give me these Dirichlet boundary conditions: $$y(0)=y(1)=0$$ Can I transform them into a mixed boundary conditions?: $$y(0)=y'(1)=0$$ I tried solving the equation, derivating...

Homework Statement I would like to know how the boundary of the inequality change when the origin of the coordinate system changes. Homework Equations The original inequality is[/B] $$ r_0 \le x^2+y^2+z^2 \le R^2$$ I would like to know the boundary of the following term, considering the...

We are using griffith's 4 edition in my electromagnetic course atm. and there's something I just don't understand about boundary conditions. It says that if we have a surface charge, and we put a pillbox on it, in such a way that half of it extends under the surface charge, and the other half...

How would you solve for the Amplitude(A) and Phase Constant(ø) of a spring undergoing simple harmonic motion given the following boundary conditions: (x1,t1)=(0.01, 0) (x2,t2)=(0.04, 5) f=13Hz x values are given in relation to the equilibrium point. Equation of Motion for a spring undergoing...

According to wikipedia "The onset of turbulence can be predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a...

Homework Statement Two magnetic materials are separated by a planar boundary. The first magnetic material has a relative permeability μr2=2; the second material has a relative permeability μr2=3. A magnetic field of magnitude B1= 4 T exists within the first material. The boundary is...

Hello! (Wave) I want to find the solution of the following initial and boundary value problem: $$u_t(x,t)-u_{xx}(x,t)=0, x>0, t>0 \\ u_x(0,t)=0, t>0, \\ u(x,0)=x^2, x>0.$$I have done the following so far: $$u(x,t)=X(x) T(t)$$ $$u_t(x,t)=u_{xx}(x,t) \Rightarrow...

Just got back from a conference where one of the invited speakers presented his work on using the Immersed Boundary method with Adaptive Mesh (to model cardiovascular flow): https://cims.nyu.edu/~griffith/ This summer, I have an undergrad modeling pulsatile flow in an elastic tube using the...

Could someone please go here... https://en.wikipedia.org/wiki/Flow_separation And explain to me the difference between Flow and Boundary Separation discussed in the opening. Because this explanation makes no sense to me. I have the problem. I just don't understand the difference.

Hello! (Wave) Let $a,b>0$ and $D$ the rectangle $(0,a) \times (0,b)$. We consider the boundary value problem in $D$ for the Laplace equation, with Dirichlet boundary conditions, $\left\{\begin{matrix} u_{xx}+u_{yy}=0 & \text{ in } D,\\ u=h & \text{ in } \partial{D}, \end{matrix}\right.$...

Griffith's writes in chapter 7 electrodynamics that D1.a - D2.a = sigma. a. But minus sine comes when we evaluate the dot product first. How does the minus sign occur without evaluating the dot product?

I am trying to decipher if an error occurred in a calculation given in this paper. It is understandable that if two compressible fluids of different uniform densities have a common interface (e.g. Figure 1), then to be in equilibrium and supported against gravity, there must be a pressure...

Homework Statement I am confused on how it's using the surrounding temperature minus the surface temperature as its the other way around in the Newton's law of cooling, Doing that would change the sign of convection right? I don't see the reason to do that, since if left side is hotter, then...

Hi everybody ! In one of my papers I need to add Gibbons-Hawking-York boundary term in order to calculate everything properly. I found a paper (https://www.sciencedirect.com/science/article/pii/S0370269316306530 ) in which authors included this term into the action. My problem is: I tried to...

Homework Statement [/B]Homework Equations shear bending diagram The Attempt at a Solution May I ask for supports like these, if shear force V= 0 or not when x=L? From the shear diagram, it is a shape increase from -0.5P to 0 there. As the shear go back to zero is owing to the reaction force...

Hi, my classmate asks me an interesting question: For a finite 4D volume in spacetime, its boundary is a 3D close surface. If the 4D volume is a 4D rectangular, the boundary consists of eight 3D surfaces. The boundary condition is specified on these eight 3D surface. Please explain the physical...

Homework Statement A particle is represented by the following wave function: ψ(x)=0 x<-L/2 =C(2x/L+1) -L/2<x<0 =C(-2x/L+1) 0<x<+L/2 =0 x>+L/2 use the normalization condition to find C Homework Equations ψ(x) must be...

I am having a problem with understanding concepts related to the speed of a wave. Here are my thoughts laid out: 1) The speed of a wave is dependent only on the medium 2) When a wave crosses from a less dense medium into a more dense medium (or visa versa) the speed of the wave is always...

I want to show that a closed unit ball is manifold with boundary and I attempted as uploaded. But I am not happy with the way I showed the boundary chart is injective. Am I right?

-If we have string of length L that has fixed ends, then we can easily find frequencies with which this string can oscillate: We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions...

I figured this would be the best place to ask as there doesn't seem to be a FEM/Simulation specific sub-forum here, but I am looking for some help regarding mesh generation in ANSYS Maxwell. I have an array of "micro-needles" that I am applying a voltage to in order to determine the electric...

Homework Statement if someone could help me with this it would be much appreciated. In physics, I used a 98Ω resistor in a series circuit and measured the current and voltage output from battery, using the current and voltage I calculated the resistance. I=0.0094A V=1 Rt=1/0.0094=106.38Ω even...

Hi PF, I'm trying to derive the Prandlt condition (not sure if it is Prandlt's work tough) for a fluid to separate from a surface in the boundary layer. The equation should be: ##\frac {\partial^2 v_x} {\partial y^2} = 0## which is quite "intuitive" to me. To derive it let's start from the...

Homework Statement Suppose we have the standard rectangular potential barrier in 1D, with $$ V = \left\{ \! \begin{aligned} 0 & \,\text{ if } x<0, x>d\\ V_0 & \,\text{ if } x>0,x<d\\ \end{aligned} \right. $$ The standard approach to solve for tunneling through the barrier is to match the...

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...