Boundary Definition and 1000 Threads

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...

Hello! I'm starting a project with one of my professors at college whose subject is the Boundary Element Method. I've studied a little bit of Finite Element Method, but BEM is new to me. This project will envolve a lot of programming in Python and Matlab. I would like to know how does BEM...

Hello! This is more of a set theory question I guess, but I have that the definition of the boundary of a subset A of a topological space X is ##\partial A = \bar A \cap \bar B##, with ##B = X - A## (I didn't manage to put the bar over X-A, this is why I used B). I think I have a wrong...

Homework Statement Homework Equations The right hand section (A) has an incident and reflected wave $$y_1=Ae^{i(kx+\omega t)} +A'e^{i(-kx+\omega t)} $$ The middle section (B) has a transmission reflected wave $$y_2=Be^{i(k_2x+\omega t)} +B'e^{i(-k_2x+\omega t)}$$ Section (C) just has the...

Homework Statement An interface is formed between a block of aluminium (density = ##2.70 \times 10^3 kg/m^3##, speed of sound =##6.40 \times 10^3m/s##) and a block of copper (density = ##8.96 \times 10^3 kg/m^3##, speed of sound =##4.76 \times 10^3m/s##). Longitudinal waves traveling through...

Hello everybody. I'm about to take a final exam and I've just encountered with this exercise. I know it's simple, but i tried solving it by Separation of variables, but i couldn't reach the result Mathematica gave me. This is the equation: ∂u/∂x = ∂u/∂t Plus i have a condition...

Homework Statement We all know that $$\tau = VQ/ It $$ how to determine the shear stress at **G** ? I'm having problem of finding Ay centroid if the solid that i found earlier is y = 98.5mm There's a dashed line from G to the bottom . It's making me confused . for Q , should i consider the...

I've been trying to come up with wave equations to describe the motion on vibrating rectangular (more specifically, square) membranes. However, most paper I find assume fixed edges. What are the boundary conditions I need to apply to the 2D wave equations in order to have an free boundary in a...

At what point does quantum physics cease and general relativity take over. Where is the boundary? Is it a quantum of mass?

I'm trying to read this paper. Right now my problem is with equations 3.16 and 3.17. I understand that in equation 3.16 we're putting some boundary conditions on the fields, but I have two problems with these boundary conditions: 1) The fields depend on both ## t_E ## and ## x##, i.e. ##...

Hey everyone Just a picture of my configuration. The assumption here is $$\epsilon_a,\epsilon_b,\epsilon_c$$ are different from one another. Really the interest of this problem is to find the scalar potential $$\phi$$, such that $$\nabla^2 \phi = 0$$. So now my question, about jump...

I have a couple homework questions, and I'm getting caught up in boundary applications. For the first one, I have y'' - 4y' + 3y = f(x) and I need to find the Green's function. I also have the boundary conditions y(x)=y'(0)=0. Is this possible? Wouldn't y(x)=0 be of the form of a solution...

Homework Statement We're working in 2-d Anti-de Sitter space with metric: \begin{eqnarray*}ds^2 = \frac{1}{z^2}(-dt^2 + dz^2)\end{eqnarray*} with 0<=z. The solution is: \begin{eqnarray*}z^2 = (t+c)^2 + B\end{eqnarray*} And we've been asked to plot this (I think its a parabola with minima at...

Hi, If the dirichlet boundary condition is being applied, what does it tell us?

Is the potential across the boundary continuous for a dielectric sphere embedded in a dielectric material, so that the potential inside the sphere can be set equal to the potential outside of it at r=R ?

Hi everybody, I’m trying to calculate the shape of a boundary line f(x) between two mediums that collimates rays from a point light source. This requires the rays to hit the boundary line under a certain angle, so I calculated the slope m(φ) of the boundary line for a ray with polar angle φ (φ...

Hello! (Wave) We consider an elliptic operator $L$ in the space $\Omega$ with $c(x) \leq 0$. We suppose that $\partial{\Omega}=S_1 \cup S_2$. What can we say about the solution of the following problem? $$Lu=0 \text{ in } \Omega \\ u|_{S_1}=0...

Homework Statement I am given the following figure: These are converging rays that appear to be going to a point F convert to a plane wave upon hitting the boundary between n2 and n1, and I am asked to find the equation for the boundary between n1 and n2 that perfectly accomplishes this...

Greetings, I hope this is the right place to ask. I have been working with modeling of thermal conductance, G [W/K] of semi-conductor nanowires as a function of temperature. To start, thermal conductivity of a nanowire is modeled using BTE (Boltzmann Transport Equation). Then the conductance...

What is a homogeneous boundary condition? Or, more explicitly, what would make a boundary condition inhomogeneous Many thanks :)

Hi PF! So after scaling Navier-Stokes for a flow over a flat plate we ultimately arrive at ##f f'' + f''' = 0## subject to ##f(0)=0##, ##f'(0)=0##, and ##f'(\infty) = 1## where independent variable is ##\eta##. The source I was reading is trying to reduce this BVP to an IVP. Thus they suggest...

This question is inspired by Gilbert Strang's Course on Computational Science and Engineering, MIT 18.085. Consider the three matrices Fixed-Fixed $$K=\begin{bmatrix} 2 &-1 & 0 &0 \\ -1&2 & -1 &0 \\ 0 & -1 &2 & -1 \\ 0 & 0 & -1 & 2 \\ \end{bmatrix} $$ Free-Fixed $$T=\begin{bmatrix} 1 &-1 & 0 &0...

I was wondering how a boundary layer would be dissipative of momentum if it was under the influence of a positive heat gradient. I understand that the reason that we don't see the boundary pressure equal the stagnation pressure is that the boundary is dissipative (so excess pressure above...

Hi everyone, This is my first time posting here I am looking to get some help with Abaqus, I wish to compare two models and find the residual stress which causes a original model to deform to the other. The deflection between the two models can be calculated by other software. I plan to do...

When compared to laminar flows, the fluid "sticks" with the solid surface longer in case of turbulent flows. For example, the angle of separation for flow over a circular cylinder is 80 degrees for laminar flows, and 140 degrees for turbulent flows. What is the reason?

Any good places to go to get a better layman understanding of the no boundary proposal other than Hawking books? Id like to see what criticisms there are of the model, how has it evolved over time and is there any chance for experimental probes of it.

Hi all. I don't have as much experience with thermal analyses in ANSYS, and I can't quite figure out a problem that I'm working on. I'm trying to find the temperature distribution in a box that has a circle in the center. I want to define constant temperature b.c.'s at the walls and the circle...

Homework Statement Uxx - SU = A ; 0<x<1 Boundary conditions : Ux(0) = 0 U(1) = 0 The Attempt at a Solution I tried to set a new variable W = u + A, I can get rid of the A in the main equation and U(1) becomes = 1. If I set U= C*esqrt(S)x into the equation, its a trivial solution because of...

Homework Statement in the formula of shear stress τ = (V)(Q) / It , Q=Ay = first moment of inertia of area, the area can be located above(or bottom) at the point of interest) when the chosen point is at the wall(boundary) , why shear stress = 0? Homework EquationsThe Attempt at a Solution When...

Hi, I was recently following an example shown in this link and just had a couple questions: http://www.scientificpython.net/pyblog/solving-the-2d-wave-equation-and-making-a-video-of-the-solution I believe I understand the steps, but was just not quite understanding the justification. In the...

What I mean by this question is the following: If, just for example, we define the surface region of a star as that where the matter undergoes a phase transition from plasma to radiation, then that boundary has an objective physical meaning (let's not bother with the fact that the transition is...

Dear all, I made a cad of floating structure (the frame only), figure attached below. It should be located in the water and moored, so it can't go anywhere. The CFD simulation was done. So I have fluid force on the structure. Now I want to do mechanical analysis of the structure by apply the...

Hello everyone, The boundary condition : P=0, z=ζ is very common when studying irrotational flows. When cast with the Bernoulli equation, it gives rise to the famous dynamic boundary conditionn, which is much more convenient : ∂tφ+½(∇φ)2+gζ=0, z=ζ But what happens if the motion is rotational ...

Can there be a bounded space without a boundary without embedding in a higher spatial dimension? This seems to be the kind of question I get stuck on when the big bang comes up. Thanks

The rate of working of the Reynolds Stress can be written as: where ui is the fluctuating velocity and Ūi is the time-averaged velocity. It is stated in the textbook that, if we integrate the above equation over a closed volume V, the divergence term on the left integrates to zero since τRij...

Hi all! I have to calculate the natural frequency of the system. Any idea of boundary conditions of this case? There is beam supported by two springs on the left side.

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...

Hello! (Wave) I want to check if the following boundary value problem has a solution $\left\{\begin{matrix} -u_{xx}-4u=\sin {2x}, x \in (0,\pi)\\ u(0)=u(\pi)=0 \end{matrix}\right.$ I have thought the following: We consider the corresponding homogeneous equation $-u_{xx}-4u=0$. The...

How can something have a definitive edge if space can always be more granular?

In calculus of variations, extremizing functionals is usually done with Dirichlet boundary conditions. But how will the calculations go on if Neumann boundary conditions are given? Can someone give a reference where this is discussed thoroughly? I searched but found nothing! Thanks

I have a BVP of the form u" + f(x)u = g(x) , u(0)=u(1)= 0 where f(x) and g(x) are positive functions. I suspect that u(x) < 0 in the domain 0 < x < 1. How do I go proving this. I have try proving by contradiction. Assuming first u > 0 but I can't deduce that u" > 0 which contradict that u has...

Homework Statement Sorry for the dull question. Problem is as shown/attached Homework Equations The waves in part ii) are traveling in a HIL dielectric of permittivity ##\epsilon_{r}## from ##0 <z<d## and then hit an ideal metal boundary at ##z=d##. The Attempt at a Solution I figure this...

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] I know dV=1/C∫idt and that we integrate the voltage from V to V0. What I don't get are the boundary conditions for t - How do we get what we get in the parenthesis? My closest assumption is that the t/T values refer to the...

does anyone know what the boundary condition is for a closing valve using the wave equation pde?

Suppose we are solving a diffusion equation. ##\frac{\partial}{\partial t} T = k\frac{\partial^2}{\partial x^2} T## On the domain ##0 < x < L## Subject to the conditions ##T(x,0) = f(x) ## and ##T = 0 ## at the end points. My question is: Suppose we solve this with some integration scheme...

I have a simple question about Lewkowycz and Maldacena's paper http://arxiv.org/abs/1304.4926v2'][/PLAIN] http://arxiv.org/abs/1304.4926v2 In section 2, they consider the scalar field in BTZ background ground and require boundary condition of the scalar field, $\phi \sim e^{i\tau}$ . This...

I have created a matrix with a class called Lattice. The lattice is filled with objects of type 'Dipole' which is created with another class. The problem I am having is with boundary conditions when I look for a neighbour. e.g If i pick a dipole on the top row, I want its 'above' neighbour to be...

Homework Statement Find the Green's function $G(t,\tau)$ that satisfies $$\frac{\text{d}^2G(t,\tau)}{\text{d}t^2}+\alpha\frac{\text{d}G(t,\tau)}{\text{d}t}=\delta(t-\tau)$$ under the boundary conditions $$G(0,\tau)=0~~~\text{ and }~~~\frac{\text{d}G(t,\tau)}{\text{d}t}=0\big|_{t=0}$$ Then...

I have a question about the following scenario involving a flow separation issue in a pipe expansion The angle of the expansion is 30* - doubling the diameter from 1D to 2D We can consider this flow fully developed with a Reynolds of 5000+ Associated with this expansion is a head loss...

I can't seem to find an explicit or analytical solution to a boundary value problem and thought I might ask those more knowledgeable on the subject than me. If t is an independent variable and m(t) and n(t) are two dependent variables with the following 8 constraints: a) m' =0 @T=0 and...