All Questions

I am working on conductive polymer modeling and supposed to do one-dimensional diffusion model in the thickness of the polymer, however, due to the small value of thickness in micro, when I use the ...

What is the fastest method (language, solver, etc.) to numerically solve elliptic equations such as Poisson or Stokes equations in a cube in 3D with mixed boundary conditions? Especially, a ...

I am trying to implement inverse kinematics solver using BFGS as stated in the paper Xia2017. In the test experiment, i created 4 objects in 3-dimensional space: Node,Node1,Node2,Node3. Each Node is a ...

I am working with the following differential equation: The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions. After solving ...

Trying to implement an adaptive step size Runge-Kutta Cash-Karp but failing with this error: ...

If each edge of a graph $G$ is unweighted or has equal weights, then the shortest path between two nodes in that graph is the path that contains the fewest number of edges. Such a path can be obtained ...

Let $V_h$ be the space of linear finite elements on triangles. From the scaling argument, we can obtain the following inverse estimate inequality: $$ \| v_h \|_t \leq ch^{m-t} \| v_h \|_m, $$ for ...

The eigenvalue problem $$\frac{d^2u}{dx^2}+2i k\frac{du}{dx}-k^2-6\sin(x)^2u(x)=-\mu u(x)$$ gives the first five eigenvalues with $k=0$ or $k=1$ which are $2.06$, $2.26$, $5.16$, $6.81$, and $7.74$....

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...

I am looking for two python solvers using these methods: Backward (implicit) Euler method with fixed step size Backward (implicit) Euler method with adaptive step size I need the solvers to be able ...

I am trying to solve the Poisson problem with Dirichlet boundary condition in 1D: \begin{equation} \begin{array}{rcl} - \mu \Delta u & = & f~in~[0,1], \\ u(0) & = & 0, \\ u(1) & = ...

i have an example of Antisymmetric i.e 1: R(1,1),(2,2) and one example of Reflexive is 2: R(1,1),(2,2). both examples are same. my question is this: Q: why same things have different names? ...

I want to use neural network to solve a simple regression problem, and I try to program by myself accroding to lecture Backpropagation and Neural Networks . However, I meet loss divergence problem. ...

This is a follow up to my previous question posted here. I am solving an optimization problem using fmincon in MATLAB. There are no equality constraints in my model....

I'm currently analysing some spatial point patterns that come from some fluid dynamics simulations and I'm having some difficulty computing the structure factor, $S(\pmb{k})$, from both the positions ...

i wanted to know how to do aggregate analysis for a complex networked system. You can assume this complex networked system to be something like an organisation where people work in several units and ...

I have coordinates of a set of points that form a closed loop that lies in a 3D surface. I know the equation of the surface and I can calculate it's surface normal at any point. I found that for a ...

I try to solve numerically the following PDE for $E(r, z)$ with a cylindrical symmetrie (i. e. $E(r, z) = E(-r, z)$). $\frac{\partial E}{\partial z} = \frac{i}{2k} \Delta E + \mathcal{N}(E)$ Where $...

Consider the explicit midpoint method, i.e $$y_{n+1}-y_{n-1} = 2hf(y_n).$$ I'm asked to apply this method to the linear test equation, $f(y_n) = \lambda y_n,$ in order to find the method's stability ...

Consider the continuity equation $$ \partial_t \rho(x,t) + \operatorname{div} (b(x,t) \rho(x,t)) = 0, \qquad t \in [0,T], \quad x \in \mathbb R^N, $$ with $b \in L^1((0,T), W^{1,p}(\mathbb R^N))$. ...

I am trying to solve the schrodinger equation for the hydrogen atom numerically, using finite elements, with matlab's solvepdeeig(). I have a hard time getting the solution to be right, and it seems ...

I want to do the following, I have a set of 20 first order differential equations and I want to estimate some of the parameters. I've got the following initial and boundary conditions. The initial ...

Given a singular matrix $A$, what is the fastest method to find a single non-zero solution to $Ax=0$? Note that we are not looking for the whole kernel, we just want any non-zero vector in it. I ...

I'm currently trying to solve a problem using numerical methods. The set-up is rather long, so I apologize in advance... TL;DR: My solutions change depending on how big my steps are and I don't know ...

By transportation logistics, I mean the application of theoretical tools like traveling salesman problem, routing problem etc. So what are these applications? Well, stuff like how to schedule a fleet ...

I have to solve a set of nonlinear optimization problems in the subspace defined as the orthogonal space to a given vector. More precisely, $$ \arg\min f(\vec x) \qquad \text{with} \qquad \vec x \...

I trying to solve this system of equations with Euler's method $$\begin{aligned} \frac{dn_0}{dt} &= -n_0(t)W_{01}(t) + n_1(t)K_{10}\\ \frac{dn_1}{dt} &= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(...

Looking for the basic things like what we can do with python in automotive.

I am looking for the most efficient way to plot a mesh using matplotlib given the following information, coordinates of each node, what nodes belong to each element, and the value each node has. Below ...

I have a diffusion problem with an internal circular dirichlet constraint and a side condition which shall enforce a certain global volume integral. $\nabla(D \nabla u(x)) = 0$ outer boundary ...

I'm trying to re-solve the governing equations in hydraulic fracturing modeling as instructed step by step in a paper. After (A-9), the author stated that by substituting A-6, A-8 and A-9 into ...

My task is to solve $$\eta_k\frac{d^2C_k}{dz}(z)=-e_k, k = 1,2,3$$ $$C_k\ge0$$ $$C_1(0)=0, C_2(0)=A, C_3(0)=0$$ $$C_1(L)=B, \frac{dC_2}{dz}(L)=0, \frac{dC_3}{dz}(L)=0$$ with $$e_1 = -\beta_1-\beta_3$...

I am trying to solve numerically (obviously) inviscid Burgers' equation with the finite difference method. The equation is the following: $$ \displaystyle \partial_t u + u \, \partial_x u = 0 $$ ...

I'm going to be doing some weak scaling of an $N$-body integrator on AWS. In the past when I've done weak scaling for this integrator I've fixed the number of particles per core ($N/n = {\rm const}$). ...

I am currently doing a computational physics homework which asked us to use leapfrog to give the relations between timevelocities and time-distance of these two objects. The full question is as ...

I have a $q$-dimensional grid, known at run, not compile-time, that has $50$ points in each direction and hence $50^3$ combinations that I would like to first build and then call a function with each ...

What is the best way of finding the capillary flow using computer vision? Procedure that I have been using so far: Selected a ROI Calculated the optical flow in the ROI to get a flow matrix ...

I want to solve a vehicle routing problem where goods are collected from multiple locations, and then dropped at collection facilities. There are multiple collection points and they should be filled ...

I have an integer linear programming problem of the form: $$\DeclareMathOperator{\tr}{tr} \min \tr WX$$ subject to: $$\begin{align} \sum_j X_{ij} < c_i && \forall i \\ \sum_i X_{ij} = 1 &...

In our assignment, we are required to find the energies of the ground state and the first two excited states of the Schrödinger equation in a harmonic potential: $$V = \frac{50 x^2}{(10^{-11})^2}\, .$...

Our data set has $10^4$ data points, but has a long baseline and many gaps. As the histogram shows, the horizontal-axis is time and most of the time, there are no data. The vertical-axis is data ...

Is it possible to repeat selected rows in numpy? For example, can we get [[1, 2,3][1,2,3][4,5,6]] from[[1, 2,3][4,5,6]] ?

Can you tell me these equations come from where in MATLAB fmincg.m? ...

Problem I want to convert the general second order linear PDE problem \begin{align} \begin{cases} a(x,y)\frac{\partial^2 u}{\partial x^2}+b(x,y) \frac{\partial^2 u}{\partial y^2} +c(x,y)\frac{\...

I have provided the R script of the project I´m working on.It works fine but computation of the required Jacobian at each step makes it costly. I need to find an alternate way to either compute the ...

I would like to make a visualization with ParaView for a paper. In order to have a high quality look, I would like the image to be, say, 300 dpi (or vector graphics). Moreover, since I know the column ...

I'm running a simulation, and some linear solvers are returning a message of ill-conditioned matrix. Hence, I'm looking for a fast, easy to implement, method to detect if a matrix is ill-conditioned, ...

I would like to "smooth" my prediction output and limit it to specific local min/max points. (The predicted line in blue - min is to low, how can I limit the polynomial equation accordingly?) My ...

In particular, if Euler's method is implemented on a computer, what's the minimum step size that can be used before rounding errors cause the Euler approximations to become completely unreliable? I ...

In many CFD text books, usually there is a dedicated chapter for advection term discretization. Why discretization of such term in advection-dominated problems and near the discontinuities is ...