# Tagged Questions

Subdiscipline of theoretical physics which consists in the study of physics problems using numerical algorithms. PLEASE NOTE that questions about computational methods and/or programming are OFF-TOPIC on Physics.SE.

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### Laser resonator modes

For a resonator, plot the intensity as a function of time for (i) when the modes have identical phases, and (ii) when the modes have random phases. Attempt Here is the equation for intensity (p. ...
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### Numerically integrate equations of motion with noise

Consider the equations of motion $$\begin{cases} \dot{x}(t) & = v(t) \\ \dot{v}(t) & = -\frac{\lambda}{m} v(t) + \frac{1}{m}F^{c}(x(t)) = a(x(t), v(t)) \end{cases},$$ where $x$ is the ...
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### Keplerian orbits and radial velocities: problem with true anomalies

I am writing a pure Python code to calculate radial velocities of stars with massive objects orbiting them. I am following the formalism from Murray & Correia (2011) (hereafter MC11). In a given ...
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### Generalized Eigenvalue Problem from linear stability analysis

I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to ...
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### 2-D Ising model temperature of equilibrium [duplicate]

I have simulated 2-D Ising model in C#, but my scatter plot for magnetization versus temperature is an decreasing line (you know that the correct plot decreases quickly in a temperature near 2.3). I'...
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### Why is more difficult for a DFT to converge with non-periodic conditions?

I am simulating a cubic amorphous silica system. When all boundaries are periodic the SCF iteration converges rapidly. However, when the boundary is not periodic in the $x$ direction, the SCF ...
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### Derivation of generation of time between two subsequent particle enters into computational domain

I have problem with understanding derivation of one equation in following problem. You have 1D computational domain (it is not 1D but because it is symmetrical and we are watching only radial ...
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### Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
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I'm working with the cylindrical coordinates. I'm using the central difference to convert the radial part of Laplace operator into a matrix. $\nabla^2 u = \frac{\partial ^2u}{\partial r^2}+\frac{1}{r}... 1answer 75 views ### Can I re-wind gravity? Suppose I perform an arbitrary simulation where I integrate the motions of a collection of particles which interact only gravitationally. Suppose I use a time reversible integrator (to be specific, ... 1answer 70 views ### How to conserve momentum when numerically-integrating the path of a charged particle through a magnetic field I have the python script attached below, which is intended to track the trajectory of a charged particle in a static, uniform magnetic field. It is very simple to calculate the instantaneous force ... 1answer 99 views ### FCC-to-BCC phase transition in NaCl, Buckingham or Lennard-Jones potentials? Background The transformation from B1 (face centered cubic (FCC) type) to B2 (body centered cubic (body centered cubic (BCC) type) structures is one of the best documented high pressure phase ... 0answers 24 views ### How is time evolution done in numerical GR? Suppose we're simulating what happens when a fairly massive object falls into a black hole. Say the object starts far away, so that the initial condition is that the metric is the Schwarzschild metric ... 0answers 17 views ### Fermi-level of lattice model I have a chain of$N$lattice points with periodic boundary conditions. Every lattice point only has one orbital for an electron to occupy and spin is not included for simplicity. The lattice points ... 1answer 68 views ### Methods for handling close approaches in$N$-body simulations In direct gravitational$N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system? 0answers 75 views ### Simulating TE011 mode in cylindrical cavity, Comsol [closed] I have been trying to simulate TE011 mode in a cylindrical cavity by modifying the example given in Comsol site(https://www.comsol.co.in/model/computing-q-factors-and-resonant-frequencies-of-cavity-... 0answers 25 views ### Choosing the boundary conditions knowing the potential So I have to apply Numerov's algorithm to solve the Schrödinger equation in spherical coordinates using the potential$V(r)=-A e^{-r/a}$, where$A=32.7MeV$and$a=2.18fm$. I have already ... 1answer 81 views ### Schrödinger equation in spherical coordinates using Numerov's method? So I need to solve the Schrödinger equation using Numerov's method. However, the problem I have assigned to me is in spherical coordinates. As it seems, I only need to take into account the dependance ... 0answers 16 views ### Spherical Harmonic fitting excess polar magnitudes I am trying to fit an expansion of spherical harmonic functions to a dataset distributed over the surface of a sphere using the least squares method. Each data point is in terms of$(r,\theta,\varphi)$... 2answers 65 views ### Current Status of the Monte Carlo Sign Problem I've been reading about the Monte Carlo sign problem, and I am a little confused about its current status. Specifically, after reading this post When is the "minus sign problem" in quantum ... 0answers 37 views ### Calculate 2D Effective mass from bulk effective mass I am trying to create a self consistent Shrodinger Poisson Solver for various semiconductors. There is already one done by Professor Hu from UC Berkeley - QM CV Simulator. Looking at the code, they ... 1answer 54 views ### Numerically finding the energy diagram of the hamiltonian I'm looking at a collection of three two level systems (qubits) coupled to each other (with known bare state energies and couplings). The hamiltonian is given by $$\mathcal{H}=\sum_{i=1}^3{\omega_ia^\... 0answers 19 views ### Standing waves and acoustic levitation i am doing a new personnal project about acoustic levitation with standing waves into ambiant air using a piezo ultrasonic tranceiver and a reflective pannel. I modelised both of the emission and the ... 0answers 24 views ### Plotting EM fields I am currently studying transformation optics and learning about electromagnetic cloaking. To plot my results(Electric and magnetic fields) i have to solve maxwell's equations given the permeability ... 1answer 37 views ### Simulating the Electric Field inside a Hollow Sphere of Uniform Charge I've recently been studying Gauss's Law and have come across some results that I want to verify. For one, I am trying to verify that the electric field inside a conductor (in this case it could be ... 1answer 97 views ### Quadratic drag projectile motion I have calculated formulas with 1 dimensional trajectory motion (free-fall) including quadratic drag, and have created the following equations. These equations of motion are not of much use on its ... 1answer 17 views ### Which are the best books I can refer for turbulent heat transfer and its computation? I am a graduate student. I wanted to do computation on heat transfer problem mainly heat convection. I am working on turbulent regime. Can you kindly suggest some good books so that I can get ... 0answers 65 views ### Which formula was used to get Gravitational Waves animation? I would like to make animation like this by myself It is from wikipedia article "Gravitational wave". But if I use formula from wikipedia article "Gravitational wave" subsection "7.2.2 Wave ... 1answer 41 views ### N-Body Simulation for Photons For my undergrad optics class I am taking we have to select final projects to work on for second half of the semester. I have spent the last few weeks working on my own project which was a GPU ... 1answer 52 views ### Review article recommendation in the field of 2d materials I am new to 2d materials. I tried to search related review articles in review of modern physics, but did not find anyone covering the whole of the 2d material area. Anybody can recommend some latest ... 1answer 380 views ### Is Machine Learning a useful tool for analyzing experimental data? [closed] Apart from being a student of Physics I'm also a developer and recently in the context of cloud development I've been hearing a lot about cloud based Machine Learning. After looking at some examples ... 1answer 82 views ### Do black hole merger simulations include regions inside event horizons? Inspired by this question, I would like to ask the following specific point. In numerical simulations of general relativity that involve black holes, like the ones used to understand the black-hole ... 2answers 75 views ### About unit definition in numerical computation [closed] I attend an undergraduate level course of quantum mechanics. I am thinking of computer computation on a quantum mechanical problem. I do not have much experience in numerical computation, so I read ... 1answer 48 views ### Calculating orbits with varying laws of physics? [closed] The general way planets orbit stars in our universe is determined by the inverse square law and the three laws of motion. Both the inverse square law and the three laws of motion are the reason that ... 0answers 23 views ### Numerical simulation of strong field gravitational vacuum solutions colliding I am interested in the current state of knowledge of strong field General Relativity learned from numerical investigations of gravitational wave packets colliding with each other or black holes. If ... 0answers 23 views ### photometric redshifts - the origin of 1 / (1+ zspec) in photometric accuracy i have a training sample of sources with known spectroscopic redshifts (z_{\rm spec}) and i run a photometric fitting code that uses a template to determine the photometric redshifts (z_{\rm phot})... 0answers 38 views ### Vortex in a Pipe / Solutions or approximations? I want to study a vortex flow in a pipe; in other words helical flow. A couple introductory texts on fluid mechanics (e.g. Shames, Mechanics of Fluids) describe the solution to vortex flow in 2D: ... 2answers 79 views ### time step in kinetic montecarlo simulation I have a doubt about how the time step is calculated in kinetic montecarlo simulations. One state with index i is connected to other N states, indexed by j=1...N, by transitions that happen ... 0answers 17 views ### Explicit solvent simulations in NVE ensemble: Molecular Dynamics I am simulating a SDS micelle system in NVE ensemble at room temperature. I am not sure if the system is equilibrated, since the pressure variations are around 100's of atm, where the average pressure ... 0answers 24 views ### Efficient ways to solve complicated kinematics problems I'm curious about the range of approaches one can take to perform motion/kinematic simulations on many 3D objects. Currently I am familiar with the iterative process of doing such a simulation, that ... 0answers 24 views ### Books on Spectral Jacobian Can anyone point me a book to better understand "spectral Jacobian". I am studying X-parameters, I have the book X-Parameters: Characterization, Modeling, and Design of Nonlinear RF and Microwave ... 0answers 29 views ### Initial guess for calculating the Universal Variable Formulation of the two-body Kepler problem I am trying to simulate orbits using the Universal Variable Formulation of Keplers two-body problem, using the algorithm provided by Howard curtis in Orbital Mecanichs for Engineering Students as per ... 0answers 30 views ### Open-source code for computing response functions Summing Feynman diagrams to compute the response functions of a microscopic model is common in many areas of physics. While conceptually straightforward, the task can be computationally intensive. ... 1answer 45 views ### Monte Carlo simulation of Breit-Wigner I am using a Monte Carlo approach to integrate a scattering amplitude which has a propagator-squared term like f(s)=\frac{1}{(s - 4)^2 + 1}, between s=0 and s=20. Using a uniform random ... 2answers 281 views ### In a Monte Carlo NVT simulation How do I determine equilibration I'm running an NVT (constant number of particles, volume and temperature) Monte Carlo simulation (Metropolis algorithm) of particles in two dimensions interacting via Lennard-Jonse potential (U = 4(\... 1answer 247 views ### Tight binding Hamiltonian for 2D finite dimensional lattice and nanowire The Hamiltonian of a 1D lattice having finite N atoms, (if we consider one basis per atom) is given by the following N\times N matrix- Here E is the onsite energy and t is the hopping ... 1answer 107 views ### Numerically solving a simple Schrodinger equation with fast Fourier transforms While trying to solve a stochastic Gross-Piaevskii equation I have found a problem that can be tracked down to something buggy occurring in the simplest Schrodinger equation possible:$$\partial_t \... 0answers 74 views ### Electromagnetic scattering$T\$-matrix in MATLAB

My problem with the inverse of the matrix T (in the photo) , the matrix consists of Bessel and Henkel functions in high order (the orders from 1 to 21), then the elements of this matrix arrived to ...