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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How does force relate to velocity?

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
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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?
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Is it possible to propagate a relativistic system of particles in time using Verlet?

The Verlet algorithm and its derivations are very popular methods to integrate Newton's equations of motion in time and obtain a trajectory for a system with $N$ particles. I work with classical ...
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973 views

Implementing simple atom model using density functional theory (DFT)

I am trying to write computer code which will find the energy and density function for an atom with $Z$ protons and $N$ electrons. I am working in 1D for simplicity and would like to make the overall ...
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407 views

Supergravity calculation using computer algebra system in early days

I was having a look at the original paper on supergravity by Ferrara, Freedman and van Nieuwenhuizen available here. The abstract has an interesting line saying that Added note: This term has now ...
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166 views

Least action principle — numerical simulation strangeness

I'm trying to get some experience with the least action principle, and for this I chose a simple 1-dimensional problem of a particle moving in some field. The least action principle would then look ...
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311 views

What equation describes the electrostatic potential in these circumstances?

I have a solver for Poisson's equation and it works nicely. It uses finite differences. It works in the presence of multiple dielectrics. It also solves the Poisson Boltzmann equation. That is, fixed ...
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579 views

Numeric method to calculate the charge distribution on a conducting surface?

If I have an arbitrary (closed?) conducting surface and a nearby charge density, is there a simple numeric way of computing the induced charge distribution on the surface?
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276 views

Simulate a physical impact of objects made of finite, small elements

I want to simulate an impact between two bodies according to gravity, and eventually considering other forces to stick matter together. I'd like to use python to do this, but I am open to alternatives....
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Statistical specific heat as energy fluctuation in spin glasses

Consider the specific heat (in statistical sense, as energy fluctuation in the canonical ensemble) of a complex model, something similar to a spin glass. Is the specific heat defined on fluctuations ...
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163 views

How close to the critical point is sufficient close for measuring critical exponents?

I am learning Monte Carlo and just manage to simulate a phase transition by computing the heat capacity or the susceptibility. I wish I can also compute critical exponents.To this purpose, I have read ...
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113 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
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192 views

Numerical Solution of the Propagation-Dispersion equation

I have asked this question on Computational Science and also on Mathoverflow, but no satisfactory answers so far. I thought maybe the physics community could shed some insight on the issue. I am ...
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321 views

Exact diagonalization to resolve ground state degeneracies

I am studying a perturbed Toric Code model that is not analytically solvable. On a torus the ground state degeneracy of the unperturbed model is 4. Once we turn on the perturbation there is a change ...
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710 views

Interpretation of Stiffness Matrix and Mass Matrix in Finite Element Method

I would like to have a general interpretation of the coefficients of the stiffness matrix that appears in FEM. For instance if we are solving a linear elasticity problem and we modelize the relation ...
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376 views

Ray tracing in General Relativity

I would like to find out what one would see at the Schwarzschild radius of a massive non-rotating black hole, if the black hole is surrounded by a bright ring. For that, I would place the observer at ...
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376 views

Future Computer Performance

Moore's law has succesfully predicted up to now that integrated circuit transister density doubles every two years. However, computer performance is dependent on additional factors like architecture, ...
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336 views

What states are satisfying an entropic area law and why do they satisfy it? More specificly why do matrix product states satisfy it?

I am currently reading some papers concerning the question why the density matrix renormalization group (DMRG) method is working well for simulating one dimensional systems and bad for higher ...
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Nanorobots. What stops us from producing them yet?

If we can already predicts accuratelly motion on molecular levels, what stops us from developing small robots to, for instance, navigate through our blood vessels looking for cancerous cells and ...
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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, ...
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426 views

Good source for numerical simulations of Wigner function?

I'm interested in simulating the time evolution of a Wigner function for a harmonic oscillator (and possibly some other potentials) and I can't seem to find a good resource for that. My background in ...
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906 views

Industry application of computational quantum mechanics?

I was wondering if anybody knew of an industry application of computational quantum mechanics. For example, the efficient placement of circuit elements on a PCB is in part motivated by classical FDTD ...
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buiding circuits from color superconductors

caveat: the sort of exotic matter engineering in here is currently beyond the reach of our technology, but, that having been said: Has their been any research on building models of these sorts of ...
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Radial Schrodinger equation with inverse power law potential

Recently I read a paper about solving radial Schrodinger equation with inverse power law potential. Consider the radial Schrodinger equation(simply set $\mu=\hbar=1$): $$\left(-\frac{1}{2}\Delta+V(\...
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Using the monte carlo method to compute the magnetic field of a curent carrying loop

I have written a program in cpp that computes the magnetic field at a point from a current carrying loop. It uses the biot savart law and the monte carlo technique to carry out the integral. The ...
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Can I use imaginary time propagation for many-body problems?

There are various ways to numerically find the ground state energy and wavefunction of a many-body Hamiltonian. You can diagonalize the Hamiltonian and pick out the lowest eigenstate, or you use ...
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On numerically solving the Schrödinger equation

I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck (1979). Link: http://iopscience.iop.org/0305-4470/10/6/001 I have some questions about section 2. Why ...
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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 ...
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Numerical solution to Schrödinger equation - eigenvalues

This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the Woods-Saxon Potential and find the energy eigenvalues and eigenfunctions but I am confused about how ...
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625 views

Integral of Sedov's self-similar solution to the spherical blast wave problem

I'm studying the Taylor-Sedov self-similar solution to the problem of a strong explosion in a homogenoeus atmosphere. The problem is discussed in Landau & Lifschitz VI (in the 2nd edition it's §...
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77 views

Finding explicit unimodular transformations for Chern-Simons K-matrices

An invertible, symmetric matrix with integer entries, $K$, that encodes the braiding and statistics of an Abelian topologically ordered state, is equivalent to another such matrix, $K'$, if there ...
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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 ...
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Philae lander simulation off by factor of ~3

I'm trying to simulate the Philae landing by writing a program to compute the position of the lander vs time. According to various mission websites, the orbiter will match its orbit to the rotation of ...
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156 views

How to find positions of $n$ masses in Newton mechanics?

I ran into a problem while doing research. The problem can be described as: consider the original $n$-body problem, and if we fix the position of them(unknowns), no interaction among them, they don't ...
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Finding $\pm 2 \pi$ defects in 2-D lattice nematic simulation

I'm working on a Monte Carlo simulation of a two-dimensional nematic system (XY-like model with even-order Legendre polynomial interactions, such that the director angle $\theta$ obeys $\theta \equiv \...
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514 views

How to solve the heat equation for compound materials with different heat conductivities numerically?

I'm solving the heat equation with time dependent boundary conditions numerically in a 2D system using the ADI scheme. For the purpose of this question, let's assume a constant heat conductivity and ...
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How to calculate dispersion relation from a Finite Difference (FD) wave simulation

I have a python code that calculates the solution of the inhomogeneous acoustic wave equation for a 2D medium with any velocity and source configuration. It was implemented using Finite Differences ...
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107 views

Nature as a calculator [closed]

I wondered whether physical experiments can find the outcome of otherwise intractable mathematical problems. For example, solitons or other non-perturbative effects in QFT cannot be seen at any ...
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352 views

Comparison between Cadabra and other Symbolic Computer Algebra software [closed]

Does anyone has some experience about working with Cadabra and it's (dis)advantage in comparison to other Symbolic Computer Algebra software such as Maple and Mathematica (physics package) in the ...
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Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} -\frac{\hbar^{2}}...
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Can computers accurately model all of the details (to the subatomic level) of macro objects in collisions?

Frequently when trying to solve cosmology questions physicists turn to computer simulations of the universe (albeit massively simplified) in order to verify or disprove their hypotheses. This got me ...
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System that is more efficient to simulate than to compute

I know some physics calculations require alot of computing to solve. Are there currently systems where it is more logical to do an experiment to "let the universe simulate the experiment for us" and ...
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Can a wavefunction be solved to any arbitrary precision, given enough computer time?

I learned that the wavefunction for the hydrogen atom can be solved analytically (we did the derivation in class), but that for more complicated atoms it is "impossible" to solve and that only ...
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Rotation matrix of Euler's equations of rotation relative to inertial reference frame

I was playing with simulation of Euler's equations of rotation in MATLAB, $$ I_1\dot{\omega}_1 + (I_3 - I_2)\omega_2\omega_3 = M_1, $$ $$ I_2\dot{\omega}_2 + (I_1 - I_3)\omega_3\omega_1 = M_2, $$ $$...
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What's the difference between “numerical methods” & “mathematical analysis” as said by Feynman in his lectures?

While reading his lectures, I came to these lines: On the basis of Newton's second law of motion,which gives the relation between the acceleration of any body & the force acting on it,any ...
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Square root of a matrix appears in massive gravity. How to solve $\sqrt{A+B}$ perturbatively

$A=\text{diag}\{\lambda_1,...,\lambda_n\}$, where $\lambda_i$ can be any number and not necessarily a small number, $\lambda_i>0$, $B$ is a positive definite symmetric matrix, and $\text{max}\{B_{...