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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250 views

How do you measure numerically the central charge of a system?

Let's say that you are doing some Monte-Carlo simulations of a statistical system on a lattice and you observe scale invariance, meaning that you are at a conformal point. Can you get a numerical ...
2
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1answer
411 views

Unexpected eccentricity in moon orbit simulation

I've used Mathematica's NDSolve function to calculate the orbit of the Moon around the Earth. I used the following initial positions (perigee): $\vec{r}_{Earth}=\begin{pmatrix}-\frac{m_{Moon}}{m_{...
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0answers
113 views

Doing numerics in physics [closed]

Soon, I am going to write my master thesis in theoretical physics. I assume there, and later on in my career, I will have to do more serious numerics than I did up to this point. That's why I want to ...
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0answers
63 views

Euler equation with single state variables [duplicate]

I want to simulate a flow using the Euler equations. For this reason I'm wondering if there's a modified version of the Euler equations. At the moment my formula looks like this: $$ \frac{\partial}{\...
2
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0answers
450 views

What is the drag coefficient of an open wedge?

To check my two dimensional CFD calculation I am looking for reference data on the drag coefficient of an open wedge. The geometry is shown below, together with the flow direction. I have found ...
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0answers
565 views

simple MHD simulation code for (self) education and play with [closed]

I would like some super simple computational code for solving magnetohydrodynamics problems. High accuracy nor performance is not my concern. I wan't it just to visually explore qualitative behavior ...
2
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0answers
66 views

Trotter splitting and entanglement entropy

I have heard that a numerical solution to the Schrodinger equation using the Trotter splitting formula for a many-body Hamiltonian can cause an artificial increase in the entanglement entropy. I was ...
2
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2answers
316 views

Strange Behavior in Spring Computer Model

To learn more about oscillatory motion which I am learning about in my high school physics class, I have created a computer model of a damped spring where the damping force is proportional to velocity....
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0answers
397 views

fun computational physics projects [closed]

I want to learn how to code in Java and am in need of some cool computational physics projects that would provide motivation to do so. I was wondering if you guys could list some medium-level ...
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3answers
147 views

Why does the Metropolis algorithm allow changes even for ∆E > 0?

In the Metropolis Monte Carlo algorithm, why can you accept changes even for ∆E > 0 (provided that a random number is less than a given probability ratio, e.g. exp(-β∆E))?
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2answers
208 views

What is a good model for computing water dropping on a surface?

Before introducing my question I would like to outline the fact that I'm a coder, so I can be wrong when using some kind of terminology. What is a good model for computing the flow, the shape and all ...
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4answers
1k views

Non-computable numbers in Physics

It is known that there are real numbers that can't be calculated (non-computable numbers). Quite probably that some physical phenomena (it is possible still undetected) depend on this numbers. Whether ...
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3answers
151 views

Langevin Equation - Stochastic Differential Equation. What are the subtleties?

I am trying to find out the motion of a particle in 3D governed by the Langevin equation, numerically. Anyway, the Langevin equation is given by $$m \ddot{x} = -(6\pi a\nu) \dot{x} + F_b $$ where $...
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1answer
114 views

Difference between Enzo & Gadget astronomy simulation codes

Enzo and Gadget are simulation codes used in astronomy. What are the largest differences between them both in terms of physics they simulate and in their implementations?
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1answer
517 views

I'm getting weird autocorrelations when simulating an Ising model below the critical temperature

So I'm simulating an Ising model using Monte Carlo and the Metropolis algorithm. After letting it reach equilibrium, I try to calculate the autocorrelation of the magnetization. As long as the system ...
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2answers
2k views

How do I integrate the Poisson equation to determine the electric potential along a particular direction (e.g., $z$)?

This question is a sequel of sorts to my earlier (resolved) question about a recent paper. In the paper, the authors performed molecular dynamics (MD) simulations of parallel-plate supercapacitors, ...
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2answers
72 views

Which timestep should I use for a $N$-body simulation of the Solar system?

I am trying to implement a $N$-body simulation of the Solar system and I am stuck on the issue of the simulation timestep size. At first I would like to use a simple Euler stepping scheme. Knowing ...
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2answers
190 views

Do electrons actually reside in orbitals?

(Following this answer on Chemistry.SE) Let's define "dwell"/"reside" as the area in which the probability to find an electron is more than 90%, for example. Calculated orbitals comprise a basis set,...
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1answer
128 views

SDSS spectra FITS format: what do the rows mean?

This might be in the FITS Header, but I couldn't find it. I am looking at the FITS files for SDSS 1D spectro images from DR7 using the SDSS Data Archive Server at das.sdss.org (there might be an ...
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2answers
145 views

Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations

How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, ...
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2answers
831 views

Acceptance probability 2D Ising Model

Disclaimer: I just found a possible solution - eventhough i don't really understand, whats wrong with my prior approach. Edit: I just tried to calculate it from scratch and found the following: $E ...
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2answers
394 views

How can one determine at which distance the Lennard-Jones potential reaches a given value?

My question is fairly simple, but I do need clarification on how to get the inverse of the Lennard-Jones potential V(x). I am working with the following expression: $$ V(x) = e\times[(R/x)^{12} -2\...
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3answers
1k views

Calculate kinematics of body movement from the set of spatial coordinates

Short intro I have a set of 3D (x,y,z) spatial coordinates of arm movement obtained using motion capture system. The example set of such coordinates looks like this (rounded up): ...
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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^\...
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1answer
87 views

Gravitational field of thin 2D ring - numerical simulation

I'm aware of Newton's Shell Theorem, which states that inside of a thin ring of uniform density, the gravitational force exerted on a point mass should be zero. I wrote a quick field simulation to ...
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1answer
196 views

Connection between bond-dimension of a matrix product state and entanglement

The bond dimension is the dimension of the truncated matrix product state (MPS). Let us assume that I am simulating some many-body system with high entanglement via the density matrix renormalization ...
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1answer
368 views

Finding the initial velocity vector of an orbiting body

I'm writing a program that simulates Newton's law of universal gravitation by simply calculating the force and applying it on the objects. The simulation works very well, but now I want to simulate ...
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1answer
138 views

Hartree Fock equations

I don't understand how the Hartree Fock equations define an iterative method! For this discussion, I am referring to the HF equations as described here: click me! Basically if you guess a bunch of ...
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1answer
314 views

Numerical solution for Friedmann equations

My problem today is to solve the Friedmann equations, for those who aren't familiar with them, here they are (in my specific case): $$ \left ( \frac{\dot{a}}{a^2} \right )^2 = \frac{\rho_1}{a^4} - \...
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1answer
527 views

Turning a finite difference equation into code (2d Schrodinger equation)

I am trying to convert the following finite difference equations into code (taken from the bottom of page 12 of this thesis by Maike Schulte Numerical Solution of the Schrodinger Equation on Unbounded ...
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1answer
200 views

Is there a normalized form of the Euler equation discretized with finite volumes?

I want to calculate a flux on my fpga using the Euler equations with the finite volume method. Unfortunately the values of the state variables differ a lot. For example the pressure has a value of ...
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1answer
147 views

Computational Fluid Dynamics methods

I have read some articles about the finite difference method on a cartesian orthogonal grid. I understand how it works when Dirichlet boundary conditions are used, or when Neumann boundary conditions ...
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1answer
80 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 ...
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2answers
72 views

Can lens designs be brute-force computed to create optically precise equipment? [closed]

It seems lens design hasn't changed much over the last 50 years or so with many older manual lenses still very much being used today. Can the order, distance between and type of lens elements be brute ...
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1answer
37 views

Does *advection* describe the change of density of massless infinitesimal tiny *thingies* injected into a fluid?

I'm considering an incompressible Newtonian fluid with uniform density and try to figure out what's meant by the term advection. Let $\Omega_0\subseteq\mathbb R^d$ be an (infinitesimal small) bounded ...
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1answer
77 views

Numerical relativity in causally pathological spacetimes

To perform numerical relativity simulations one almost universally adopts the so called "3+1" approach: spacetime is divided up into spacelike slices, each representing a "moment in time". After some ...
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1answer
51 views

Reading ensdf files

I understand that this is more of a computing question, but I still think the appropriate place to ask it is here. The Evaluated Nuclear Structure Data Files are on the internet, available for ...
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2answers
78 views

Guidelines for $n$-body problem inital conditions

I'm trying to solve a 5-body problem (for the sake of the argument it can be any given $n$) numerically, yet every initial condition I choose seems to eventually drive the bodies apart to infinity or ...
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2answers
329 views

Incompressible Navier-Stokes pressure solve in simulations

I am a complete newcomer when it comes to fluid simulations. I'm currently working through some tutorials to understand the idea of of the discretized Navier-Stokes equations for numerical simulations....
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2answers
88 views

Difference in calculated and simulated ellipsies

My task here is to determine orbit parameters, using current values: $\mu=GM$ - standard gravitational parameter $r$ - distance to the object with Mass $M$ $v$ - speed of the object in the point $r$ ...
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1answer
84 views

Getting nonphysical results when solving for the index of refraction of a slab?

I'm trying to computationally find the refractive indices (real and imaginary) for a thin slab suspended in air (so the only indices to deal with are air and my material's). I've experimentally taken ...
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1answer
222 views

Smoothed Particle Hydrodynamics, Chemical Reactions and Stiffness [closed]

Dear people from stackexchange physics. I have been using SPH for quite a while to simulate free boundary flow, and just recently we tried to include some kind of (simple) chemical reaction in our ...
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2answers
149 views

Discrete approximation of charge density

Given the electric potential $\Phi(r)$ and the Poisson's equation: $$ \nabla^2 \Phi(r) = - 4\pi \rho(r)$$ Consider the 2-dimensional case and let's say that I want to discretize this using a square ...
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1answer
161 views

Deriving the change in the Helmholtz free energy in the context of the free energy perturbation method

I am reading Free Energy Calculations: Theory and Applications in Chemistry and Biology by Chipot and Pohorille. At the beginning of the text (page 19, for example), the authors define the Helmholtz ...
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1answer
138 views

reversible cellular automata

Let's suppose a cellular automaton has a value $b(r,t)$ belongs to $Q$ at site $r$ and time $t$, where $Q$ is the set of possible states at each site. Let $N(r, t)$ be the values of the states of all ...
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2answers
446 views

How to decide convergence of the ensemble average in a Monte Carlo process

I am simulating electromagnetic scattering off a rough surface. The usual process is to do a Monte Carlo simulation, which is briefly described as follows. Generate a randomly rough surface, and ...