Questions tagged [simulations]

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Metropolis-Hastings and underlying Markov process

I FOUND A MISTAKE IN THE POST, TO BE EDITD OR DELETED SHORLTY I tried to understand the workings of the Metropolis-Hasting algorithm. As far as I can understand, it allows to draw samples from an ...
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Numerical solution of 2D Wave Equation using Fourier Transform and Finite Difference

This is the 2D Wave equation: $$ u_{tt} = u_{xx} + u_{yy} $$ using initial condition: $u(x,y,0)=f(x,y), \:\: u_{t}(x,y,0) = 0$. The inverse Fourier transform used is: $$ u(x,y,t) = \int\int \hat{u}(\...
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Interlink among different length scales of simulation and modelling techniques

I found this figure in the following paper A Review on Multiscale Modelling and Simulation for Polymer Nanocomposites However, I am skeptical about its correctness, as this paper is not peer-...
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ODE solver for Hamiltonian evolution of a finitely-dimensional pure quantum state

I want to simulate evolution of a finitely-dimensional pure quantum state: $$\frac{d\psi}{dt} = - i H(t) \psi$$ The wavefunction $\psi$ is a $n$ dimensional complex vector, and the Hamiltonian $H$ is ...
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Quantum measuring simulation

Hi I want to understand a concept that I been thinking about. I'm trying to simulate the energy measurement of a system (a many body quantum system to be precise), and I'm trying to simulate a quantum ...
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Liquid Oxygen and its paramagnetic properties

How do you calculate the magnetic attraction force on liquid oxygen due to a strong permanent magnet? And if calculating it by hand isn't an ideal solution, which software is the best for handling ...
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Simulating Torsion Springs

First of all, I'm just a measly IT student and have very limited physics knowledge, so sorry, if my mistake is super obvious. So basically I am trying to simulate a robot with a torsion spring in its ...
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31 votes
3 answers
4k views

Why aren't Runge-Kutta methods used for molecular dynamics simulations?

One of the most used schemes for solving ordinary differential equations numerically is the fourth-order Runge-Kutta method. Why isn't it used to integrate the equation of motion of particles in ...
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2 votes
1 answer
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How to Model the Forces within Inflatable Tube Man

I have a CPP setup for a cloth simulation. Currently it takes in forces for wind simulation and gravity and these forces act on individual "point masses". I'm trying to figure out how to ...
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Visualising the time dependent 2d schrodinger equation

So I managed to visualise the 1d schrodinger equation using the following algorithm: First solving the time independent schrodinger equation (1d) for the particle in a box potential, $$\psi_n(x) = \...
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Create a plausible vibration signal from a sliding RMS window

So lets say I have observed many vibration signals and build a sliding window of the RMS of said vibration signals as well as other statistical measurements such as the variance and nth order ...
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Adding gravity to (Elcott07 "Stable, Circulation-Preserving, Simplicial Fluids")

The paper is quite popular, and I thought to implement it as an exercise for DEC. I added an initial vortex force, and indeed it's preserved throughout the simulation due to incompressibility and ...
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Are there any resources for simulating the Kuramoto model/solving the system of coupled ODEs for the oscillators?

I want to simulate the Kuramoto model and I am following a review by Strogatz to read up the theory. Are there resources that explain how to simulate the model and solve the coupled ODEs, or the mean ...
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What formula should I use to calculate the total energy of a linear polymer chain?

I am using the Bead-spring model to model a polymer chain. Suppose, the polymer has 3 monomers in its chain: $$ A_1-A_2-A_3$$ And, I can use the following formula to calculate the total Lennard-Jones ...
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Where should I apply the harmonic spring function in the case of polymer simulation?

I need to simulate the off-lattice movement of a polymer chain in a 3D space using Monte Carlo simulation. Note this is not a simulation of polymer growth; rather this is about polymer movement/motion....
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$n$-link pendulum solution methods

I want to simulate a $n$-link pendulum without using the Lagrangian method. The reason is that the formula for the Lagrangian becomes large and depends on the number of the links $n$. Therefore, I ...
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Polymer simulation

I am absolutely new to Polymer simulation. I am trying to understand the simulation by analyzing source code written by others. Can anyone tell me what are the differences between the following three ...
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1 answer
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Which forces act on a ball in the air (including air friction) including their equation? [closed]

I am trying to write a ballistic throw simulation with the forces which act on the ball I take into consideration being the gravitational force, and drag. I know that the Magnus effect and another ...
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1 answer
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Using finite difference to solve Cahn-Hilliard Equation in 2D using Octave

I am trying to use the finite difference method to solve the Cahn-Hilliard equation in 2D to study phase separation in metallic glasses. The equation is given as follows. $$\frac{\partial c}{\partial ...
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Depressurization formula for multiple holes with varying outside pressures

I'm working on a simulation that should with relative accuracy simulate the flow of air/pressure in a system of rooms (on a space ship). I found http://www.spaceacademy.net.au/flight/emg/spcdp.htm ...
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1 vote
2 answers
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When setting up 2nd order first derivative approximations in a finite differencing scheme, why are these equations equivalent?

In approximating a first derivative term (assuming $\delta z$ is the distance between two spatial grid points) using a finite differencing scheme I came up with these basic equations: $$\phi \frac{\...
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How to take care of singularities or discontinuities in a numerical Time-Dependent Schrodinger Equation simulation using the Split-Operator method?

I am currently trying to numerically simulate a two-dimensional Hydrogen atom using a split-operator method (elaborated below). I have tested that the code produces a good result for an isotropic ...
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11 answers
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Is angular momentum just a convenience?

I'm wondering whether angular momentum is just a convenience that I could hypothetically solve any mechanics problems without ever using the concept of angular momentum. I came up with this question ...
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Do most climate models use the absolute temperature or the temperature anomaly under the hood?

Climate models for the climate impact of anthropogenic global warming almost never report the climate impacts of the average global temperature reaching some absolute threshold. Instead, they almost ...
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How can I model convection in a simple and effective way?

I have a project in which we're trying to model heating of a room. We are modelling the room in 3D. The room has realistic walls, windows and a door, which will loose heat through them. To balance the ...
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Is there a way to estimate the force of this impact?

https://www.youtube.com/watch?v=UKuPuRRNa5Q&ab_channel=BigCatPublicSafetyAct Let's assume that the tiger weighs 500 lbs, is there a way to estimate the force absorbed by its shoulders when it hit ...
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1 answer
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When should smartphone be declared as static using accelerometer reading? [closed]

I wish to know when should I declare an smart phone static by reading its 3 axis accelerometer reading. I have notice that modulo of all 3 axes gives 9.8 when ever smart phone is static. What does it ...
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Reference request: Numerical techniques, Monte-Carlo (MC), Density Matrix Renormalization Group (DMRG), Dynamical Mean-Field Theory (DMFT)

I am an undergraduate student and my previous learning in physics is more on theory instead of numerics. I would be very grateful if you can point me to good introductory lecture notes/lecture videos ...
13 votes
1 answer
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How can one detect a device (phone) falling using its 3-axis accelerometer?

I am working on an Android app to use its 3-axis inbuilt accelerometer to find if the phone falls. I googled and found that if the following value is less than 2: $$a = \sqrt{x^2 + y^2 + z^2}$$ (where ...
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Pointers for dealing with instability in fluid simulation?

I have been working on a 2D fluid simulator, and I have fallen victim to the problem of jumping in before doing enough research. I naively implemented a finite difference form of the continuity and ...
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0 votes
1 answer
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Boundary conditions and normalization of wavefunction in time-dependent Schrodinger equation

I came across this confusion when trying to numerically solve the time-dependent Schrodinger equation. The short version of my question is: when solving for time-dependent wavefunctions $\psi(t,x)$ on ...
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Calculate optimal new vector for a virtual spaceship

I'm working on a 3D game as a demo for some unrelated technology. In it I have a spaceship that I move in the game engine by applying a force along a vector $(x,y,z)$. So I'm happily flying along ...
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-1 votes
1 answer
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Simulation algorithm question

I have been looking at various simulation algorithms, like Barnes-Hut and a few others, and the Laplace operator, the wave equation, etc., and I was wondering why it's necessary to compute the mass/...
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Rate Dispersion is the distribution of rates on a rate spectrum. What are the quantities physically associated in a Rate Spectrum?

I am working on a project to decipher the "origin of rate dispersion" arriving because of Heterogeneity in our system using correlation function analysis in Python. Rate Dispersion, non-...
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1 answer
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How does (air) pressure balance under constraints?

I'm playing around with building a very basic simulation of (air) pressure in a grid environment. The idea is that I have this 2d (or 3d) grid of cells. Each cell has a certain atmosphere. Between the ...
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0 votes
1 answer
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Meaning of 'thermalization' in Markov Chain Monte Carlo simulations

In performing MCMC simulations, it is standard practice to 'equilibriate' or 'thermalize' the system and then discard the initial data before useful sampling is done. My question is about the concept ...
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2 votes
1 answer
78 views

Making Lorentz equation dimensionless for simulations

\begin{equation} \frac{dv}{dt}=\frac{e}{m}(E+\frac{v}{c}\times B) \end{equation} I'm making a numerical simulation and I need to make the equation dimensionless. I'm having trouble in doing so. I was ...
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Difference between the softening parameter in a Plummer model of a star cluster vs. the softening parameter in a softened gravitational potential

I am doing a gravitational N-body simulation of a star cluster. I set up my initial conditions using the Plummer model, which has potential $$\Phi_P = -\frac{G M}{\sqrt{r^2 + a^2}},\tag{1}$$ where $M$ ...
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Mixing position and force based simulation

I have read quite a bit on rigid body physics engines and feel I have a reasonable understanding of how systems evolve with force based simulation. What I am kind of confused on still is how you mix ...
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Bogoliubov-de Gennes equation and how to diagonalize

Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when ...
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1 vote
1 answer
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Poisson-Nearst-Planck equations with normal distribution as initial condition

I am having a hard time trying to think of this model: Imagine you have a normal distribution of +q charges in 2D $$\rho(r,t=0)=\rho_0 e^{-\frac{r^2}{\sigma_0^2}} $$ where $\sigma_0$ is the width of ...
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Absorbing regions in Physics

How would you define an absorbing region (at the walls of a finite numerical simulation) in physics and how would you implement it? Can it be simulated by a high potential, low negative potential at ...
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What is the reason that in DPD (LAMMPS) we can define a protein (or any material with a flexible geometry) without the material loosing its shape?

I am new to LAMMPS/DPD (Dissipative particle dynamics), but as I read through DPD model which is a coarse graining model, there are only three main forces between beads (beads are the spheres ...
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LAMMPS: How to enter a simple potential for Dissipative Particle Dynamics (DPD)?

I apologize if this is off-topic and if so would be grateful for someone to point me to a relevant source of information. Dissipative Particle Dynamics (DPD) is a quick simulation technique that ...
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1 vote
0 answers
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Difference Between a Time-Domain and a Simulation Domain Acoustic Pressure Simulation

I would appreciate it if someone would be able to clarify my doubts. I'm currently working on acoustic simulations in COMSOL and is currently confused on the information provided by the simulations ...
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Transparent Boundary Conditions for Finite Difference ADI PR 2D TDSE solution

I want to put (non-dirichlet) boundary conditions inside the code I wrote to solve the 2dim TDSE using the alternating direction implicit Peaceman - Rachford method. $$ (1 + iB\Delta t/2 ) \psi^{n+1/2}...
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Trinocular optical ray tracing reference

I am new to the optical tracing, was looking for ray tracing refence that shows what kind of lens used in trinocular optical train. Most what is out there is an explnation of microscope theory and ...
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1 vote
1 answer
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Conservation of energy in a numerical simulation of a particle in magnetic field

I'm currently working on my physics project in Mathematica. My goal is to simulate a 3d trajectory of a charged particle, moving in constant magnetic field generated by a loop (with the electric ...
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1 answer
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Conceptualizing time series data of fluctuating sizes of particle aggregates

I am working with simulation data (a time series of positions) of aggregating particles. I want to look at the overall distribution of aggregate size. A colleague calculated the number of aggregates ...
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1 vote
1 answer
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Hamiltonian Monte Carlo: Kinetic and Potential energies

In HMC (good intro here) the Hamiltonian is defined as \begin{align} H(p,\theta) &= -\log p(q,\theta) \\ &= -\log p(q) - \log p(\theta). \end{align} Here $p$ is the momentum coordinate and $\...
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