Questions tagged [monte-carlo]
Questions on Monte Carlo methods, methods that require the repeated generation of (pseudo-, quasi-)random numbers for computing their results.
112
questions
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50 views
Why is perfect sampling not used in large-scale lattice model simulations?
The statistical physics literature is replete with papers describing simulations of lattice models, such as the Ising model. Typically, these are done through Monte Carlo methods, such as the ...
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0answers
35 views
Error in Monte Carlo integration
I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling
For Importance Sampling I have that the error is just ...
2
votes
2answers
126 views
Use Monte Carlo integration to compute the volume and centre of mass in Python
In particular, I want to focus on finding the volume $V$ because I will need it to start working on solving the centre of mass
This $3D$ homogenous body (Torus section) is defined by
$$x^2 + \left(\...
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0answers
33 views
Numerical simulation for a bounded process. Is slight deviation a “normal” fact?
Suppose I have to numerically simulate a process $\{y_t\}$ such that $y_t\geq0$ $\forall t\in\mathbb{N}$, with $t$ denoting time-step.
Let's suppose I use MonteCarlo with $\mathscr{N}$ simulation ...
2
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0answers
37 views
Discretization formula for a system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?
Consider the following stochastic differential equation
\begin{equation}
dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1}
\end{equation}
where $A$, $B$ and $C$ are parameters ...
1
vote
2answers
199 views
Different questions about “Inverse Physics problems”
I am in a context of forecasts in astrophysics. Don't be too rude if questions seem to you stupid or naive but rather indulgent, I am just looking for better undertsand all these numerical methods of ...
1
vote
1answer
58 views
Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?
I have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC).
Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm.
We have at the ...
2
votes
1answer
51 views
Question regarding the energy computation of the Ising-Spin Model
In most of the Monte-Carlo-Algorithms I studied, I found, at the place where they compute the energy, always a line of code, where they divided by four.
For example, this code-snippet is taken from ...
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0answers
30 views
Markov chain Monte Carlo with stopping time
I asked the same question two days ago on MSE, but received no answer. So I post it here in hope to get any suggestion. As long as I have answer, I will close the other one.
Let $(X_t)$ be a ...
2
votes
0answers
54 views
Random Orthogonal Matrix Generation
This post is inspired by N. Higham post "What is Random Orthogonal matrix?".
In this post, N. Higham links to the two papers:
G. W. Stewart, The efficient generation of random orthogonal matrices ...
1
vote
1answer
65 views
Is this behaviour normal for a Lennard-Jones monte carlo simulation?
I am simulating a Lennard-Jones fluid using MC simulation. The code always uses a reduced unit. I want to find the potential energy of the system. Periodic boundary condition implemented. I have ...
0
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1answer
100 views
Why the magnetisation shows abrupt behaviour for this 3D ising spin system
I am trying to simulate a 3D Ising spin system (+1 & -1) using Monte Carlo Metropolis Algorithm. I want to get different physical quantities from this simulation like magnetization, Average Energy,...
4
votes
1answer
194 views
Absence of Discontinuity in Specific Heat Plot Simulated by Ising Model
I am working on 2D Ising model, when I plot "specific heat vs temperature", I can't see any discontinuity at critical temperature around Tc ~ 2.7K. I am enclosing results of all other thermodynamic ...
3
votes
0answers
49 views
Hit-n-Run Monte Carlo on convex polytope
So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...
3
votes
1answer
240 views
Calculation of Mean Square Displacement for Brownian dynamics system with Lennard Jones interactions in python3
I have a problem getting a sensible result for the Mean Square Displacement (MSD) for a simulation of $N$ particles under Brownian dynamics with Lennard-Jones interaction between them with or without ...
3
votes
1answer
150 views
How to optimize sampling for global sensitivity analysis
What is a good way to sample parameters for performing global sensitivity analysis? Some methods are defined using integrals, some are use Monte Carlo. How do these compare?
5
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0answers
81 views
Probability approximation: monte carlo VS sde
I have a probability measure $\mu$ (say, in $\mathbb{R}^{d}$, with density) and I want to approximate it numerically. Today I noticed that my measure is ergotic for a certain Stochastic Differential ...
3
votes
1answer
85 views
Computing autocorrelations of configurations in Monte Carlo simulations
In the context of Monte Carlo simulations, I am trying to learn how I should ensure that the configurations of my system are not correlated for the chosen interval of measurements. I have found out ...
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0answers
40 views
Monte Carlo domain not-so-dense
I already posted it on Physics SE, but maybe this is a better place:
I have a 5D integral being calculated with a Monte Carlo uniform random sampling. The issue is that the region of integration is ...
0
votes
1answer
89 views
Dealing neighbor list in NVT Monte Carlo (MC) simulation
I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction.
I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...
1
vote
1answer
43 views
Change of random variables and check by plot
Question
As a test, I transform a uniform distribution over the unit square.
But when I check the transformed distribution with Monte Carlo, it is wrong.
What went wrong?
Thanks.
Problem
Random ...
0
votes
1answer
75 views
Monte Carlo - Random Walk Simulation - polyfit the log log data points?
This is part of the code in matlab for a random-walk simulation.
To test the code, I'm using steps=[30]; there will be more values, but I want to run it for 1 trial to decrease code processing.
<...
-1
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1answer
82 views
Writing parallel code for molecular computation [duplicate]
I recently moved towards computational biophysics from an experimental science background. As of now, I am learning the fundamentals and doing some basic monte carlo simulations of LJ fluid on my ...
2
votes
2answers
48 views
Generating a random number based on a numerical distribution function
I have a probability distribution function that I don't have its analytical form (so I can't determine its CDF). How can I generate random numbers based on this distribution function? I'm looking for ...
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vote
2answers
1k views
2D Ising Model, heat capacity decreases with lattice size
The problem
I'm trying to make a metropolis simulation of the 2D Ising model.
Basically, it's the following, for each monte-carlo step:
Visit each lattice site,
Compute energy required to flip ...
1
vote
1answer
130 views
Weighted Monte Carlo Integration
I have a function $F(x)$ which drops exponentially (like differential QCD cross section vs. Invariant mass). I want to perform Monte-Carlo integration. The problem is that only small $x$'s which have ...
4
votes
2answers
276 views
Mean-squared displacement in Monte Carlo studies
Is measuring mean-squared-displacement in Monte Carlo simulations uncommon? I'm very interested to find out if this has actually ever been tried.
For instance, in the context of spheres, or ...
1
vote
0answers
58 views
Is there a software package for Quantum Monte Carlo estimation of the exchange correlation functional?
Quantum Monte Carlo (QMC) calculations historically have been used to parameterise the exchange-correlation functionals for Density Functional Theory (DFT). For example, this article explains a way to ...
2
votes
2answers
743 views
Computing the Ising Model for NiO
I am trying to compute the Ising model for NiO. As O carries no magnetic moment, I only need to consider the case of Ni which requires a second nearest neighbour Ising model. As can be seen in the ...
0
votes
1answer
108 views
Sampling simulation steps logarithmically
The common case of for instance a Monte Carlo simulation is, if we want to run our simulation for $N$ steps, we define a delta $\Delta,$ such that $N/\Delta = n$ tells us the frequency with which we ...
3
votes
1answer
126 views
Diffusion properties of hard spheres in Monte Carlo simulation
In standard Monte Carlo simulations, say for hard sphere systems, how should one compute the mean-squared displacement of the spheres in order to extract dynamical properties such as the diffusion ...
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0answers
22 views
Uniform distribution in 3D space [duplicate]
Posted this at math stack exchange as well, but alas no replies! So, I have been trying to find ways of distributing particles of spherical or other shape in 3D space, e.g. rectangular space. Random() ...
2
votes
1answer
10k views
2D Ising Model in Python
I am trying to calculate the energy, magnetization and specific heat of a two dimensional lattice using the metropolis monte carlo algorithm.
...
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0answers
527 views
Using C/C++ for Markov chain Monte Carlo (MCMC) methods
I'm working on optimizing the parameters of a mathematical model to fit experimental data, using an existing formula for the likelihood of observing the data given a set of parameter values. At the ...
4
votes
1answer
162 views
Simple Monte Carlo in C++, result dependent from seed
I implemented as an exercise a program to sample the statistics of the escape time of a Brownian particle in a potential well. I used the Euler-Maruyama method to numerically integrate the ...
0
votes
2answers
70 views
Physical meaning behind the choice of the proposal distribution in Markov Chain Monte Carlo (MCMC) methods
Let us consider the conventions on names used in the theoretical derivation of Metropolis-Hastings Monte Carlo as outlined here, for the sake of common nomenclature.
What we are building is a step-...
0
votes
1answer
60 views
Applying pressure on simulation box
We have a 3D simulation box (cubic, side $L$) filled with $N$ non-overlapping objects (say spheres). We are interested to study the evolution of the system under an applied pressure in the z-direction ...
4
votes
0answers
120 views
How to stochastically estimate the trace of a matrix?
Specifically, the diagonal elements (can possibly both positive and negative) of the matrix can be computed efficiently but the total number is large ($\mathcal O(10^{18})$).
My first thought about ...
0
votes
2answers
192 views
Monte Carlo Simulation algorithm
The algorthim use for updating the voltage of each componant at every time step is
$$v(t+\Delta t)=\begin{cases}
v(t)e^{-\gamma \Delta t},& n=0\\ v(t)e^{-\gamma \Delta t}+h_{*}& n=1\end{cases}...
10
votes
2answers
953 views
Estimate information entropy through Monte Carlo sampling
I am looking for methods that allow estimating the information entropy of a distribution when the only practical ways of sampling from that distribution are Monte Carlo methods.
My problem is not ...
3
votes
1answer
148 views
Why are Hamiltonian dynamics used in MCMC?
In Hamiltonian Monte Carlo, Hamiltonian dynamics are used to generate new proposals from the current state. I understand why these dynamics are used as opposed to random walk behavior to generate ...
2
votes
2answers
395 views
optimization problem. Monte Carlo stochastic method or another one?
I have the following problem, there is an objective function f() depending on 7 variables x=(x1,x2,...x7), so f(x)=f((x1,x2,...x7)) and I want to find the combination of variables that minimize the ...
0
votes
1answer
1k views
Use Monte Carlo method to simulate consecutive decay in MATLAB
I'm trying to use MATLAB to simulate an atom decay process by using Monte Carlo approach. The process is as follow:
Suppose that atom 1 decay to atom 2, which, in turn, decay to stable atoms of type ...
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0answers
76 views
Metropolis algorithm and thermal sine-Gordon model
I try to simulate thermal version of 1D $(x, t)$ sine-Gordon field model. I am interested in finding thermal static solution that minimizes functional of energy $E$:
$$E = \int dx \left( \frac{1}{2} \...
0
votes
2answers
213 views
Fast Python implementation of short-range interacting particles under Metroplis algorithm
Can anyone write a Python implementation of a set of particles interacting in 2D according to a short-range particle-particle force and evolving in time under a Metropolis algorithm, which randomly ...
1
vote
1answer
74 views
RNG float range for metropolis monte carlo
I have a robust RNG that generates random 32-bit (unsigned) ints. As is probably well known, for metropolis MC simulation, a random number between 0 and 1 is needed to determine acceptance/rejection ...
1
vote
1answer
322 views
Efficiently rotate vector in 2D (and 3D)
I need to efficiently rotate a 2D (and 3D) vector in a CUDA kernel. I was thinking about generating random unitary rotation matrices. I don't need to know the angle, it just has to be randomly ...
10
votes
3answers
2k views
Parallel Mersenne Twister for Monte Carlo
Recently, I came across a comment claiming that almost all researchers doing Monte Carlo methods are doing it wrong. It went on to elaborate that merely choosing different seeds for different ...
2
votes
1answer
70 views
Use of Metropolis-Hasting algorithm for gathering statistics
I understand how MH work, I'm able to use it to simulate e.g. 2D Ising model. What I don't understand is what you actually take average of.
When I run the simulation, it reaches equlibrium after some ...
4
votes
1answer
141 views
Efficient Quadrature Methods for Indicator Functions?
I am looking to numerically solve many different integrals where the integrand is simply the indicator function for a region (i.e. 1 on the region, 0 outside. This is for measuring areas). The ...
