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Questions tagged [simulation]

Simulation is the imitation of the operation of a real-world process or system over time.

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Methods for generating dense packings of capsules

Are there methods inherent to Mathematica that offer efficient ways of filling a finite cubical box by as many capsules as possible (or given a target number) without any overlaps between them? ...
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1answer
30 views

Manual control plots differ from StateResponse and OutputResponse

So In my quest to try to learn some control theory inspired by the following link, I have been modeling an inverse pendulum regulated with a flywheel. The system model is pretty ok I think, and when ...
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Evaluate value of pi using monte carlo method. This is to be done for Circle inscribed with in Equilateral triangle [duplicate]

I am to able to solve the problem in the Monte Carlo method, where we have to find out the value of PI when a circle is inscribed with a square. But I am trying solve similar problem , when circle is ...
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0answers
40 views

Inhomogeneous Compound Poisson process

I need to use a compound Poisson process with time-varying jump intensity. Mathematica has the function of compound Poisson process as well as inhomogeneous Poisson process, but no combination of ...
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3answers
145 views

Improving the run time of random walk simulation

One of our professors told us that during his thesis he used Mathematica in simulating it since it is about networks, I don't know how he did it but all I know is he said it took about two weeks to ...
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2answers
128 views

How to simulate a random walk to randomly generated particle to another particle fixed at the center of a grid?

I am new in Mathematica, it is my first program. Many codes of diffusion-limited aggregation are available but, they are too difficult to understand. I basically want to create a simulation of the ...
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1answer
384 views

Random walk in one dimension — meeting of two particles

I'm new to Mathematica and still teaching all by myself, hope you bear with me. I have the code: ...
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1answer
37 views

How to plot lines using consecutive points from an array using ParametricPlot3D or so?

I was trying to simulate Gravitational Orbits using Newtonian Gravitation. I did not use NDSolve[] but instead used finite differences; coded myself. The code for ...
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1answer
126 views

How to directly input calculated Geodesic differential equation into *NDSolve*

I am trying to find the trajectory of a test particle around a relativistic object. Initially, I was trying the Kerr metric as spacetime but the final simulations clearly were not correct as I saw the ...
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1answer
66 views

Random normalised variable generation

I want to generate 8 random variables (in reality to form 4 complex numbers) such that the sum of the 8 variables squared is equal to unity. The aim of generating such numbers is to perform a quantum ...
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1answer
62 views

Infinite potential, prevent value to go beyond zero, initial value problem

How do you make a wall potential in Mathematica. Meaning : I want my potential to have a wall at 0 : $ U(x)=\left\{ \begin{split} & x>0 : U(x) = f(x)\\ &x=0: U(x)=U_0 \\ & x<0: U(x)=...
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1answer
121 views

Including periodic boundary conditions when drawing box of particles

This is essentially a follow-up question to this older post. Given a configuration of tubes (or for simplicity cylinders), we draw them in a box using Graphics3D, ...
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1answer
150 views

Tutorials on complex analysis

Where can I find some good tutorials (.nb files) about complex analysis theory & applications using Mathematica, still now I can only find a book by Shaw.
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0answers
52 views

NDSolve can solve two systems of equations separately but not simultaneously

I want to solve a system of coupled equations. After facing problems solving the coupled system, I reduced it to both of the systems uncoupled. Even uncoupled, the equations will not solve ...
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1answer
209 views

Gross-Pitaevskii equation with NDSolve

I want to solve the Gross-Pitaevskii equation with NDSolve, I tried the following code: ...
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2answers
230 views

Schrödinger equation with a potential step

I want to simulate a Gaussian wave packet colliding with a potential step. I tried this (it indicates what do I want to solve, however I know it is naive): ...
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0answers
46 views

How to simulate two coupled birth-death-immigration processes?

I am simulating a birth-death-immigration process for two coupled populations that interact by virtue of the birth-rate in one population being equal to the death-rate in the other population. The two ...
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2answers
66 views

How do I pull a multiple pieces of data from a while loop and put into a table

I am wanting to pull multiple pieces of data from a while loop and put it in a list. The example I have added below is a table with inputted data that I found. Im pretty sure the syntax is unrelated ...
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2answers
76 views

How do I get my simulation to run?

I am simulating a birth-death population process. My code is ...
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1answer
173 views

Using Random walk on a region [duplicate]

I want to simulate a random walk on two dimension equation using module. Checked the input so the path works ...
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2answers
92 views
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3answers
112 views

2D Random walk under specific boundary

I try to create the code so that from initial point (that I can set), code runs so that it performs random walk, yet it turns off once the point hits the wall. I tried this method however, I was not ...
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0answers
42 views

Simulation of aberration in axicon lens system [closed]

Is it possible to simulate axicon in mathematica and analyzed different properties like the aberration?
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1answer
347 views

Best Mac for Mathematica [closed]

I am looking to buy a new Apple laptop or desktop for running Mathematica. What Mac is best, especially if I want to run numerical simulations in Mathematica? (A similar question was asked a few ...
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2answers
321 views

Birth Death Process with Delay

I would like to simulate birth process with time delay. Here is a reference ref on page 3. Note there is two species whereas in my case I have one species. So only equation (1) and (2) should be ...
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59 views

Evaluating a SeedRandom simulation

I have the following code it runs the model one time with 6000 iterations: ...
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1answer
251 views

Schemes for nonlinear advection equation

I am working in the traffic flow problem using the Lighthill-Whitham-Richards model together with the Greenshields equation. The equation of that model is this: $$ \frac{\partial\rho}{\partial t}+v_{...
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3answers
94 views

Number of realizations in NExpectation, Method Monte Carlo

I have been looking in NExpectation about how large the sample size is when Mathematica performs Monte Carlo simulation. For example, if we write ...
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1answer
136 views

Michaelis–Menten kinetics using Tau-Leaping

I am trying to implement Michaelis–Menten kinetics using Tau-Leaping. It works fine as expected. Only issue here is when substrate reaches zero the algorithm stop since PoissonDistribution[0] gives ...
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2answers
569 views

Simulation of diffusion in a grid

I want to simulate a diffusive process in a 2D grid, for a central initial value of 1 to the adjacent cells initially at 0. At each time step, the value of the +1 level adjacent cells are increased ...
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1answer
99 views

Solve simultaneous integral equations [closed]

I am a beginner at mathematica, so I have made huge blunders in my code which gave too many errors so I did not think it would be relevant to post it. I will try and explain my target as well as ...
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3answers
585 views

Creating random configurations of spherocylinders or cylinders

About the setting: We have a 3D simulation box with side $l$ and our catesian coordinate system is set with its origin at the centre of the box. We have a number $N$ of spherocylinders of aspect ...
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0answers
65 views

How to organize code for simulating many ODEs?

I have a large model with many variables (about a hundred) and many differential equations (non-linear). What is the best way to handle a system this size in Mathematica? Note that I am not asking ...
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2answers
831 views

Two bouncing balls in 1 dimension, issues with two different methods?

I'm trying to simulate 2 balls with the same mass and diameter bouncing one on top of another under gravity, see the illustration below (not ideal, but this is the best result I've got so far, the ...
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2answers
272 views

Michaelis–Menten kinetics using Gillespie Algorithm

I am trying to implement Michaelis–Menten kinetics using Gillespie Algorithm. $$\text{Reaction 1:}\quad E+S\rightarrow C$$ $$\text{Reaction 2:}\quad C\rightarrow E+S$$ $$\text{Reaction 1:}\quad C\...
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5answers
865 views

Simple Birth Death Process

I am trying to implement simple birth death process. Why my code does not work? Any suggestion. Thanks. Cross posted http://community.wolfram.com/groups/-/m/t/1205656 ...
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1answer
270 views

Monte Carlo simulation of a financial market

I'm fairly new to Mathematica and i want to review the average prices of this model. In order to do that i need to perform a Monte Carlo simulation on my financial markets model: ...
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1answer
84 views

How can I improve performance of my simulation code?

1) Generate nNsamples from beta distribution (a, b) and the parameter of wighted c ...
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3answers
218 views

How to extract data points from two graphics and find the intersections between them?

I am working on a mathematical problem called "Buffon's Needle". Here is the setup I made: ...
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1answer
127 views

Random placement of non-overlapping disks

I am trying to create a Monte Carlo simulation for a physical situation. The situation is a layer of disks are lying on a plane. The disks have a known mean radius and standard deviation, and a known ...
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1answer
131 views

Place spheres randomly in a box without collisions?

Suppose I have a distribution of sphere radii, $P(r)$. I need to sample configurations of $N$ spheres in a cubic box of side $L$ (assume they fit), where the $N$ spheres have radii following the ...
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1answer
146 views

Basic Gaussian Process simulation/ white noise - massive problem

I have a certain problem with Mathematica or more precisely, myself handling it. It is correlated with a mathematical problem and its realization/simulation in Mathematica. I want to start with the ...
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1answer
109 views

How to use FindFit to do kinetic simulation?

I'd like to simulate the chemical kinetic model by fitting the experimental data. Here are my codes for simulation. ...
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0answers
45 views

Random Number Generation on Parallel Cores [duplicate]

So, I've noticed an odd trend in some of my Mathematica results recently- I'm running large Monte Carlo simulations on a system that involves running several jobs independently, each on a different ...
3
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1answer
166 views

Time varying delay differential equations

I would like to know if it is possible in Mathematica to simulate a differential equation with varying delay for example the logistic equation: $$x'(t)=x(t)(1-x(t-\tau(t)))$$ where for example $\tau(...
2
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1answer
83 views

How to simulate data points from the following distribution?

I have the random variable $X\sim0.5Normal[2,2]+0.5Normal[20,2]$ and I am trying to use Mathematica to simulate, say, 500 points from this distribution. I briefly looked into Monte Carlo Simulation ...
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4answers
123 views

Monte Carlo or how to calculate the model several times

follow question: How can I calculate this model several times automatically. ...
2
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1answer
139 views

RST controller in Mathematica

I was wondering, if it is possible to simulate an RST controller using Mathematica ? This is what I tried, but the computation of the closed loop does not work: ...
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0answers
81 views

Why does the domain of an interpolating function not match the corresponding ParametricNDSolve solution range?

Question I had believed - and mostly observed - that when I use ParametricNDSolve the obtained ParametricFunctions given as the ...