Questions tagged [simulation]
Simulation is the imitation of the operation of a real-world process or system over time.
3
votes
2answers
114 views
Initial values of position (x) and speed (v) of a particle visualizing using Mathematica
$$\vec{F}(\vec{r})=-m\omega^2\begin{pmatrix}x\\4y\end{pmatrix}$$
I have the force $F$ shown above. How could I specify the initial values of position ($x$) and speed ($v$) in Mathematica using the <...
0
votes
1answer
225 views
Solving Differential Equation System for HIV Treatment Model
I was working on a project about optimal strategies for HIV treatment, models used from [Butler, Kirschner, and Lenhart] 1997. This model explains the spread of HIV viruses in the human body, where ...
0
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0answers
33 views
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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1
vote
1answer
34 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 ...
0
votes
0answers
36 views
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 ...
3
votes
0answers
44 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 ...
5
votes
3answers
150 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 ...
6
votes
2answers
138 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 ...
5
votes
1answer
386 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:
...
1
vote
1answer
39 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 ...
3
votes
1answer
145 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 ...
7
votes
1answer
120 views
Efficiency in calculation on graphs: Compile?
Basic Question
I have a looping calculation that I need to perform on some large lists a very large number of times, and as I have written the functions the computational speed is prohibitively slow. ...
5
votes
1answer
67 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 ...
0
votes
1answer
34 views
1
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1answer
64 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)=...
3
votes
1answer
132 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, ...
2
votes
0answers
59 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 ...
0
votes
1answer
234 views
Gross-Pitaevskii equation with NDSolve
I want to solve the Gross-Pitaevskii equation with NDSolve,
I tried the following code:
...
1
vote
2answers
252 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):
...
1
vote
0answers
47 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 ...
1
vote
2answers
69 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 ...
0
votes
2answers
77 views
0
votes
1answer
188 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
...
1
vote
2answers
92 views
3
votes
3answers
124 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 ...
1
vote
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?
0
votes
1answer
398 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 ...
5
votes
2answers
328 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 ...
0
votes
0answers
59 views
Evaluating a SeedRandom simulation
I have the following code it runs the model one time with 6000 iterations:
...
3
votes
1answer
300 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_{...
1
vote
3answers
102 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
...
5
votes
1answer
145 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 ...
19
votes
2answers
594 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 ...
0
votes
1answer
111 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 ...
9
votes
3answers
608 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 ...
0
votes
0answers
69 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 ...
11
votes
2answers
840 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 ...
0
votes
2answers
288 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\...
9
votes
5answers
886 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
...
2
votes
1answer
274 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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0
votes
1answer
88 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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8
votes
3answers
223 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:
...
0
votes
1answer
136 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 ...
3
votes
1answer
147 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 ...
4
votes
1answer
156 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 ...
2
votes
1answer
118 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.
...
5
votes
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
votes
1answer
176 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
votes
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 ...
3
votes
4answers
123 views
Monte Carlo or how to calculate the model several times
follow question:
How can I calculate this model several times automatically.
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