Questions tagged [simulation]

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

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1answer
87 views

Simulating a poker win rate over time

Poker players start with a fixed bankroll (bankroll) and play with a win-rate winRate (say measured in dollars per hour) and ...
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29 views

Simulating a function with no closed form solution

So I am trying to simulate a function in 3d. Suppose our function looks like this: f=k*r*a I am interested in simulating the numerical values of k when r is ...
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0answers
34 views

Is it possible to speed up SDE simulation?

Is it possible to speed up SDE simulation in Mathematica? I am simulating a large number of Heston processes that look like the following (note this code is only a slight modification of the ...
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41 views

Simulating a bicycle going around a circle

I want to simulate a bicycle moving around a circle. Instead of graphs and calculations, I want to almost see an actual simulation of this happening. How could I do this? I tried looking up ...
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1answer
146 views

Monte Carlo Simulation of a Double Well Potential (Edited)

I am looking for a possible way to simulate the temperature effect on a collection of atoms sitting within a double well potential, say something like ...
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1answer
121 views

Numerical simulation for density of strings in a ball

I am trying to numerically reproduce the Mathematica result for the density of strings in a sphere as explained here. The program is to generate random, uniformly distributed pair points on a unit ...
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70 views

Noise covariance matrix

I am trying to find the noise covariance matrix of a random vector $\mathbf{x}$ with itself. The elements of this vector represent image pixels and are treated as random variables i.e, $\mathbf{x}=\{...
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2answers
1k views

Animating wave motion in water

Further to this question I found on MSE, I tried to replicate from here this is as far as I got: ...
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26 views

Simulates Timeseries with Table

i need your help again. I would like to calculate EW[k_] with EW[1],EW[2] and EW[3]. My code works only for one calculation from EW (in the code below it is EW[1]) but i would like to calculate the ...
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1answer
179 views

Trying to compute the heat capacity for the 2D-Ising model

I'm trying compute the heat capacity $C_v$ out of my simulation for the 2D-Ising model which is given by $C_v = \frac{\langle E^2 \rangle - \langle E \rangle^2}{T^2N^2}$ ($E$: Energy, $T$: ...
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2answers
128 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 <...
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265 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 ...
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1answer
49 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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61 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
169 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
251 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
406 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
61 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
294 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
138 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. ...
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1answer
71 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
37 views

How to (efficiently) generate and catch some data-set that has similar correlation?

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1answer
70 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
183 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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0answers
75 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
398 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
431 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
63 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
79 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
81 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
400 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
94 views
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3answers
338 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
47 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
606 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
364 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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65 views

Evaluating a SeedRandom simulation

I have the following code it runs the model one time with 6000 iterations: ...
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1answer
463 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
112 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
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1answer
170 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
741 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
152 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
702 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
74 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
892 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
365 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
935 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
315 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
91 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
234 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: ...