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

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6
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90 views

3D orbits of moons around their respective planets

I have seen a lot of solar system models (both animated and not), but I am trying to replicate the same thing with moons. Either just one planet and its lunar system or the our whole solar system with ...
10
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1answer
296 views

Partial Differential Equation in Parallel

is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ...
8
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0answers
123 views

How best to simulate n-body systems in a functional way

I want to simulate a N-body system in the most functional way possible. The system I'm modeling are metallic colloidal particles in a solution of peroxide water, as here ...
1
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1answer
39 views

Generate a simulated covariance matrix

I am working on a problem where one of the input variables is the level of covariance between the entries in a particular matrix. To simulate this problem in Mathematica, I will need to feed my code ...
4
votes
2answers
118 views

Confining/Periodic boundary conditions implementation for 2D Random Walker

I am new to Mathematica, and am having trouble implementing confining boundary conditions for a random walk simulation confining the walker to a pre-defined region (periodic boundary conditions would ...
0
votes
1answer
123 views

WSMModelData Error

I am getting this error message when I run simulation in Mathematica that makes iterations to a SystemModeler model. ...
6
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1answer
320 views

Battery charge simulation not clipping properly as it iterates

My code for simulating a batterylevel-state throughout a year in 15min-steps doesn't work. There is a certain list-inputs which simulates the charge state and the batterylevel-state, additionally ...
3
votes
2answers
120 views

Roulette simulator for a particular series of events

I'm new to Mathematica, and I would like to simulate the game of roulette. I want to bet like $1 on the opposite color every time four reds or four blacks come up. I would like to know if I will gain ...
8
votes
2answers
182 views

Evolution of a trait in an asexual population (performance tuning)

I just coded a simple simulation module that looks at the evolution of a continuous trait in a haploid asexually reproducing population under density dependent competition in discrete time (i.e. ...
4
votes
1answer
766 views

Circular membrane vibration simulation

I'm new in Mathematica and I'm trying to simulate the vibration of a circular membrane for math project but I don't even know how to start. The wave equation describes the displacement of the ...
5
votes
2answers
715 views

Simple Monte Carlo simulation

I want to find the Monte Carlo simulation of the integral $$\int_0^1 \sqrt{1-x^2}\mathrm dx$$ The Cesàro mean is $$I_n=\frac1n\sum_{k=1}^{n} f(U_k) $$ I want to plot the scatter plot ...
4
votes
1answer
115 views

Impact Crater Sim. with added criteria

I have been trying with out success to edit this impact crater simulation script into producing a variable which calculates crater density. In addition I have been trying to figure out how to ...
37
votes
1answer
488 views

Random polyhedra walk

I would like to recreate ssch's random polyhedra random walk, which he posted in the chat. For convenience here it is again: This is my best attempt so far: You can download the notebook with ...
7
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1answer
746 views
1
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0answers
55 views

Multivariate Path Construction using Sobol numbers

I am sharing my code,which I have tried to perform as per the instruction mentioned below. Please correct it so that I could get my output. Instruction: Use the first m dimensions of the Sobol vector ...
8
votes
7answers
970 views

How to model rolling a pair of dice 100 times (Monte Carlo)

Like the title says, I'm having trouble trying to write out a function that will find the probability of finding the sum of a pair of dice 100 times to find the probability of each sum of 2,3,4,5...up ...
10
votes
2answers
415 views

Impact Crater Simulation

I have been trying to model crater formation on a given planetary surface - $500\,\textrm{km}^2$. The locations of impacts are random, however, if an impact is within $30\,\textrm{km}$ of another, the ...
1
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1answer
112 views

How to simulate Multifractional Brownian Motion?

The maximum I would ask, is hints, how to model MFBMotion. Link to paper Firstly, i wanted to simulate in MATLAB that code: ...
33
votes
7answers
1k views

Nice formatting for the results of a dice game simulation

One of my Mathematica interests is in problems related to the formatting of output. Getting nice formatting from Mathematica is often frustrating, but occasionally Mathematica will delight me by ...
1
vote
2answers
189 views

Simulation Beta Distribution

Suppose a function such as: $\phi^{\alpha} (x,y) = \left\{ \begin{array}{l l} \alpha x & \quad \text{if $x < y$}\\ x & \quad \text{if $x = y$}\\ \alpha x + (1 -\alpha) & ...
6
votes
1answer
240 views

Simulation Sample Paths for Stochastic Approximation Algorithm

Let $X_t$ be IID random variables in $[0,1]$ and CDF $F(\cdot)$. Suppose there exists a variable $Y_t$ given by: $Y_1 = X_1$ and $Y_t = \phi(X_t, \overline{Y}_{t-1}), \forall t >1$, where ...
2
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0answers
129 views

Creating an orrery

I am interested in creating an orrery, ideally with SystemModeler. I have been experimenting with the MultiBody library since that allows you to do animations. The most relevant example seems to be ...
8
votes
3answers
305 views

When does a list contain only ones?

I am starting with a list of length n that contains all -1's. For instance, when n = 6 the list is {-1, -1, -1, -1, -1, -1}. I ...
2
votes
2answers
109 views

How to create a bar graph that evolves in time to monitor a simulation

I imagine a random process that proceeds as follows: Suppose there are $n$ dice. ($n$ is pretty big). They exist in an arena. They are all bouncing around. They start in a random configuration. If ...
8
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1answer
450 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
4
votes
1answer
95 views

Adding extinction factor to Monte Carlo analysis

I'm looking to add an absorption component to this Monte Carlo analysis, essentially I want there to be a 1% chance that a photon gets absorbed at each event as it travels through the medium, once the ...
4
votes
2answers
663 views

How to set up a simple Monte Carlo Simulation

there is a 1% chance that there will be a scattering event, if there is a scattering event the direction of scattering will be determined by a random sample of the custom[a_] function and if there is ...
12
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4answers
1k views

3D Random Walk with Periodic Boundary Conditions

I am working on a 3D random walk with periodic boundary conditions and have written a program that will do this for me, but it is extremely slow. Does anyone have any suggestions on how I could speed ...
4
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1answer
72 views

RandomVariate does not evaluate a Hyperbolic Distribution

Any Idea why I can't get a result from this expression: ...
20
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2answers
5k views

Creating a simulation of our Solar System

As the title says, my objective is to create a simulation of the motion of the planets in our Solar System using Mathematica. All the theoretical background regarding the equations of motion of ...
1
vote
2answers
153 views

Simulation of LogNormal process for an asset pricing

I'm new to Mathematica programming, so forgive my rather unsophisticated question. I need to simulate 5000 "walks" of a process value (of a stock) that starts from its current value, at ...
2
votes
2answers
236 views

Solving coupled first-order autonomous differential equations

I am trying to run a simulation of a circuit to observe chaotic behavior, and have obtained a set of differential equations from an analysis of the circuit. I thought perhaps I could produce a plot ...
18
votes
4answers
2k views

Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 \leq 1$ in the first octant: ...
1
vote
1answer
348 views

Marking the points of x-intercept on a plot

OK, I have a nice plot of some oscillating motion. I can read some stuff off the graph, but I thought it would be cool to show a dot where the curve hits the x-axis and a little label showing the ...
20
votes
2answers
2k views

Animation of double pendulum

Sadly, I am a completely newbie. I am studying Physics and in our theoretical physics class we got the task to solve the double pendulum using Mathematica. We just got the program, but no introduction ...
4
votes
2answers
262 views

Evaluation problems with NDSolve using the fixed step ExplicitEuler-Method

Motivation I am using Mathematica to implement System Dynamics (SD) models, e.g. differential equation models as applied to management/economic problems following the "methodology" of Jay W. ...
3
votes
1answer
94 views

How to deal with Part in a function?

I need to iterate several functions such as {3 x[[1]]^2 + x[[2]], x[[2]], x[[3]]}, {Exp[x[[4]]], x[[2]], x[[3]], x[[4]]},etc. ...
5
votes
3answers
263 views

Split list of states by run lengths and discontinuous changes in state

I was asked to look into writing some simulation code for a user, where the simulation output (x) would oscillate between three possible states: ...
0
votes
1answer
90 views

My simulation is not never finishing and it is taking so much time?

I am running simple code which involves calculation of two first order differential equations.It is taking so much time and i am unable to get the results as the simulation is never finishing. ...
2
votes
2answers
128 views

How to speed up a system simulation?

I need to simulate a series of nonlinear (and linear) with thousands of state variables. Here is a simple linear example ...
4
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1answer
1k views

Solar system simulation (n-body physics) with OpenCL

I would like to simulate a n-body solar system in Mathematica. I have found the following example: ...
1
vote
1answer
71 views

How would I go about simulating conditional random birth 100 times?

So I have the following scenario: Assume you have this organism that reproduces by itself. An organism either reproduces 0, 1, 2, or 3 organisms at a time. Assume they're asexual and reproduce only ...
5
votes
3answers
1k views

How to define a distribution that 90% of the time gives me 0?

This maybe a simple question, but I am just stuck with it. I want to do some simulation, say with 0.9 probability, I get a 1, and 0.1 probability get a 0. How would I do that? Where should I start? ...
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vote
2answers
119 views

Random walk using Module [closed]

I want to create a random walk using Module. The walk start at {0, 0}. At every step, x ...
8
votes
3answers
429 views

Simulate random data with correlation

I would like to simulate some random data e.g. between 0 and 1, but with a given correlation. In other words some data where the correlation between two datasets is e.g. a constant or within a give ...
0
votes
0answers
77 views

Simulation of the semicircle Wigner Theorem

Let's begin with some termes: For $1\le i<j<\infty$ let $X_{i,j}$ be independant and indentically distributed (i.i.d) real random variables with mean $0$ and variance $1$ and set ...
5
votes
0answers
292 views

Computational Bayesian analysis in Mathematica: Any plans to develop MCMC?

Does anyone know if there are any plans to develop an MCMC capability in Mathematica? My reasoning for asking is that as it stands, I can't seem to find any 'out-of-the-box' functions/capabilities ...
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0answers
165 views

Simulate a polygon bouncing with collision detection inside a circle/polygon

Simulate a polygon bouncing with collision detection inside a circle/polygon. the example can be see in help page by searching WhenEvent; ...
0
votes
1answer
83 views

How can I use manipulate on multiple lists within a function?

So I have my N-Body Problem set up like so, and I can plot it in ListPointPlot3D, but I cannot figure out how to stick this into a manipulate function. ...