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

learn more… | top users | synonyms

110
votes
7answers
19k views

How to generate a random snowflake

'Tis the season... And it's about time I posed my first question on Mathematica Stack Exchange. So, here's an holiday quest for you Graphics (and P-Chem?) gurus. What is your best code for generating ...
37
votes
1answer
485 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 ...
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 ...
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 ...
20
votes
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 ...
19
votes
1answer
519 views

Simulating Theatre puzzle

I have been trying to simulate the process of the theatre puzzle from the Joy of X (Strogatz). The puzzle, and some relevant material are here. My simplistic coding for this process follows: ...
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: ...
15
votes
1answer
692 views

Simulating Stochastic Processes the MMA way

This question is really a specific problem and a methodological one concerning MMA best practices. I want to simulate a system of stochastic processes. If this were a geometric Brownian motion or ...
14
votes
3answers
840 views

How can I simulate this toggle mechanism?

I've been introduced to Mathematica very recently. Basically, I haven't actually "solved" anything in my Mathematica lifetime, but I've done some simulations. With my fractional knowledge, I tried ...
14
votes
2answers
639 views

Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...
14
votes
1answer
729 views

Simulating discrete time stochastic dynamic systems

What is the canonical way of simulating discrete time stochastic dynamical systems in Mathematica using the new functionality of Random processes? To take a concrete example, lets consider the ...
13
votes
3answers
578 views

Simulate a simple spinner

I'm teaching some simple ideas in probability to students in grade 7. The "spinner" below works, but I'm wondering how I could make it just a bit more realistic by having it actually "spin" around a ...
13
votes
3answers
3k views

How to do System dynamics simulations / diagrams in Mathematica?

System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. What ...
13
votes
2answers
660 views

Efficient GeometricBrownianMotionProcess Monte Carlo simulation

Following the answers in this post, I'm trying to implement something similar. If the GBM stays inside the corridor [L, U] between predefined times it should return ...
12
votes
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 ...
11
votes
2answers
953 views

How to improve the accuracy of this Monte Carlo simulation

A friend of mine went on an interview and he was asked to calculate the angle between the hour hand and minute hand of an analog clock when the time was 3:15. Arguably, this is a trivial problem that ...
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 ...
10
votes
2answers
686 views

Fluorescence Correlation Spectroscopy Simulation

I am simulating Fluorescence Correlation Spectroscopy which basically involves tracking the random motion of particles in a box with periodic boundary conditions and then calculating their intensity ...
10
votes
1answer
293 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 ...
9
votes
0answers
994 views

Resources on Mathematica and strong AI (a.k.a. AGI)

David Deutsch (physicist / quantum computing theorist) wrote an article for Aeon Magazine last year: On Artificial Intelligence that got me thinking. The article assesses and critiques the ...
8
votes
7answers
960 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 ...
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 ...
8
votes
3answers
425 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 ...
8
votes
2answers
180 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. ...
8
votes
1answer
448 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: ...
8
votes
0answers
119 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 ...
7
votes
1answer
744 views

Detecting a collision in n-body simulation with NDSolve

Consider this three-body system: ...
7
votes
1answer
329 views

1D Random Walk with Excluded Sites and Variable Time-Step

Here is the physical problem I would like to simulate: Consider the following variations to the 1d random walk: allow for certain, random sites to be excluded with probability 1/2. allow for the ...
6
votes
2answers
3k views

Making mathematical animations with Mathematica

I recently stumbled upon the Cycloid and was working on finding its length and such when I found this animation on Wikipedia. Strikingly pretty and small in size too (66KB) So on searching how he ...
6
votes
1answer
983 views

Is there a free version of the Springer book “Mathematical Statistics with Mathematica”?

Is there a free version of the Springer book: $$\text{Mathematical Statistics with Mathematica}$$ by Rose and Smith ... available on the internet?
6
votes
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 ...
6
votes
1answer
239 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 ...
6
votes
1answer
1k views

Monte Carlo simulation using geometric Brownian motion

I'm relatively new to Mathematica programming, so forgive my rather unsophisticated question: I'm trying to do a Monte Carlo simulation using geometric Brownian motion (GBM). I want to write a ...
6
votes
1answer
402 views

Changing a wave simulation

I want to adjust some code that I found on this Wolfram Demonstration: http://demonstrations.wolfram.com/WaterRipplesPassingThroughASlit/ Basically it shows a wave passing through a single slit. I ...
6
votes
1answer
783 views

How to start simulating physical problems?

I'm quite new to Mathematica, I have version 9. I need to use it to simulate some physical problems. I know the equations (like Maxwell's equations and Newton's laws and so on), but I have no real ...
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? ...
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: ...
5
votes
2answers
707 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 ...
5
votes
2answers
315 views

Simulating a Stochastic Process within certain bounds

I would like to simulate paths of a Geometric Brownian Motion till it hits one of two barriers, say 10 or 200. ...
5
votes
0answers
285 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 ...
4
votes
1answer
763 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 ...
4
votes
5answers
564 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
4
votes
2answers
650 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 ...
4
votes
2answers
115 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 ...
4
votes
2answers
254 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. ...
4
votes
4answers
2k views

Finding the area of a circle using monte carlo simulation [duplicate]

I wrote the following code to find the area of the circle $x^2+y^2=1$ using monte carlo simulation : ...
4
votes
2answers
489 views

How do I represent a system dynamics feedback loop?

In System Dynamics, if I want represent the relationship between Speed and Distances, I create a Flow (Speed) and a Stock (Distance) as you can see in this Insight Maker Sample . Heres an Image of how ...
4
votes
1answer
297 views

Monte Carlo Volume Calculation and Speed Up

I am trying to do a Monte Carlo area calculation for an irregular area defined by: $$0 \le x \le 1, 10 \le y \le 13, y \ge 12 \cos(x), y \ge 10 + x^3$$ I used the code with modifications (so I can ...
4
votes
1answer
258 views

Simulating a bounded continuous random walk in $n$-dimensions

You're given three $n$-dimensional real vectors, $\mathbf{x_0}$, $\mathbf{a}$ and $\mathbf{b}$, with $\mathbf{a} \le \mathbf{x_0} \le \mathbf{b}$ (vector inequality means component-wise inequality). ...
4
votes
1answer
72 views

RandomVariate does not evaluate a Hyperbolic Distribution

Any Idea why I can't get a result from this expression: ...