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

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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 ...
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3answers
434 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 ...
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50 views

Moving the start of a graph to the right, finding maxima in an oscillator

I have the following code written to simulate a driven damped oscillator ...
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88 views

Simulation code performance tuning

The following simulation takes over 20 seconds for evaluation. I have difficulty re-coding it with Nest and Map or Compile functions to make it more efficient. Can some one help with this? The ...
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1answer
39 views

NDSolve with arrays and Tables of Equations and WhenEvent

I've been toying around with NDSolve for a while, and read through the website. By doing so I discovered that I could use it for vectors and arrays with much pleasure. So I wanted to write a simple ...
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1answer
199 views

Simulating a quick return mechanism

Last time, I got a satisfying answer for simulating a toggle mechanism, just as expected. NDSolve is great. I tried playing with it (as a matter of fact, @MichaelE2 ...
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7answers
14k 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 ...
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0answers
308 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: ...
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5answers
332 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 ...
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2answers
271 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 ...
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4answers
437 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 : ...
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3answers
729 views

Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 = 1$ in the first octant: ...
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0answers
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Approximating a stochastic integral with a Wiener process

I would like some assistance to solve the following: $\sum\limits_{i=0}^{n-1} e^{-k(n\Delta t -i\Delta t)}\Delta z_i$ where $z$ is a Wiener process, $\Delta z_i = z((i+1)\Delta t)-z(i\Delta t)$. ...
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2answers
488 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 ...
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1answer
377 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: ...
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0answers
518 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 ...
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1answer
183 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 ...
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1answer
165 views

Calculating mean of multiple stochastic processes and setting a lower threshold

Thanks to “Rod Lm” I got some very nice input for the following problem. My intention is to simulate within a Manipulate function a given number of possible stock ...
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1answer
92 views

Random variation inside NMaximize

I am using NMaximize as following code. ...
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2answers
184 views

Problem in simulating discrete time stochastic

I have been playing with some stochastic questions and specially the problem here.It seems no matter for the first time in bet, gambler is going to lose the first bet.Am I right?How can we correct the ...
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1answer
150 views

Making an animated simulation without procedural loops

I'm still new to Mathematica and this is the first time I've wanted to do something more complicated than plotting and changing parameters of mathematical functions. I want to make a simple ...
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3answers
2k 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 ...
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2answers
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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 ...
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2answers
1k 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 ...
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2answers
180 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. ...
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1answer
175 views

Symbolic Simulations

I have 9 nonlinear equations and 10 unknowns. It is not possible to obtain a numeric solution but I do get a parametric solution. It is useful in my case because I want to observe how parameters (p1, ...
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3answers
423 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 ...
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1answer
393 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 ...
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263 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 ...
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2answers
481 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 ...
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1answer
693 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
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1answer
253 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 ...
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1answer
465 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 ...
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2answers
484 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
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2answers
403 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 ...
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0answers
231 views

How to save (large) data generated from simulations

The following is a simple example of a much larger simulation that I want to run Define some processes ...
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1answer
238 views

Speed up iterated manipulations of a graph / table

I am trying to generate a version of Watts' model of cascading shocks to a network following the discussion on p. 20-25 of this article. The basic premise is to use the ...
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1answer
473 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 ...
6
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4answers
870 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 ...