# Questions tagged [simulation]

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

294 questions
Filter by
Sorted by
Tagged with
35k 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 ...
• 5,536
1k 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 the ...
• 71k
3k 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 ...
• 108k
7k views

### 2D random walk within a bounded area

I want to simulate a random walk in two dimensions within a bounded area, such as a square or a circle. I am thinking of using an If statement to define a boundary. ...
• 3,876
4k 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 ...
• 3,167
10k 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 ...
• 351
11k 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 ...
• 8,810
4k views

### Gillespie Stochastic Simulation Algorithm

The Gillespie SSA is a Monte Carlo stochastic simulation algorithm to find the trajectory of a dynamic system described by a reaction (or interaction) network, e.g. chemical reactions or ecological ...
• 47.1k
2k views

### Interstellar Image Effects

I'd like to know how to create this type of gravitational lensing effect in an image (here are some star fields from the hubble) "I wrote down the equations and I tested them in Mathematica by ...
• 31.7k
981 views

### How to model wooden joints with Mathematica's FEM?

This is a dovetail joint: and I'd like to see the stresses and deformation on the joint.I haven't seen any modeling of disconnected regions with FEM, only connected regions, so I'm curious if you can ...
• 2,661
3k 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: ...
• 8,830
3k views

### How to simulate the true reflective movement of a particle bouncing around in an ellipse?

Please help me to simulate the movement of a particle inside a region with elliptical walls such that particle is reflected from the walls and continues to move. A friend was able write code to ...
• 283
2k views

### Simulating molecular dynamics efficiently

The following website offers a very nice molecular dynamics simulation: http://physics.weber.edu/schroeder/md/. It is pretty neat and quite a few physical phenomena can be described from that small ...
• 14.4k
1k views

### Modeling the spread of an infection in networked computers

I would like to show the iterative stages of infection for problem 2 in this link. In case the link dies, I have copied the text for the problem below: One hundred computers are connected in a ...
• 8,830
2k 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 http://arxiv.org/pdf/1502....
• 2,661
1k 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 ...
• 311
7k 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: ...
• 355
2k 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 ...
2k 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 ...
• 970
704 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: ...
• 63k
2k views

### Efficiently Mowing Grass with Mathematica

Recently, I was mowing my yard and was thinking about how to use the least amount of time/fuel and how to simulate. Mowing a yard that is shaped as a convex polygon is not difficult, you can just make ...
• 114
2k views

### Bouncy Bubbles animation

I want to make a bouncing bubbles animation, looking like this. Here is a start: ...
• 7,180
1k views

### Obtaining a 3D animation as a drop in a liquid surface

Someone could get a similar solution like this animation? I believe the solution is useful for demonstrations in class to other users who teach Math. Spreading of a Thin Liquid Drop Under the ...
• 9,263
1k 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 ...
• 315
995 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 ...
• 846
5k 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 ...
• 930
1k 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 ...
• 3,780
868 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 ...
• 846
390 views

### Gravitation simulation and interaction of N (1000) massive objects

Is there an implementaion of the Barnes-Hut algorithm running with Mathematica? Thanks a lot
• 345
757 views

### Multiple reflections of a laser beam in a triangle

I want to make a animation that multiple reflections of a laser beam in a triangle looked like, I have tried following, but it's not a good way, I'm looking for a better way(Nested solution). ...
• 7,180
2k 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?
3k views

### How to make a Cahn–Hilliard model GIF

The question derived from @Jason B 's answer.I wanna make it but don't how to do.But we can get some rule about the GIF The change of the total pixel is very small. ...
• 27k
1k views

### How to implement lane-change rules for Nagel Schreckenberg model

I am trying to extend the Nagel-Schreckenberg model for traffic flow to include two lanes of traffic. I have a function that generates information about a random initial road configuration. A road ...
• 131
920 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 ...
• 151
9k 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 ...
• 1,129
3k 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 ...
• 481
715 views

### Beam deformation due to localized force distribution

I would like to simulate the deformation of a beam which is fixed on one end and has some localized forces applied along the top. I have been inspired by this Mathematica example: http://www....
• 2,510
2k 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 ...
• 3,074
499 views

### Solve and design "water flow"

In some strategy game I play, I'll have to change the terrain to make the water flow in some specific way to fulfill my goal. The water flow changes with terrain so if I can change the terrain wisely ...
• 9,640
5k 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 ...
• 311
1k 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 ...
• 675
2k views

### Resources on Mathematica and strong AI (a.k.a. AGI) [closed]

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 ...
• 14.5k
5k 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 ...
• 153
1k 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 ...
• 3,005
1k 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 ...
592 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 ...
• 113
1k 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 ...
• 10.9k
768 views

### Writing compiled functions as fast as Python's Numba

I want to write some code to simulate a damped oscillator that is just as fast as code written using Numba's @njit decorator. I've written the mathematica code and ...
• 1,844