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

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What code can I use to calculate, integrate, and visualize the electric field for an arbitrary shape? [duplicate]

I'm looking for a Mathematica program/function with which I'd be able to specify two objects in 3D space, each at a different surface potential, and then the program would calculate (using Finite ...
4
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1answer
94 views

How can I choose a suitable refresh rate to make a good animation of the wagon-wheel effect?

I'm trying to make an animation of a rotating wheel to show the effect of aliasing in sampled systems. Here is my code, where I use Manipulate to adjust ...
19
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1answer
252 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 ...
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0answers
55 views

Animation of the wavefield

I was trying to animate contour plot as a function of time. Basically, it is contour plot of wavefield that is changing throughout the time. Here is my attempt: ...
4
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1answer
73 views

Issues with modeling pulses in a very simple system of DAEs

Some time ago I had asked this question about evaluation difficulties using Euler Integration to solve a system of ODE where discrete pulses occur. While I have now abandoned Euler integration and ...
4
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2answers
239 views

Calculate $\pi$ using Monte Carlo methods

I know that we can have an estimate of $\pi$ using Monte Carlo methods. I know that we make a huge loop and each time we take randomly two numbers in the range [0,1] and calculate the number of ...
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3answers
229 views

Simulation with two random walkers on a lattice with periodic boundaries

I am having some difficulties implementing a Monte Carlo simulation in order to compare the results to analytical calculations. The following code simulates a case with one random walker and a ...
-1
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1answer
126 views

Periodic boundary conditions for two walkers

For some reason I'm getting infinite loops most of the time i run this. Perhaps the periodic boundary conditions are wrong. Seems like the probability of the two positions to be the same is extremely ...
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1answer
110 views

Simulating a “Coin Tossing” Game

i was wondering if i could simulate the following Coin-tossing-game in Mathematica: Two Persons are playing "Coin-tossing" against each other. If one wins, he gives one Dollar to the other. Game ...
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1answer
270 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 ...
8
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1answer
129 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: ...
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1answer
122 views

How to add moon to orbit Earth that Orbit Sun

I want to add moon(Blue) that orbiting earth(Red). while Earth is orbiting Sun. this is my code so far that consist of earth, sun and moon. how to write a code so that Moon is orbiting earth instead ...
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2answers
251 views

How to see phase difference of two pendulum

i want to see the simulation of two uncoupled Simple Harmonic Motion (SHM) pendulum with different Lengths and released at different initial displacement angles. in this case adding one more pendulum ...
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2answers
88 views

How to make A simulation of 2-Dimensional Projectiles

Lets say two cannon is fired at different initial position, initial angle and initial speed. let say initial speed,angle and position for projectile 1= ...
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0answers
135 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 ...
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1answer
89 views

Simulating a Wave Pulse

How to construct a code that superimpose n=10 one dimensional sinuisodal waves. each with an angular frequency ...
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0answers
50 views

How to do multi-agent modeling?

There are tons of examples here: http://demonstrations.wolfram.com/topic.html?topic=multi-agent+modeling&limit=20 But I been unable to find a good guide explaining what is the recommended ...
5
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2answers
924 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 ...
3
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0answers
177 views

How to solve the Tsunami model and animate the shallow water wave?

Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation. How to establish and solve the initial and boundary conditions ...
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1answer
299 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 ...
3
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2answers
154 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 ...
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4answers
2k 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. ...
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1answer
204 views

Ball rotating in a Turntable

I made a turntable to make some experiments and make some studies about Coriolis and Euler forces acting in different frames of reference. ...
10
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1answer
316 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 ...
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0answers
158 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 ...
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1answer
54 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 ...
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2answers
142 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 ...
6
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1answer
324 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 ...
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2answers
194 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
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1answer
875 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
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2answers
818 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 CesĂ ro mean is $$I_n=\frac1n\sum_{k=1}^{n} f(U_k) $$ I want to plot the scatter plot ...
4
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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 ...
40
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1answer
565 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 ...
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1answer
789 views
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0answers
63 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 ...
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7answers
1k 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 ...
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2answers
429 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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1answer
136 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: ...
35
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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 ...
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2answers
198 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) & ...
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1answer
246 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 ...
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0answers
143 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 ...
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3answers
308 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 ...
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2answers
113 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
477 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
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1answer
98 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 ...
12
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4answers
2k 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 ...
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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: ...
22
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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 ...
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2answers
165 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 ...