Questions tagged [simulation]

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

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3
votes
1answer
102 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. ...
0
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1answer
133 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. ...
3
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1answer
193 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 ...
1
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1answer
89 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 ...
48
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1answer
997 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 ...
7
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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? ...
4
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1answer
153 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 ...
2
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2answers
620 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 ...
10
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3answers
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 ...
0
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0answers
220 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 $X_{j,i}=X_{...
9
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2answers
4k 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 ...
1
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1answer
148 views

Find maximum Log likelihood for repeated random variates

I have the following code ...
38
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3answers
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 ...
1
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1answer
430 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; ...
9
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1answer
430 views

Solving 2-D Mechanical Systems

I'm trying to use Mathematica to solve a particular 2-d mechanical system. The system comes from "DESIGN AND OPTIMIZATION OF AN EIGHT-BAR LEGGED WALKING MECHANISM IMITATING A KINETIC SCULPTURE, “WIND ...
3
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0answers
161 views

How to control pedestrians to enter the simulation region with random functions?

I am working on simulating crowds of a cross-typed region, given that pedestrians entering from 4 gates of north, east, west and south, ...
0
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1answer
99 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. ...
4
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1answer
557 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 ...
0
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1answer
65 views

Simulating from Custom Function

I am going through an old research paper and I am stuck in one area of the coding. I'll spare you with most of the details but the function I want to simulate from is a complicated multivariate beta ...
1
vote
1answer
487 views

Making animations with Mathematica [duplicate]

I want to export an animation for polar plot $r=\cos 2\theta$, instead of directly using Animate. But I want a table of snapshots: movie = ParallelTable[...] and a point that produce its animations ...
2
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0answers
214 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 ...
2
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1answer
390 views

How to plot torsion prismatic beam

I dont know why dont work but I want to animate torsion prismatic beam. ...
0
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0answers
107 views

How do I perform the following numerical integration [duplicate]

I have the following integral to evaluate numerically: $$x(t) = \frac{1}{f(t)}\int_0^{t_b} t^m (t + n)^o \sin(pt) \mathrm{d}t \quad m,n,o,p \in \mathbb{R}$$ ...
8
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1answer
672 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: ...
2
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1answer
135 views

Stochastic Approximation and Simulation using Running Median

I have a function $$F(X_{t+1},Y_{t}^{med})= \alpha X_{t+1} + (1-\alpha) Y_{t}^{med},$$ where $$Y_{t}^{med} = Median(Y_1, Y_2,... Y_t).$$ Moreover, $Y_1 = X_1$ and $Y_t = F(X_{t},Y_{t-1}^{med})$ $\...
0
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0answers
80 views

How to set the boundary fixed and apply the Young's modulus in Mathematica's FEM? [duplicate]

Provided the drawing .stl is given, and the Young's modulus is know, how to start a FEM vibration mode test in Mathematica? The boundary is required to be fixed and the interested focus is on the ...
8
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1answer
334 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 $\...
40
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6answers
6k 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
votes
0answers
99 views

Determining the total illumination of a polygon

Is it possible to determine the total illumination of a particular polygon with the given light sources? I truly acknowledge that Mathematica is not supposed to do this modeling, but it is what is ...
6
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2answers
2k views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
1
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2answers
279 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) & ...
1
vote
1answer
318 views

Potential hill simulation

I attempted to simulate the motion of a particle approaching to a potential hill. The particle should experience a force of -1/r^2, if the equation for the ...
6
votes
1answer
3k 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 ...
21
votes
2answers
825 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 ...
14
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1answer
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?
6
votes
1answer
481 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). ...
0
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0answers
46 views

Works in mathematica but not as cdf preview or web embedded cdf [duplicate]

I have a curvature simulation with the help of m_goldberg that works in mathematica but does not work as a cdf in cdf preview. In mathematica it says nothing while in cdf preview or while web embedded ...
3
votes
2answers
170 views

how can I make a control for my vector equation in my simulation?

I'm trying to build a control selector or menu for equations to put into my curvature simulations. However all the code I've tried hasn't worked.Does anyone know how I could make a control selector or ...
2
votes
1answer
200 views

Randomly generated polymer with certain spatial density

For simplicity's sake, let the polymer's composing particle be integer 3-tuples (on 3D Cartesian grid), such that: Polymer-ness -- for all particle there is an directly adjacent neighbor. i.e in ...
34
votes
3answers
8k 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 ...
3
votes
1answer
304 views

How to simulate the 1-D motion of a particle under constant acceleration? [duplicate]

I am trying to represent the position of an object under freefall, but am completely lost. Here is my attempt so far: ...
5
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3answers
291 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: ...
4
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1answer
85 views

RandomVariate does not evaluate a Hyperbolic Distribution

Any Idea why I can't get a result from this expression: ...
3
votes
2answers
2k 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 ...
1
vote
1answer
219 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 ...
2
votes
1answer
642 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 ...
2
votes
1answer
566 views

Combining Newtonian 3D N-Body Simulation Output and Earth Sphere

I'm trying to figure out how to make a simulation whereby two satellites orbit Earth, but have run into a little bit of a snag. I have a solution to the system of ODEs for the n-body output, and I ...
7
votes
1answer
1k 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 ...
8
votes
3answers
330 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 ...
18
votes
3answers
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 ...