Questions tagged [simulation]
Simulation is the imitation of the operation of a real-world process or system over time.
245
questions
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How can I solve the 2D diffusion equation over a region that contains mobile sinks?
I am looking for guidance on how to simulate the following system in 2D.
I have a region, assumed to be rectangular for simplicity. A substance is diffusing into this region from its boundary. Again ...
0
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0answers
53 views
Numerically Solving Fourth Order PDE with Boundary Condition at Infinity
I am trying to numerically simulate (using NDSolve) the following differential equation with the following boundary conditions:
$$\partial_x^2\psi +c\partial_x^4\psi - b(a\psi + \psi^4)= \lambda\...
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2answers
63 views
Antithetic Variates in Monte-Carlo simulations (code taking too long to execute)
I am trying to use the Antithetic Variates method to reduce error in stock price estimates. Essentially, I generate pairs of negatively correlated RV's and use them to simulate stock price. The ...
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0answers
206 views
Fokker-Planck equation [closed]
Is there any package for simulation of Fokker-Planck equation in Mathematica? Or, in general for stochastic differential equations?
0
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1answer
36 views
How can I get the compensated compound Poisson process in Mathematica
Let us consider the following martingale "compensated compound Poisson process" $M_t=\sum_{k=1}^{N_t} Z_k-\lambda t E(Z)$ where $N_t$ is a Poisson process with intensity $\lambda$, $Z_k$ is ...
0
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1answer
67 views
Simulating electrons passing through a beam splitter for random number generation
I would like to write a program that would simulate the trajectory of an electron/photon passing through a 50-50% beam splitter and depending on which detector the particle is measured, it would ...
0
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1answer
77 views
NDSolve not finding the right solution for a mass hanging of a thread
My NDSolve isn't predicting the right trajectory for one particular case of a problem.
System
Consider a mass vertically hanging by an almost inelastic thread. The ...
1
vote
1answer
112 views
Too slow using Dsolve
I am referring to the accepted answer to the question: Solving n simultaneous differential equation
The issue is that the code is running too slow for even N=5! Is there any way to make it faster?
I ...
1
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1answer
52 views
Trying to make the animation showing the process of integration using Wolfram Mathematica
I'm pretty new here, I'm trying to make a animation of integration in Wolfram Mathematica, but it's getting me a headache I really don't know how to do this.
The point is to ilustrate the process of ...
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1answer
47 views
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1answer
81 views
Simulate spring wire through fixed points
Suppose we have a wire made of an ideal spring steel. If we bend it and then release any external force it will straighten itself into a perfect line.
Suppose also that the wire is attached to some ...
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2answers
69 views
How to find estimators of unknown parameter of a distribution using method of least square estimation
I had defined pdf of distribution, generate data and specify the least square function.I am not aware of the code for finding estimators and bias of this distribution using method of least square ...
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2answers
65 views
Building up functions from data sheet
I'm trying to use a list of data points from a csv file to perform multiple calculations and plot the end result. Basically I have 3 columns of data in my csv, I need the second and third to be pulled ...
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2answers
236 views
How to add an attractive potential (migration term) named component to Mass Transport PDE
Wolfram Mathematica 12.2 now features "Named Partial Differential Equation Terms"
For specific physics fields, relevant PDE terms have been packaged as
components and augmented with ...
4
votes
1answer
129 views
Trouble iterating my forest fire simulation
I'm having some trouble iterating my simulation of a forest fire. I'm new to Mathematica, so apologies for poor coding. I'm sure there are far neater and more efficient ways of doing this, but I would ...
0
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1answer
67 views
Numerical simulation
I want to generate a numerical simulation in table for an equational output. I have used following code. But somehow I can't get any output. I am very novice to Mathematica. Can anyone please ...
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0answers
162 views
How can we improve transonic flow visualization?
With this code we can make 2D FEM simulation of transonic flow around airfoil NACA 0012 at Mach number of 0.925. It takes about 5 minutes on the XENIA-15 laptop of 32 GB memory with processor Intel ...
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2answers
366 views
Cumulative plot of a function
I'm working on a SIR model (differential equations):
eqS = s'[t] == -b s[t] i[t];
eqI = i'[t] == b s[t] i[t] - k i[t];
eqR = r'[t] == k i[t];
I get a solution of ...
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3answers
165 views
Empirical mean excess plot of (μ, e(μ))
Say I generated n random variates from the standard cauchy distribution. I want to construct the empirical mean excess plot of (μ, e(μ)) , where
e(μ)={Σ(xi-μ) *I {xi>=μ}}/Nμ . Nμ is the number of ...
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0answers
85 views
"If" not working when solving piecewise differential equation
This is a part 2 to my previous question:
Solving Piecewise Differential Equation
I am embarking on a physics project and this is the simulation that I would like to do. More information is included ...
2
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1answer
131 views
Solving Piecewise Differential Equation
I am trying to simulate something using differential equations. However, the equations are piecewise.
Here is my code:
...
0
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1answer
93 views
Find the Hill Estimator of "alpha"
I am trying to get the Hill estimator of "alpha" and the Hill-plot graph from a standard Cauchy distribution. So, how to get it? Thanks!
Hill estimator can be outlined as follows.
Generate ...
2
votes
1answer
59 views
Shaky Point[] objects in simple animation
I'm making a simple animation of wave motion. Each point is supposed to be moving exactly along a circle, and for some reason the purple & orange points seem to shake as they rotate about their ...
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2answers
101 views
Translating MATLAB code into WL code [closed]
I want to solve the following problem by simulation.
There is a bus with 100 labelled seats (labelled from 1 to 100). There are 100 persons standing in a queue. Persons are also labelled from 1 to ...
0
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1answer
56 views
Simulation of a recursive stochastic process
I would like to simulate and plot multiple paths of the following stochastic difference equation, for any initial condition $\pi_{0} \in (0,1)$:
$\pi_{t+1} = \gamma \pi_{t}$ with probability $1/3 \pi_{...
1
vote
1answer
146 views
How to do importance sampling to estimate variance?
For a random variable X with density $q(x)=e^{(1/3)∗|x|^3}$, I can estimate its variance by numerical integration method.
Then, how can I do importance sampling using a standard normal proposal (...
1
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1answer
102 views
Geometry3D objects as functions of parameters
I want to make a simulation of a rigid body with mathematica, but I want to use a Geometry3D object instead of a Graphics3D primitive.
Mainly I don't know how to rotate the 3D model, I know how to do ...
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votes
2answers
233 views
Accelerate the speed of selection in Random
Tossing 4 points on a circle at a time, and calculate the chance of all 4 points on the upper part of the circle.
This is very simple by math:
$$\left( \frac{1}{2} \right)^4 = 0.0625$$
But I want do ...
10
votes
1answer
551 views
Writing compiled functions as fast as Python's Numba
I want to write some code to simulate a damped oscillator that is just as fast as code written using Numba's @njit decorator. I've written the mathematica code and ...
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0answers
60 views
Equal point charges on the sphere
I have coded a simulation where $n$ equal charges are randomly placed on the surface of the conducting sphere. I added a damping term proportional to velocity so that the charges arrange in a stable ...
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0answers
57 views
Explicit time dependent force in NBodySimulation
I'm looking for a way to use [NBodySimulation](https://reference.wolfram.com/language/ref/NBodySimulation.html) to simulate the application of a force stemming from ...
2
votes
0answers
41 views
How can I efficiently save multidimensional data that is retrievable by key?
I am doing some simulations in Mathematica, where I calculate a spectrum intensity(frequency) for a variation of parameters in my samples. So in the following image, for example, I vary the charge ...
0
votes
1answer
21 views
Calculation time differs between segmented loops and one whole loop
I stumbled on a strange issue while simulating a large number of random values, $10^8$ to be precise.
I generated the numbers at first by the following code:
...
2
votes
3answers
394 views
Compute volume of ellipsoid using Monte Carlo methods
I have following code in Mathematica:
https://pastebin.com/zRB9vEx8
and I need to compute volume of ellipsoid with given parameters:
$$\frac{x^2}{9} + \frac{y^2}{4} + \frac{z^2}{4} = 1$$
Can anyone ...
2
votes
0answers
66 views
How to make following feynman path integral simulation [closed]
I want to do the simulation of Feynman path integral which is given in here. How should I proceed?
0
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0answers
93 views
Is it possible to create the following simulation in mathematica?
Consider a set of discrete "states" $|1\rangle,|2\rangle,|3\rangle,\dots,|N_{\text{max}}\rangle$). Next, assume that there are 1000 "particles" occupying the state 1 at the initial moment of "time". ...
1
vote
2answers
335 views
Dice Rolling Simulation [closed]
I'm simulating a sequence of dice rolls by choosing a random integer between 1 and 6. I need to use FoldList to generate a function that returns a list which describes how the cumulative total varies ...
3
votes
2answers
175 views
Plotting tens of thousands of functions together on the same axes
I'm trying to plot a large number of functions together on the same axes. Each of these functions is the result from one iteration of a Monte Carlo simulation. Essentially, I'm varying parameters of a ...
8
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2answers
2k views
How can I show that a sphere is rolling in a simulation?
I recently wrote code to simulate a table tennis ball rolling on the ground.
v0 = 10; w0 = 8; R = 4; mu = 0.2; g = 9.8;
δ = (2 (v0 + w0 R))/(5 mu g);
This gives ...
0
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1answer
114 views
Simulating a poker win rate over time
Poker players start with a fixed bankroll (bankroll) and play with a win-rate winRate (say measured in dollars per hour) and ...
0
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0answers
54 views
Simulating a function with no closed form solution
So I am trying to simulate a function in 3d. Suppose our function looks like this:
f=k*r*a
I am interested in simulating the numerical values of k when r is ...
1
vote
0answers
53 views
Is it possible to speed up SDE simulation?
Is it possible to speed up SDE simulation in Mathematica? I am simulating a large number of Heston processes that look like the following (note this code is only a slight modification of the ...
1
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0answers
51 views
Simulating a bicycle going around a circle
I want to simulate a bicycle moving around a circle. Instead of graphs and calculations, I want to almost see an actual simulation of this happening. How could I do this?
I tried looking up ...
2
votes
1answer
293 views
Monte Carlo Simulation of a Double Well Potential (Edited)
I am looking for a possible way to simulate the temperature effect on a collection of atoms sitting within a double well potential, say something like
...
1
vote
1answer
141 views
Numerical simulation for density of strings in a ball
I am trying to numerically reproduce the Mathematica result for the density of strings in a sphere as explained here.
The program is to generate random, uniformly distributed pair points on a unit ...
2
votes
0answers
278 views
Noise covariance matrix
I am trying to find the noise covariance matrix of a random vector $\mathbf{x}$ with itself. The elements of this vector represent image pixels and are treated as random variables i.e, $\mathbf{x}=\{...
28
votes
2answers
2k 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:
...
5
votes
1answer
545 views
Trying to compute the heat capacity for the 2D-Ising model
I'm trying compute the heat capacity $C_v$ out of my simulation for the 2D-Ising model which is given by
$C_v = \frac{\langle E^2 \rangle - \langle E \rangle^2}{T^2N^2}$ ($E$: Energy, $T$: ...
3
votes
2answers
163 views
Initial values of position (x) and speed (v) of a particle visualizing using Mathematica
$$\vec{F}(\vec{r})=-m\omega^2\begin{pmatrix}x\\4y\end{pmatrix}$$
I have the force $F$ shown above. How could I specify the initial values of position ($x$) and speed ($v$) in Mathematica using the <...
2
votes
1answer
356 views
Solving Differential Equation System for HIV Treatment Model
I was working on a project about optimal strategies for HIV treatment, models used from [Butler, Kirschner, and Lenhart] 1997. This model explains the spread of HIV viruses in the human body, where ...