Questions tagged [modeling]

Questions about approaches for simulating physical systems or phenomena by building from related understanding and basic principles.

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5
votes
1answer
142 views

Mass Transfer Value

I'm trying to model the following boundary condition using MassTransferValue. $$ D_A \frac{\partial[A]} {\partial x} + D_B \frac{\partial[B]} {\partial x}+ D_C \...
11
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3answers
478 views

Mass Transport Model

I've asked similar questions before about Mathematica's Mass Transport model. My aim is to model these systems and show how they change by manipulating various parameters. This time it's the following ...
2
votes
2answers
143 views

Showing that a Hopf bifurcation exists?

I have the following system of ODEs: dx/dt = a/(1 + z) - Q*z dy/dt = Qx - qy dz/dt = qy - cz/(K + z). Assuming K = 1, Q = q < c, and a = c*(Sqrt[c/Q] - 1), is there a way to use Mathematica to test ...
0
votes
1answer
141 views

Can Mathematica do thermal/mechanical analysis of modeled solid systems?

I want to do thermal and mechanical analysis of various parts which may have complicated geometries. I am contemplating buying SolidWorks because it does this: you model the part and then use their ...
11
votes
1answer
287 views

Generating random sequence of integers with ordering constraints

I would like to write a Mathematica routine for generating random musical melodies that obey (some of) the constraints of traditional tonal harmony. For simplicity's sake, I'm interested only in ...
8
votes
1answer
307 views

Can LearnDistribution learn conditionality?

I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example: ...
4
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0answers
60 views

Why is EstimatedProcess so slow for a vector ARProcess?

I'm trying to fit some 4 x N data to a vector auto-regressive model. However, EstimatedProcess is very slow for this. For a 4-th order vector AR process, it takes more than 10 seconds (for N approx. ...
2
votes
1answer
71 views

select the right numbers based on a condition

I want to optimize my stock portfolio based on three components: the price of the different stocks the number to buy of each of the stocks the expected return of each stock (after 12 months) For ...
1
vote
0answers
52 views

Non linear differential equation plot [closed]

Consider the following paper: https://reader.elsevier.com/reader/sd/pii/S0096300306007715?token=2B98E3B12F1E623C99A0787996469AF36E8EF230F6ED5289EAFB60B64CE79A6ACCF74B946A34F3370C65D4FC99018648&...
4
votes
2answers
696 views

Is it possible to find the transfer function of these three differential equations using Mathematica

Imagine you are attempting to obtain a model of a device with two inputs [u1, u2] and three outputs [O1, O2, x] from the Lagrangian. After some of Lagrangian work, you find the following three ...
18
votes
2answers
573 views

Large deformation of solids

Link to notebook with this question and code I'd like to understand how large deformations of solid mechanics work and how they are implemented. For this am looking at the following reference problem: ...
0
votes
1answer
78 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
2answers
70 views

How to model the following system of ODE's in Mathematica with plots of the solution?

Consider the following (i) \begin{align} \frac{d S}{dt} &= -\frac{\beta S I}{N}\\[2ex] \frac{dI}{dt} &= \frac{\beta S I}{N} \end{align} Where $N=S+I$ is the total population. (ii) \begin{align}...
1
vote
1answer
64 views

Help with plotting the bifurcation diagram $R_0$ vs $I.$ [closed]

I am working on the paper "A short study of an SIR model with inclusion of an alert class, two explicit nonlinear incidence rates and saturated treatment rate" by Kumar, Nilam and Kishor and ...
1
vote
1answer
239 views

Solving time dependent Schrodinger equation for a wavefunction and harmonic oscillator [closed]

How can I obtain a GIF/graph similar to these ones here by solving the time-dependent Schrodinger equation $$ i\hbar\frac{\partial ψ(x,t)}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2ψ(x,t) + V(x)ψ(x,t)$$...
7
votes
2answers
256 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 ...
1
vote
0answers
72 views

2D transient heat equation resolution

I'm writing a code to get the analytical solution mentioned in Sun et al., 2013. I will copy here the passages needed to solve the equation. The 2D transient heat equation is: First of all, I set the ...
3
votes
0answers
69 views

Graph embedding constrained to a surface?

Have been contemplating it for a while, but did not dare to post as I felt like this must be a major undertaking to implement. Then saw the excellent answers to a recent question RegionPlot3D KnotData ...
1
vote
0answers
50 views

Microcontrollerembedcode unable to connect to Arduino Yun

Hi Mathematica enthusiasts, I am trying to follow this tutorial off Wolfram reference for microcontrollers Real Time Data Acquisition I have an Arduino Yun Rev2 hooked up exactly as it is from the ...
2
votes
1answer
368 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 ...
0
votes
1answer
43 views

finding FWHM of a dataset with unknown mathematical equation

I have a dataset. I have plotted using "Listloglinearplot". Now I need to find the FWHM (full width half maxima) of the same, However I dont know which mathematical eqution describes best to ...
16
votes
4answers
4k 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 ...
0
votes
0answers
83 views

NDSolve for ODE-PDE Problem

happy holidays, I am solving a coupled ODE - PDE system -for simplicity all coefficients are taken as 1-. I checked other questions on the issue but couldn't find any suitable answer or comparison. ...
1
vote
1answer
141 views

How to make this model in wolfram mathematica?

A model production possibility curve (nonlinear case). I used 1/4 of a circle in the code. ...
0
votes
0answers
59 views

How to formulate NDSolve[...] for a two-sector SIR model

The following Code aims to simulate the employment effects of a pandemic, drawing on the conventional SIR model. I extended the SIR model with two economic sectors (...
3
votes
1answer
98 views

Does mathematica have support for mixture models?

Does Mathematica have support mixture models? Similar to the R language libraries mclust or ...
6
votes
3answers
688 views

Time dependent Schrödinger equation in 2D

I have the following Schrödinger equation in $2D$: \begin{cases} \partial_t \Psi(x,t) = V(x,t) \Psi(x,t) \quad x \in [-10,10]^2\\ \Psi(x,0)=\exp( \frac{1}{2} (-x^2+y^2)) \end{cases} where the ...
0
votes
1answer
92 views

Equation Plotting

I'm using the mean field theory approximation and the Ising Model for magnetization to come up with the following equation: m(T) = tanh(m(T)/T) where T is an ...
2
votes
3answers
179 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
1
vote
1answer
137 views

Smoothing a function after interpolation + trying to fit 3D data into model without accurate prior knowledge

I have a physical problem simulation that generates this data set in the two cylindrical coordinates $(r,z)$ (doesn't include $\phi$ dependence). The data set (see .wdx file) is in the flattened form $...
2
votes
1answer
117 views

Linear Quadratic Integrator

With a given linear drive system ...
0
votes
0answers
107 views

Magnetostatics analysis of Switched Reluctance Motor in Mathematica

Accidentally stumbled upon magnetostatic calculation in Mathematica. https://www.wolfram.com/language/12/nonlinear-finite-elements/magnetostatics.html?product=mathematica I would like to ask a ...
3
votes
1answer
199 views

Stiff System of ODEs: NDSolve Convergence Issues

I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem. ...
2
votes
1answer
138 views

How to Make a Bifurcation plot of a non linear system of ODEs

I am modelling bacterial growth. I have a quite difficult non linear systems of ODE's. I have 2 bacteria that i'm modelling with competition, as wel as transfer to a different place. so there are 2 ...
0
votes
0answers
93 views

Error in Monte Carlo simulation. Now Random walk (dotted curve) doesn't fit to the analytical curve (dashed curve)

I've been trying to code a kinetic monte carlo simulation for a system of consecutive chemical reactions using a fixed (repaired) code that the user flinty gives me in the last questions I post: ...
2
votes
1answer
149 views

NDSolve Convergence Issue for Coupled Field Problems

I have tried to use NDSolve to solve a coupled field Eqs (see the attached Codes). The MMA solver seems to failed to converge to the requested accuracy or precision within 100 iterations ...
11
votes
1answer
841 views

Modelling the effect of a structure on a "tsunami" (hyperbolic wave equation)

So, the hyperbolic wave equation can be quite easily solved in Mathematica like this: ...
1
vote
1answer
81 views

Strange error not found in a monte carlo code, Infinite expression 1/0 encountered

I've been trying to code a kinetic monte carlo simulation for a dimerization reaction, 2M ---> D. However I have a kinetic Monte Carlo code for a first order decomposition reaction of AIBN (that's ...
8
votes
2answers
303 views

Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
4
votes
2answers
176 views

Find the best fit with some conditions

I have this code to find the best values for $l$, $s$ and $j$: ...
1
vote
2answers
144 views

FindFit problem, some models work -- and some do not

I asked this question. Answers and comments were appreciated. But (some) of the comments did not make satisfied. [Maybe due to my bad English I did not describe my problem very well]. Let me try ...
1
vote
3answers
148 views

FindFit, FindFormula, Fit, NonlinearModelFit - Which one to use? (I got no good curves & plots)

See this code, what mistake I did? (I got no plot) ...
0
votes
1answer
39 views

Having trouble with NDSolve [closed]

I'm trying to plot the solutions to the following set of differential equations, I'm doing this through NDSolve with the following code, ...
2
votes
1answer
81 views

FindFit low speed when fitting polynomial coefficients: is it possible to significantly increase the speed?

I work in Mathematica with a Butterworth filter, the transfer function of which depends on the selected order and cutoff frequency. I want to evaluate the change in the location of the roots on the ...
2
votes
1answer
121 views

How to model the movement of a mass over a dome?

I'm trying to replicate the graphs and animation found in this page that studies the movement of a mass over a dome solving numerically the differential equation ...
4
votes
1answer
78 views

Trying to recreate a plot which tracks the age of individuals inside a compartment model

I am using a compartment model from this paper. I am trying to recreate Figure 6. I will be honest, I have no clue how to approach this. The paper doesn't give information on how to achieve the ...
5
votes
1answer
177 views

Conditional Random Walk

I am attempting to model a physical process I'm observing in the lab with a random walk generator. I need to find a way to impose a condition such that when the random walk runs into a point in the ...
2
votes
1answer
301 views

Find best equation for data and the area under curve

How can I find the best formula that describe the following Figure and also find the area under the curve (the numerical value): The data for the figure can be found here: https://pastebin.com/...