# Questions tagged [modeling]

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

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245 views

### Plotting Incidence function of the SIR Model

I am working on the SIR model and I am trying to plot the incidence function on a specific time interval. ...
91 views

### Predict with Deep Learning in Mathematica

I have two series of number (Tmax,Tmin) and my target is (ET). I want modeling this and I have one code for this operation but this code is not very acceptable. Can you help me to improve or use an ...
96 views

### Need an equation for modeling Tytler's Cycle

In all cultures over all time there appears, in different languages for different countries, the maxim "Shirtsleeves to shirtsleeves in three generations." This is a function with three ...
1 vote
203 views

### Finding a continuous distribution that fits the empirical density of dataset $1,1/4,1/9,1/16\ldots$

I have a list of coefs of the form $1,1/4,1/9,1/16,\ldots,1/d^2$ sampled with relative sampling frequencies $1,1/4,1/9,1/16,\ldots,1/d^2$. How do I find a nice continuous density whose CDF closely ...
1 vote
116 views

### Implementing and testing boundary conditions in polar coordinates for convection-diffusion equation

I am modeling a system using the convection-diffusion equation on a 2D, radially symmetric space. I wanted to do some sanity checks to make sure I am coding it correctly. I set up a situation where I ...
58 views

### Nucleation models in Mathematica

Are there any nucleation models available in Mathematica? In particular, I am looking to implement a version of the Kolmogorov-Johnson-Mehl-Avrami model to analyze phase-transition kinetics in one ...
165 views

### FindDistribution analog: automated data modeling with all Wolfram statistical distributions

BOUNTY GOAL To get bounty I am asking to build a function that serves as an analog of FindDistribution. You can also simply re-implement ...
265 views

### Alternative Material Models for Finite Element

The Solid Mechanics capabilities of Mathematica make it an interesting alternative to using other software especially when considering multi-physics problems. I would like to collect here (for the ...
105 views

### Spalart-Allmaras turbulence model

In this post Alex gives an implementation of the Spalart-Allmaras turbulence model [1, 2]. The example produces reasonable results, as far as I can tell. However, the implementation Alex uses deviates ...
146 views

### Extension of: Numerically solving a system of SDE's with Levy noise?

A great answer by Alex is to be found here for my original question: Numerically solving a system of SDE's with Levy noise? Now Let us perturb this system with time delays so the system is: \begin{...
369 views

### Implementation of FEM to steady-state coupled fluid flow and heat transfer

This is a steady-state conjugate heat transfer problem (the time-independent version of this problem). The problem is conjugate as the energy equation is being solved in thermally connected solid and ...
284 views

### Modelling heat transfer in periodically reversing flow

This is a heat transfer problem, which involves reciprocating (fully-reversing) fluid flow over a heated block of solid. The objective is to determine the temperature field in the solid and the fluid ...
818 views

### How to Create Kapitza's Pendulum?

Hi, I have never worked on a project of this kind before. I am having difficulty using Kapitza's Pendulum (inverted pendulum with moving vertical base). It is hard for me to make the model equations, ...
333 views

### Refining mesh size leads to absurd results for a coupled heat transfer FEM model

I have been recently solving a conjugate heat transfer problem, which involves fully-reversing or reciprocating flow of fluid over a heated block of solid. The problem is 2D and the temperature field ...
140 views

### Directly calculating the cyclic steady state of a time-periodic conjugate heat transfer problem

Context The following transient problem is the reciprocating (i.e., fully reversing) flow of a fluid $0<x<L, 0<y<d$ over a thick heated block $0<x<L, -e<y<0$ until the system ...
1 vote
73 views

### Some conceptual doubts about steady and transient solvers of the NS + energy equations

Recently, I have been solving some transient and steady, flow and heat transfer problems in Mathematica. The transient problem is essentially the reciprocating (i.e., fully reversing) flow of a fluid ...
437 views

### Numerically solving a system of SDE's with Levy noise?

Consider this system from the following paper titled: The long-time behaviour of a stochastic SIR epidemic model with distributed delay and multidimensional L´evy jumps https://arxiv.org/pdf/2003....
101 views

### ParametricPlot for phase field error (case: Predator-Prey Model) [closed]

so I have a task that need to draw a phase field of predator-prey model, but first I tried my lecturer's coding: ...
1 vote
58 views

### Modeling Experimental data with a CDF

I have some data plotted above which relates two variables that were derived experimentally. I'm trying to fit a cumulative distribution function to it so that we can take a sample of Y at X. I've ...
1 vote
113 views

### Fitting a sum of three lorentzian based on a dataset

as you can see below, I have developed a code that allows me to fit the present dataset via a Lorentzian. Now what I should do is to develop a sum of three Lorentzians based on this model so that this ...
220 views

### Fitting a Lorentzian curve to data

Good morning everyone, regarding my research "high resolution laser spectroscopy" I would like to fit the data obtained from the experiment with a Lorentzian curve using Mathematica, so as ...
1 vote
60 views

### How to take a derivative of a function with respect to another function inside the function?

I have these two equations: ...
577 views

### My model has not finished evaluating in more than a day so can't test if it works, what is wrong with it?

Hello I have this modified monocentric city model that I have been working on for a while. Sorry for the long post, I wanted to add the whole code, because it's all connected. My suspicion is that it ...
219 views

### The nonlinear state-space model of a spherical pendulum cannot be linearized and cannot be controlled?

I am attempting to model and control a spherical pendulum. I have derived the equations as follows: ...
206 views

### How to plot elements from an array?

Im trying to solve a differential equation for a range of parameters (1->4). I then want to automatically plot a graph for each of those parameters. ...
722 views

### Error: "ReplaceAll: ... is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing." when solving a root

I have this code: ...
522 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 ...
307 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 ...
201 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 ...
75 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. ...
81 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
88 views

393 views

### Can LearnDistribution learn conditionality?

I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example: ...
892 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: ...
102 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
93 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
119 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 ...
569 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 ...
1 vote
709 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 $$i\hbar\frac{\partial ψ(x,t)}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2ψ(x,t) + V(x)ψ(x,t)$$...
157 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 \...
412 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
117 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 ...
104 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
79 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 ...
176 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 ...
91 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. ...
82 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 (...
151 views

### Does mathematica have support for mixture models?

Does Mathematica have support mixture models? Similar to the R language libraries mclust or ...
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 ...