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Questions tagged [modeling]

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

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2 votes
1 answer
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Fitting data to a system of ODE using ParametricNDSolveValue

I am trying to create the following code to fit data to a system of ODE. ...
shewlong's user avatar
1 vote
0 answers
46 views

How does NDSolve deal with a delay variable [closed]

For a project I'm using an SIR model to simulate a Zika virus outbreak. And I solve a set of differential equations using NDSolve with specific initial conditions. ...
SollyPolly's user avatar
1 vote
1 answer
116 views

Problem Encountered when Solving a System Consisting of Two PDEs and an ODE in a Semi-NDSolve-based Approach

This is a continuation for question 300522. Firstly, I have changed the equation for $C_{2\text{b}}^* $ in my system. The updated $C_{2\text{b}}^* $ is expressed as below: $$ \begin{equation} C_{2\...
Johnson's user avatar
  • 357
0 votes
0 answers
79 views

Specifying Prescribed Mesh to Solve for a System Consisting of Two PDEs and an ODE

I am solving the following equations: $$ \frac{\delta C_{1\text{f}}^*}{\delta t^*} = \frac{\overline{t}}{\overline{x}^2} \frac{\delta}{\delta x^*} \left\{ \mathcal{D} \left[ \frac{\delta C^*_{1\text{f}...
Johnson's user avatar
  • 357
0 votes
0 answers
32 views

Modeling with different outputs size

I have lists of input and output. I want to perform the prediction operation but my outputs are different for each input and this causes an error. Can someone help me to write the model in such a way ...
Erfan's user avatar
  • 169
1 vote
1 answer
57 views

Troubleshooting NDSolveValue::rdelay Error in a Dengue Epidemic Model with Delay Differential Equations in Mathematica

I am modeling the vector dynamics of a dengue epidemic using a system of delay differential equations (DDEs) in Wolfram Mathematica. My model includes a complex interplay of host-vector interactions, ...
Lennert Saerens's user avatar
-2 votes
1 answer
83 views

Novice Mathematica User: Plots are very small despite changing image size option

I'm currently writing a paper about marine chemistry and I'm trying to include a reactive transport model that was written in mathematica by a collaborator. I have a lot of experience in SAS, but I ...
yousavdj's user avatar
1 vote
2 answers
297 views

Graphing curves formed by a rolling polygon

I am trying to make a Mathematica graphing function that would generalize common phenomena. How would I do this? From a circle, we can generate a cycloid (if rolling on a line) or a sine wave (if ...
Teg Louis's user avatar
1 vote
1 answer
345 views

Fitting delay differential equations (DDE)

I have the following differential equations: $$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(t)}{6.19} \Big)- \frac{a}{1 + B(t)} S(t),$$ $$B'(t) = c (1 - B(t)) - d B(t) S(t) - 3 c (1 - B(t - 18)),$$ where $B(t -...
user avatar
3 votes
2 answers
252 views

Optimizing an ODE fitting algorithm with interpolated data

Given data, I want to find parameters $p_1,p_2,k_1,k_2>0$ that fit the following ODE system $$ \begin{align} b'(t)&=p_1 a(t)-k_1b(t)\\ c'(t)&=p_2b(t)-k_2c(t) \end{align} $$ where $a(t)$ is ...
sam wolfe's user avatar
  • 4,863
0 votes
1 answer
199 views

Finding Contours in Photo to Create a Topographical Map

I am setting up a special table to simulate the scenario in this problem in this problem, but instead of finding the geodesics, I want to create a topographical map using the contours. Here is a ...
Teg Louis's user avatar
3 votes
1 answer
127 views

How to optimize ODE parameter fitting?

Consider the data ...
sam wolfe's user avatar
  • 4,863
1 vote
1 answer
57 views

How to fit a linear ODE system?

Consider the equations $$ \begin{align} b'(t)=p_1 c(t)-k_1b(t),\\ c'(t)=p_2b(t)-k_2c(t) \end{align} $$ Given data on $b$ and $c$, and initial conditions, how do I find the best fitting parameters $k_1,...
sam wolfe's user avatar
  • 4,863
0 votes
1 answer
91 views

Tracking сode performance with the conservation of energy

I am working with the Momentum Principle as defined by Chabay and Sherweood in their text Matter and Interactions (pf = pi+Fnet dt). The following code has been created to automate the process of ...
JEM's user avatar
  • 1,165
5 votes
3 answers
280 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. ...
Athanasios Paraskevopoulos's user avatar
0 votes
0 answers
127 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 ...
Erfan's user avatar
  • 169
2 votes
1 answer
104 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 ...
Rogo's user avatar
  • 930
1 vote
3 answers
217 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 ...
Yaroslav Bulatov's user avatar
2 votes
1 answer
221 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 ...
BioPhysicist's user avatar
  • 1,124
0 votes
1 answer
66 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 ...
sam wolfe's user avatar
  • 4,863
3 votes
0 answers
175 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 ...
Vitaliy Kaurov's user avatar
8 votes
2 answers
374 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 ...
Dunlop's user avatar
  • 4,023
5 votes
1 answer
135 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 ...
user21's user avatar
  • 39.9k
0 votes
1 answer
150 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{...
Math's user avatar
  • 407
4 votes
1 answer
434 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 ...
Avrana's user avatar
  • 297
7 votes
1 answer
314 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 ...
Avrana's user avatar
  • 297
13 votes
2 answers
932 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, ...
Tetrasreal's user avatar
7 votes
1 answer
361 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 ...
Avrana's user avatar
  • 297
2 votes
1 answer
160 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 ...
Avrana's user avatar
  • 297
1 vote
0 answers
75 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 ...
Avrana's user avatar
  • 297
7 votes
1 answer
501 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....
Math's user avatar
  • 407
4 votes
2 answers
117 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: ...
Meow Nyan's user avatar
1 vote
0 answers
68 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 ...
BBirdsell's user avatar
  • 1,196
1 vote
1 answer
146 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 ...
Albano Tabacchi's user avatar
2 votes
1 answer
248 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 ...
Albano Tabacchi's user avatar
1 vote
0 answers
61 views

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

I have these two equations: ...
Victor Nielsen's user avatar
4 votes
1 answer
582 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 ...
Victor Nielsen's user avatar
2 votes
1 answer
264 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: ...
Maher 's user avatar
  • 23
0 votes
0 answers
244 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. ...
Pingu's user avatar
  • 1
0 votes
0 answers
912 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: ...
Victor Nielsen's user avatar
6 votes
4 answers
737 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 ...
tardigrade's user avatar
11 votes
1 answer
314 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 ...
Kim Fierens's user avatar
  • 1,857
0 votes
1 answer
218 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 ...
Tyler Durden's user avatar
  • 4,102
4 votes
0 answers
79 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. ...
Amanda's user avatar
  • 276
2 votes
1 answer
95 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 ...
Michiel van Mens's user avatar
1 vote
0 answers
110 views

Non linear differential equation plot [closed]

Consider the following paper: https://reader.elsevier.com/reader/sd/pii/S0096300306007715?token=2B98E3B12F1E623C99A0787996469AF36E8EF230F6ED5289EAFB60B64CE79A6ACCF74B946A34F3370C65D4FC99018648&...
Math's user avatar
  • 407
9 votes
1 answer
449 views

Can LearnDistribution learn conditionality?

I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example: ...
M.R.'s user avatar
  • 31.5k
20 votes
2 answers
1k 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: ...
user21's user avatar
  • 39.9k
0 votes
1 answer
109 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 ...
lineage's user avatar
  • 1,154
1 vote
2 answers
104 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}...
Math's user avatar
  • 407

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