Questions tagged [modeling]
Questions about approaches for simulating physical systems or phenomena by building from related understanding and basic principles.
204
questions
2
votes
1
answer
159
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 ...
- 403
4
votes
2
answers
243
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 ...
- 4,179
0
votes
1
answer
149
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 ...
- 403
4
votes
1
answer
114
views
1
vote
1
answer
55
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,...
- 4,179
0
votes
1
answer
88
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 ...
- 1,165
5
votes
3
answers
253
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.
...
0
votes
0
answers
98
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 ...
- 159
2
votes
1
answer
99
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 ...
- 790
1
vote
3
answers
208
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 ...
- 8,135
1
vote
1
answer
176
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 ...
- 920
0
votes
1
answer
59
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 ...
- 4,179
3
votes
0
answers
168
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 ...
- 71.9k
8
votes
2
answers
299
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 ...
- 3,923
5
votes
1
answer
118
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 ...
- 39.1k
0
votes
1
answer
147
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{...
- 407
4
votes
1
answer
405
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 ...
- 297
7
votes
1
answer
296
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 ...
- 297
13
votes
2
answers
848
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, ...
- 143
7
votes
1
answer
340
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 ...
- 297
2
votes
1
answer
142
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 ...
- 297
1
vote
0
answers
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 ...
- 297
7
votes
1
answer
472
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....
- 407
4
votes
2
answers
107
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:
...
- 41
1
vote
0
answers
61
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 ...
- 1,156
1
vote
1
answer
122
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 ...
2
votes
1
answer
225
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
0
answers
60
views
How to take a derivative of a function with respect to another function inside the function?
I have these two equations:
...
- 263
4
votes
1
answer
579
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 ...
- 263
2
votes
1
answer
236
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:
...
- 23
0
votes
0
answers
221
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.
...
- 1
0
votes
0
answers
805
views
6
votes
4
answers
585
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 ...
- 431
11
votes
1
answer
310
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 ...
- 1,857
0
votes
1
answer
208
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 ...
- 4,048
4
votes
0
answers
76
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. ...
- 276
2
votes
1
answer
91
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 ...
- 2,615
1
vote
0
answers
105
views
Non linear differential equation plot [closed]
Consider the following paper:
https://reader.elsevier.com/reader/sd/pii/S0096300306007715?token=2B98E3B12F1E623C99A0787996469AF36E8EF230F6ED5289EAFB60B64CE79A6ACCF74B946A34F3370C65D4FC99018648&...
- 407
8
votes
1
answer
423
views
Can LearnDistribution learn conditionality?
I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example:
...
- 31.2k
20
votes
2
answers
953
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: ...
- 39.1k
0
votes
1
answer
105
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 ...
- 1,114
1
vote
2
answers
101
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}...
- 407
1
vote
1
answer
141
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 ...
- 113
11
votes
3
answers
580
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 ...
- 351
1
vote
1
answer
815
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
$$ i\hbar\frac{\partial ψ(x,t)}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2ψ(x,t) + V(x)ψ(x,t)$$...
- 347
5
votes
1
answer
158
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 \...
- 351
8
votes
2
answers
419
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 ...
- 36.2k
1
vote
0
answers
120
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
0
answers
107
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 ...
- 1,874
1
vote
0
answers
81
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 ...
- 23