Questions tagged [modeling]
Questions about approaches for simulating physical systems or phenomena by building from related understanding and basic principles.
47
questions
7
votes
1
answer
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....
- 455
20
votes
2
answers
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: ...
- 39.2k
15
votes
1
answer
2k
views
Speed up NDSolve compared to Python (calls to LSODA)
I migrated a numerical model code from Python to Mathematica and am surprised how much faster the Python version runs. Profiling of the Python version tells me that it is about 100 times faster (120 ...
- 7,663
3
votes
2
answers
486
views
Lagrangian of three-mass system with Mathematica
Before proceeding to calculations in Mathematica, I would like to clarify with knowledgeable people.
There is an ordinary linear three-mass system.
If we write its Lagrangian, we get the following ...
- 2,344
21
votes
1
answer
2k
views
Couple a PDE and ODE in NDSolve
I would like to solve an example of non-stationary heat transfer with a coupled PDE and ODE. Let's assume that we have 1 dimensional bar of length $L$ with uniform initial temperature. The right end ...
- 6,483
14
votes
1
answer
2k
views
How does Mma compute Confidence Intervals?
I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example:
...
- 2,118
8
votes
2
answers
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 ...
- 35.9k
42
votes
1
answer
1k
views
In what way can M11.3's system modelling features be used by those who don't have SystemModeler?
Mathematica 11.3 includes some functionality from SystemModeler, but not the full SystemModeler environment.
I assume that most people here are familiar with Mathematica, but not SystemModeler, or ...
- 232k
29
votes
5
answers
4k
views
Mathematica Implementations of the Random Forest algorithm
Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
- 403
22
votes
1
answer
2k
views
Backtesting a Probability of Default (PD) model
Background
PD models
Financial institutions use Probability of Default (PD) models for various purposes such as client acceptance, provisioning and regulatory capital calculation as required by the ...
- 65.5k
13
votes
2
answers
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, ...
- 143
11
votes
1
answer
898
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:
...
- 5,311
8
votes
1
answer
523
views
Fitting multiple data with model and NDSolve with different initial conditions, and other shared parameters
I know that there are already questions about fitting multiple datasets and about NDSolve and about shared and non shared parameters, but I tried to apply them and some things are still not clear.
...
- 1,245
8
votes
2
answers
346
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 ...
- 297
7
votes
1
answer
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 ...
- 297
3
votes
1
answer
1k
views
Model fitting to noisy data with a custom minimization function
I'm looking into fitting some data with Mathematica. I've got my head around how NonlinearModelFit works (I've been using the Levenberg-Marquardt algorithm for some ...
- 8,698
2
votes
1
answer
431
views
Caclulate second partial derivatives of a numerically defined function
I am performing a chi square minimisation with respect to some parameters x,y,z that are themselves part of the kernel involved in a numeric integral. I therefore ...
- 510
2
votes
1
answer
159
views
Fitting data with 3 linear fits
I have a dataset that can be easily approximated by a piecewise function composing of 3 linear functions, but i am unable to get an accurate fit once the third linear function is required. The model ...
- 63
16
votes
4
answers
5k
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 ...
- 918
15
votes
1
answer
537
views
Implementing the Biham–Middleton–Levine traffic model as CellularAutomaton
In an attempt to understand how to make rules for CellularAutomaton[], I set out to try to implement the Biham–Middleton–Levine traffic model.
It is a 2D, ...
- 517
13
votes
2
answers
3k
views
Mathematica Package for Bayesian Networks
Are there any packages that allow the simulation of Bayesian Networks with Mathematica? I found what seemed to be a promising package (Dynamics) on a Brown University URL,
http://www.cs.brown.edu/...
- 231
13
votes
3
answers
907
views
What's the analogue of UML in Mathematica land?
What's the analogue of Unified Modeling Language (UML) in Mathematica land? Mathematica has elements of object-orientation, but most Mathematica programs or applications aren't of object-oriented ...
- 8,626
10
votes
1
answer
4k
views
RSquared: LinearModelFit vs NonlinearModelFit
I'm trying to understand the differences between LinearModelFit and NonlinearModelFit. One thing I notice is that the ...
- 411
8
votes
1
answer
702
views
Computing launch parameters for hitting a point in 3D with projectile under influence of wind
The end goal of this problem is to compute functions which describe the launch parameters which are needed to hit a specified goal in 3D in the presence of wind disturbances. This is as far I have ...
- 462
7
votes
1
answer
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 ...
- 297
6
votes
3
answers
1k
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 ...
- 411
5
votes
2
answers
1k
views
How to model Macroeconomic dynamics?
I am rather new to Mathematica and I wanted to see if I could get some help with the following.
I am trying to generate a model of macroeconomic indicators defined by the following functions, but I ...
- 63
4
votes
1
answer
341
views
How can I calculate the maximum number of grid layout possibilities?
I am doing some modelling where I am trying to randomly layout some points on a grid. What I know:
How big the grid is
The number of objects that have to be laid out on the grid, at a point
The ...
- 43
4
votes
2
answers
895
views
How do I represent a system dynamics feedback loop?
In System Dynamics, if I want represent the relationship between Speed and Distances, I create a Flow (Speed) and a Stock (Distance) as you can see in this Insight Maker Sample . Heres an Image of how ...
- 918
4
votes
2
answers
12k
views
Curve fitting using an asymmetrical sigmoid function
This is probably going to sound trivial, as I am new to Mathematica and still busy reading the Getting Started materials.
I have a series of observations:
[(duration, speed sustained for duration), ....
- 43
4
votes
2
answers
885
views
Non-linear-Model-Fit problem in mathematica
I have written the following code to fit the function g2 to data (a,b,c,d) but I don't realize where I have made a mistake,without ...
- 41
4
votes
2
answers
954
views
FindFit and NMinimize to fit a parametric model (minimize the distance of two curves)
I am trying to find a fit to the cumulative distribution of a set of points using FindFit or NMinimize.
In particular, I would like to find the parameters of the cdf of the Beta Distribution that ...
- 661
3
votes
0
answers
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 ...
- 70.9k
2
votes
1
answer
174
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
...
- 1,816
2
votes
1
answer
145
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 ...
- 33
2
votes
1
answer
395
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/...
- 421
2
votes
1
answer
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 ...
- 297
2
votes
3
answers
206
views
Fitting two equations to diferent parts of the same dataset
I have a system that transit between two different states. Each state output varies linearly with time, given by $m t+c$, where both lines intersect the $x$ axis in the same point. The output of this ...
- 1,022
1
vote
1
answer
88
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 ...
- 13
1
vote
3
answers
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 ...
- 8,059
1
vote
1
answer
727
views
How to simulate Multifractional Brownian Motion?
The maximum I would ask, is hints, how to model MFBMotion.
Link to paper
Firstly, i wanted to simulate in MATLAB that code:
...
- 27
1
vote
1
answer
615
views
Estimating parameters on system of differential equations
I am looking for some help estimating the parameters of a series of differential equations to assist fitting the experimental data I have collected.
The Problem:
The equations are based off of the ...
- 65
1
vote
3
answers
198
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)
...
- 280
1
vote
1
answer
1k
views
How do I properly use Sow and Reap within a Do loop?
The problem is that reap only returns one value when I was expecting a string resulting from Do.
For context:
This is a simple democratic deficiency model. Where m is the
number of periods, n is ...
0
votes
1
answer
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{...
- 455
0
votes
0
answers
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.
...
- 191
0
votes
2
answers
1k
views
How can I fit a differential equation to experimental data?
I would like to add a fit to the following data. Here is the differential equation I am using. g=9.81 l=0.2 m=0.09
...
- 135