Questions tagged [modeling]

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

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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
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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
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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
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How to optimize ODE parameter fitting?

Consider the data ...
• 4,179
1 vote
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• 351
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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
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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 ...