44 votes
Accepted

In what way can M11.3's system modelling features be used by those who don't have SystemModeler?

I'm one of the developers behind this functionality, so I might be biased, but in my opinion this does provide a huge new feature set to Mathematica users. What practical use do these new functions ...
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  • 2,442
28 votes
Accepted

Backtesting a Probability of Default (PD) model

This kind of backtest is often performed using approximations, for instance with normal distributions, which may not be always valid. An exact test would be very nice to have. The probability ...
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24 votes

My Girlfriend is going to prison...Save her with Math

Similar to previous answers, only I don't make the instantaneous absorption assumption since it isn't really necessary. The equation can be found here on page three, where ka and ke are the rates of ...
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21 votes
Accepted

Couple a PDE and ODE in NDSolve

Modified Newton Cooling Law implementation and reduced FEA cell length ...
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  • 7,247
16 votes
Accepted

Sound synthesizer using Manipulate

First let me observe that your coding style makes debugging difficult, I highly recommend breaking giant expressions into manageable pieces. Second, in the code below I have used a different ...
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  • 83.6k
16 votes

Generating random sequence of integers with ordering constraints

Perhaps have a look at DiscreteMarkovProcess using an appropriate transition matrix embedding your constraints? Here's a simple example, implementing 1-5 above, to ...
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14 votes

My Girlfriend is going to prison...Save her with Math

Assuming the simplest kinetic model for elimination (and making the simplifying assumption of "instant absorption" to peak concentration): ...
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  • 55.2k
14 votes

Mass Transport Model

OK. Let me extend my comments to an answer. First of all, I'd like to point out why OP's attempt doesn't work: "NDSolveValue should return a list with three ...
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  • 54.2k
13 votes
Accepted

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

Here a couple of changes/suggestions. Using a decimal dot for all constants forces most algorithms to switch from symbolic to numeric routines with machine floating point arithmetic; that's typically ...
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12 votes
Accepted

Why does NonlinearStateSpaceModel linearise?

Consider a model where the nonlinearity is in $x'(t)$ and not in the highest derivative $x''(t)$. eq1 = {x''[t] + Sin[ x'[t]] + x[t] == u[t]}; Choose the first ...
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  • 8,382
12 votes
Accepted

Can I use a differential equation as a model to make a fit to experimental data?

Mimicking the examples in FindFit >> Applications >> DifferentialEquations NonlinearModelFit >> Generalizations and Extensions ...
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  • 350k
12 votes
Accepted

Speed up NDSolve compared to Python (calls to LSODA)

First question. I'm pretty sure that the difference is due to what happens with machine underflow. As of V11.3, underflow goes to machine zero instead of to arbitrary-precision numbers (as it does in ...
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  • 220k
11 votes
Accepted

Implementing the Biham–Middleton–Levine traffic model as CellularAutomaton

The following code simulates the Biham-Middleton-Levin traffic model for 1000 iterations using explicit rules. According to Wikipedia the blue and red cars take turns to move, which means each step is ...
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  • 68.9k
11 votes
Accepted

Use a picture as the initial distribution of an agent based model

You have to use ColorNegate and other image processing functions to make the area that you want to sample is white, while the rest is black. After that you can use <...
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  • 68.9k
11 votes

Large deformation of solids

It is not 2D problem, but 3D problem. So we actually need some 3D model to describe deformation. But before do this, we can describe the problem in the beam theory. Fortunately, this problem has exact ...
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  • 34.7k
11 votes
Accepted

Large deformation of solids

I think you guys are using the wrong theory, as far as I understood the code above. Sadly I only have little time, and in this answer I can only give you the theory without code. If I read your code ...
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10 votes

Mathematica Implementations of the Random Forest algorithm

As of version 10.0 there is a built in implementation of Random Forests which is accessible through the Classify function. ...
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10 votes

My Girlfriend is going to prison...Save her with Math

I have no experience with what you are trying to do so this is entirely guesswork but maybe you want something like this? ...
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  • 265k
10 votes

Why does NonlinearStateSpaceModel linearise?

My guess is to be able to have the same internal representations as for linear systems. It is not possible to represent a system using A,B,C,D state space standard ...
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  • 113k
10 votes

Mathematica code for bifurcation diagram in 3D

Looks like a little three-species food web model -- a perfect excuse to use my new EcoEvo package. First, install the package (one-time only): ...
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  • 18.1k
9 votes
Accepted

Computing launch parameters for hitting a point in 3D with projectile under influence of wind

You may use NMinimize[] on the results of ParametricNDSolve[] like this: ...
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9 votes
Accepted

Why doesn't Mathematica completely draw the fit?

Add the option PlotRange (say PlotRange -> {{0, .006}, {0, 90}}), and use data2 as <...
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  • 350k
9 votes

Mass Transport Model

Thanks to @xzczd answer we can reproduce solution with FEM. First we should note that $[A]+[B]+[C]=[A]_{bulk}$ in a case of equal $D_A=D_B=D_C$, therefore we can exclude equation for $[A]$ and resolve ...
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  • 34.7k
8 votes
Accepted

Find fit of an experimental PDF

Pure GammaDistribution does not seem at all like a good fit even visually. You need probably a MixtureDistribution. You could ...
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8 votes
Accepted

Find best equation for data and the area under curve

A curve that is a multiple of a gamma distribution seems to fit: ...
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  • 34.8k
7 votes

Use a picture as the initial distribution of an agent based model

you can use PixelValuePositions ...
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  • 8,568
7 votes

Solving Differential Equation System for HIV Treatment Model

Structuring the script. ...
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  • 3,643
7 votes
Accepted

Fitting multiple data with model and NDSolve with different initial conditions, and other shared parameters

The subject of parameter fitting comes up frequently on MSE. Parameter fitting is a difficult subject and will depend on your data quality, your model, and your intial guesses. I have been dabbling ...
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  • 16k
7 votes
Accepted

Find the best fit with some conditions

I'm not sure why FindFit can't manage it, but if I construct the objective function myself to minimize square residuals and I use ...
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  • 20.5k
7 votes
Accepted

Time dependent Schrödinger equation in 2D

Something like the following should do. It employ the finite element method. ...
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