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 ...
- 2,471
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 ...
- 65.6k
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 ...
- 19.6k
22
votes
Accepted
Couple a PDE and ODE in NDSolve
Modified Newton Cooling Law implementation and reduced FEA cell length
...
- 7,485
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 ...
- 84.6k
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 ...
- 4,325
16
votes
Accepted
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):
...
- 58.7k
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 ...
- 63.4k
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 ...
- 104k
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 ...
- 8,576
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
...
- 384k
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 ...
- 233k
12
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 ...
- 41.8k
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 ...
- 69.9k
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 <...
- 69.9k
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 ...
- 5,423
11
votes
Accepted
Refining mesh size leads to absurd results for a coupled heat transfer FEM model
This is a typical numerical instability due to FEM matrix inversion. On the fine mesh there are big numbers in Navier-Stokes equation of about $1/h^2$, therefore at $h\rightarrow 0$ we have singular ...
- 41.8k
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?
...
- 270k
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 ...
- 136k
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):
...
- 19.5k
10
votes
How to Create Kapitza's Pendulum?
Elaborating on Alex Trounev's solution. The trick with this inverted pendulum is, that for some frequencies it stays upright instead of falling down. Here is an example where I adjusted the frequency.
...
- 47.1k
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 <...
- 384k
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 ...
- 41.8k
8
votes
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:
...
- 40.3k
8
votes
Accepted
Time dependent Schrödinger equation in 2D
Something like the following should do. It employ the finite element method.
...
- 104k
8
votes
Accepted
Showing that a Hopf bifurcation exists?
We can use my EcoEvo package, despite the fact that this doesn't seem like an ecological model.
First, install the package (only needs to be done once):
...
- 19.5k
8
votes
Accepted
Numerically solving a system of SDE's with Levy noise?
To simulate Levy jumps we can use numerical model described in the paper Analysis of a stochastic SEIS epidemic model with the standard Brownian
motion and Lévy jump. In this model we use ...
- 41.8k
8
votes
Accepted
Finding a continuous distribution that fits the empirical density of dataset $1,1/4,1/9,1/16\ldots$
Note: Edited to focus on the CDF rather than the moment generating function.
If $X$ is a discrete random variable taking on values $1,1/2^2,1/3^2,1/4^2,\ldots$ with relative frequencies $1,1/2^2, 1/3^...
- 40.3k
Only top scored, non community-wiki answers of a minimum length are eligible