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Questions tagged [modeling]

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

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1answer
189 views

Solving Differential Equation System for HIV Treatment Model

I was working on a project about optimal strategies for HIV treatment, models used from [Butler, Kirschner, and Lenhart] 1997. This model explains the spread of HIV viruses in the human body, where ...
0
votes
1answer
30 views

Fit data with a given function depending on parameters

I want to fit the data of a star's temperature with a function from a model. That function depend on several parameters. I want to know how can I find the value of those parameters. The data is: <...
0
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1answer
56 views

Model fitting for concave curve: test if asymptote or convergence exist

I am asking a double check if conceptually I set up proper model and proceeding in good direction to drive conclusions. I have a distribution that looks like this: I want to test if for increasing x ...
12
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1answer
352 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 ...
2
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3answers
115 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 ...
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1answer
74 views

Finding the limit of a function

I have the following code: ...
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1answer
62 views

Infinite potential, prevent value to go beyond zero, initial value problem

How do you make a wall potential in Mathematica. Meaning : I want my potential to have a wall at 0 : $ U(x)=\left\{ \begin{split} & x>0 : U(x) = f(x)\\ &x=0: U(x)=U_0 \\ & x<0: U(x)=...
1
vote
1answer
106 views

How to plot a trajectory of Lorenz attractor system model (SystemModelSimulate - v11.3)

I'm using one of the system models provided with Mathematica 11.3. (I found it by evaluating SystemModelExamples[].) ...
0
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2answers
62 views

Difficulties in compiling the steady state of a biological model

I am modeling the yellow fever for an EDO system, in which I have to find the stationary states of the system, and I have great difficulty in finding something that can be very simple. I put the ...
38
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1answer
867 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 ...
0
votes
2answers
370 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 ...
9
votes
1answer
501 views

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

I've done an experiment where I swung a pendulum under air resistance. Is it possible to model the data using the following differential equation and find a b-value? ...
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0answers
46 views

Dealing with Vector Outputs from ItoProcess, RandomProcess (Stochastic Differential Equations)

I'm modeling stochastic chemical kinetics and the ItoProcess[] function has served me well. I am trying to write an efficient code to analyze many (Paths) trajectories of several different reagents (...
2
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1answer
102 views

determining solution to PDE with Mathematica

Bug introduced in or after 10.3, persisting through 11.2. It's been a while since I have touched separation of variable and not too keen to "get my hands dirty" if I may avoid it. The given PDE is ...
3
votes
2answers
127 views

Solving ODEs with ParametricNDSolve and fitting parameters to data (Not a list of real numbers)

I saw some similar posts here, but none of them gave me a solution. I have this set of data: ...
2
votes
1answer
107 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 ...
3
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2answers
163 views

Is it possible to find the transfer function of these three differential equations using Mathematica

Imagine you are attempting to obtain a model of a device with two inputs [u1, u2] and three outputs [O1, O2, x] from the Lagrangian. After some of Lagrangian work, you find the following three ...
7
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2answers
482 views

Why does NonlinearStateSpaceModel linearise?

The documentation for NonlinearStateSpaceModel says: In NonlinearStateSpaceModel[eqns, ...] the Taylor linearization is with ...
0
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0answers
108 views

Help to model fitting a distribution of weights in weighted graphs : power or exponential law?

I found this post https://math.stackexchange.com/questions/164436/difference-between-power-law-distribution-and-exponential-decay useful, but not sufficient for me to understand which law may best ...
0
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1answer
134 views

Random placement of non-overlapping disks

I am trying to create a Monte Carlo simulation for a physical situation. The situation is a layer of disks are lying on a plane. The disks have a known mean radius and standard deviation, and a known ...
-3
votes
1answer
237 views

How to approximate the data curve with a function? [closed]

I want to approximate a data curve (the purple curve in the picture) with one function, so I can use it in my engineering simulation. Some explanation of purple curve The curly part is a sinusoid; ...
1
vote
0answers
127 views

2D Electro-diffusion Model with NDSolve

Set Up I am attempting to make a 2D model of the diffusion of ions in solution due to concentration gradients and an electric field. The equation that needs to be solved to describe the diffusion is ...
4
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0answers
85 views

Implementing a model of electro-diffusion [closed]

I am an undergraduate researcher. I have been working with Mathematica for roughly a month. I have been assigned a modeling task. My objective is to model the diffusion of ions in solution under the ...
3
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0answers
152 views

Power law fitting package that optimizes fitting parameters based off of the KolmogorovSmirnov MC method

I'm exploring power law fitting and would like to get to a point of making a power law package like what was discussed in this post, where OP references the R poweRlaw package. As per the comments/...
3
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1answer
90 views

How to compute “SinglePredictionConfidenceIntervalTable”-Values on validation data with NonlinearModeFit?

When I perform a NonlinearModelfit I get a FittedModel object and I can see the values of the property "SinglePredictionConfidenceIntervalTable". Now I apply the FittedModel object on a new data case (...
4
votes
1answer
145 views

How to use FindFit to optimize parameters of a WSM model via WSMLink for a parametric curve

I have I-V (current-voltage) data which I am trying to use to calibrate a PV solar cell model in WSM using WSMLink from mathematica. I am using the FindFit function which simulates the model with each ...
0
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3answers
131 views

Reduce (or Solve) a set of inequalities assuming some independent variables are unbounded

First a summary of the general problem I'm trying to solve: I want to get a set of inequalities for a very complex function (If you are interested is the no-arbitrage conditions Black-Scholes equation ...
8
votes
2answers
418 views

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

I am trying to make an agent based model similar to http://demonstrations.wolfram.com/DiffusionLimitedAggregationARealTimeAgentBasedSimulation/ http://demonstrations.wolfram.com/...
1
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1answer
119 views

Creating an Interactive Module that plots a graph and a highlighted vertex

For an assignment, I have to do the following: Build an interactive model with two controls, n and u, that generates a random ...
3
votes
1answer
164 views

Local optimization of parameters in a Coupled Non-Linear System

I have a system of differential equations : $\frac{dX}{dt} = (0.8+0.4c_{1})X-(0.007+0.006c_{2})XY$ and $\frac{dY}{dt} = (0.048+0.004c_{3})XY-(0.4+0.2c_{4})Y$ where $0\le c_{i}\le1$. Varying $c_{i}...
41
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5answers
15k views

My Girlfriend is going to prison…Save her with Math

Salacious title, but true story. ...
1
vote
1answer
600 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 ...
4
votes
2answers
420 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 ...
0
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2answers
125 views

Can NonlinearModelFit be used instead of TimeSeriesModelFit without loss of generality?

I am trying to model sales seasonality. As I am unfamiliar with TimeSeriesModelFit[], I am using NonlinearModelFit[]. However, ...
17
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1answer
817 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 ...
3
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2answers
4k 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), ....
0
votes
2answers
188 views

From the data the growth of tumor spheroids determine doubling time using Mathematica and by hand

Task: From the data the growth of tumor spheroids determine doubling time Link to the data. My idea was to use least squares method and Mathematica to helps me find result. But I think that this is ...
5
votes
1answer
210 views

Manipulating 2D graphics along the surface of a 3D sphere according to their centroids' latitude/longitude

I'm trying to make an unsophisticated 3D model of a continent's path on a globe consisting of snapshots of the planet surface that follows the historical trend of continental drift. By "...
0
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1answer
147 views

Help Modeling Average Of A Gaussian And A Function

I am trying to recreate some results from a simulation that I have but I am having trouble re-creating the expressions/funcitons in mathematica. In my simulation I have a data set consisting of (z,x,...
14
votes
1answer
311 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, ...
2
votes
1answer
105 views

How to model a two-phase motion with Manipulate

I was trying to use Manipulate to model a simple two-phase motion. In the first phase, a cart moves on a track in one-dimension with a certain acceleration and velocity. Then in the second phase, the ...
2
votes
1answer
348 views

plotting and manipulate plot for logistic model (recursive function)

For a larger project on chaos, I am trying to write a short program that graphs the logistic model with different constant values, in this case the constant being "r". A) Is there a way to use Table ...
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2answers
145 views

Solving ODE's on Mathematica [closed]

I'm having trouble solving a system of ODE's on mathematica. Any help would be appreciated ...
2
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0answers
181 views

Modelling heat exchange between flowing fluid and surroundings

Starting from this question: Couple a PDE and ODE in NDSolve I would like to modify the fluid from static to a flowing one in the y direction. that's the original code that I modified a little bit: ...
1
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1answer
165 views

Why is NonLinearModelFit giving me a (significantly) more accurate result than LinearModelFit for a linear model?

I am working with a fairly large dataset, and at one point I need it to be fit to a complicated model (along the lines of ...
17
votes
1answer
678 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
votes
2answers
325 views

Sound synthesizer using Manipulate

Sound synthesizers, both digital and analog, often include a parameter section for shaping the amplitude of a sound wave over time. This parameter section is commonly known as an "ADSR EG" (attack, ...
1
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1answer
676 views

Multivariable non-linear fitting

I have a function called "C" that I know it depends on 6 variable. I have a set of data points, 6 rows by 9 columns, in which in each row only one variable is changing and the rest of the variables ...
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1answer
115 views

How to make this model in wolfram mathematica?

A model production possibility curve (nonlinear case). I used 1/4 of a circle in the code. ...
4
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1answer
94 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...