A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

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Building a dynamical system

Suppose I have a 4 dimensional system with 4 fixed points: $Q_1 = \left(p_1,0,0,0 \right)$, $Q_2 = \left(0,p_2,0,0 \right)$, $Q_3= \left(0,0,p_3,0 \right)$, and $Q_4 = \left(0,0,0,p_4 \right)$. ...
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36 views

What is elnekiti's triangle? (edited) [on hold]

Elementary ceĺular automata shows amazing complex systems such as pascal's triangle is similar to " wolfram rule 90 " , so i looked over youtube searching for extra content and i found this video Here ...
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Modeling smoke cloud as expanding Gaussian / ellipse

I am making a simplified model of smoke coming from a train's smokestack. You can imagine that if you want an accurate model you have to think in 3D and use computational fluid dynamics and stochastic ...
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8 views

What are the mathematical descriptions for a spatially dependant concentration to be 'well mixed'?

Suppose we have a concentration $c(x)$, suppose for instance it is a chemical species, in the region $[0,L]\subset\mathbb{R}$. What are the different ways you could mathematically describe the 'well ...
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1answer
16 views

linear programming : Absolute value in constraint in mathematical model

I have a model have an constraint with evaluation of absolute value , a example can be: function objective : $\max \sum(x_i)$ statement: $x_i\geq |(y_i-t_i)|$ for all $i$ but value absolute ...
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24 views

Population models - 13 months in a year

I'm currently studying mathematics at university and have come across a question about finding the population of rabbits in a colony, where the growth rate is given in terms of per month. However ...
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38 views

exact solution to lotka-volterra equations

I am looking for exact or perturbative solution realistic lotka-volterra (the one with logistic term in one of the equations) equations in population dynamics. Any reference where they have done it ...
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1answer
58 views

Heat equation — Modelling a real-life situation

I have read through a lot of books and lecture notes that cover the heat equation and I am still not sure how I would model the easiest real world situations. For example, take a rod at constant ...
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189 views

Explaining Mathematical Modelling to a nonmathematician

Due to the interdisciplinary nature of my project, I find myself collaborating a lot with nonmathematicians especially biologists, medical doctors, etc. I work mostly on mathematical models as applied ...
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17 views

Markov-Chain Monte-Carlo: Are transformations on the inputs valid?

The problem: I am trying to solve a high dimensional (up to ~50) class of data fitting & modelling problems. The user specifies the problem, so I would like to make the configuration as easy as ...
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3answers
22 views

How can mathematical models be applied to image analysis

I'm quite interested in how mathematical models can be used in analysing images. For example, I'm aware that mixed effect models can be using in image analysis but I was just wondering if there are ...
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29 views

How to model compartment chemical concentration with permeation through a membrane

Suppose we have one chemical species $V$ and two compartments in which $V$ can be, $A$ and $B$, with volumes $\Omega_A$ and $\Omega_B$ respectively, where $\Omega_A < \Omega_B$. Compartments $A$ ...
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Given a set of arbitrary data, is it possible to model this data using differential functions.

Problem At the moment, I have a problem with seven variables: $S, A_1, A_2, R_1, R_2, P_0, P_1 $ and $P_2$. Each of these variables draws a smooth line through time. My question is, is there any ...
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62 views

Math behind No Man's Sky, or Math of Minecraft in Space [closed]

I recently received a question from one of my students which is a bit outside my life experience. However, I expect this may be of interest to many: I was reading up on a new video game that's ...
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14 views

Understanding compound distribution and plotting the mixed distribution graph

If $N$ takes the values $0, 1$ and $2$ with probabilities $½, ¼ $ and $¼ $ respectively, and the $X_i$ ’s have a $U(0,10)$ distribution, draw a sketch of the frequency distribution of $S$. $N$ is the ...
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31 views

How to generate a function with multiple variables to fit experimental data?

I am researching methods to increase the accuracy of an algorithm that is currently used to analyse radiation patterns as they hit our sensor. (For the non-physicists, we will mainly see Alphas, ...
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3answers
38 views

How to re-write the following equation?

I am a molecular biologist and reading a book on mathematical modeling. In this book I encountered the following algebraic conversion and could not figure out how the conversion is performed. Please ...
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23 views

Survival analysis with a parametric model for recurrent events and time-dependent covariates

My goal is to model waiting times between recurrent events with time-dependent covariats with parametric models (Poisson, Weibull, log-normal etc.). This is not an issue time-dependent covaraits as ...
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2answers
60 views

Integrating a First Order Differential Equation (The West Equation)

I am currently doing a project about Growth and have found this really interesting Math Model by Dr. Geoffrey West et al in 2001 while researching. The paper can be found at this link. I was ...
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1answer
34 views

Spring-mass System Phase Plane

If a spring-mass system has a friction force proportional to the cube of velocity, then $$m\frac{d^2x}{dt^2} + a\left(\frac{dx}{dt}\right)^3 + kx = 0$$ (a) Derive a first-order differential ...
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31 views

How to transform one polynomial curve into another

I have a problem: I have two polynomial splines: For red curve I have used Rational fraction function with p=3/q=2 and for blue curve I have also used rational fraction function with p=1/q=3 It ...
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51 views

Differential equations, chemical reactions

A chemical substance A changes into substance B at rate $\alpha$ times the amount of A present. Substance B changes into C at rate $\beta$ times the amount of B present. If initially only substance A ...
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2answers
23 views

ordinary differential equations-morphogen gradient

I am reading a paper by Merkin and Sleeman (2005) Find the approximation solution of $(u')^2=\frac{2}{k}(u-\frac{1}{k}\ln(1+ku)); ~~u(0)=1$ for $k$ sufficiently small. they gave the following ...
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60 views

Can car traffic be managed by mathematical formula? [closed]

How car traffic is managed? Is it managed by mathematical algorithm? Or by human(operator)? If it's by operator, can it be managed mathematically? Or is it by physics? By what theories/formula? ...
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System of separable diff. eqns, explicit solution and curves, Lotka-Volterra model

In the book on p.68 is a system of differential equations for a Predator-Prey model (Lotka-Volterra) given as: $$ \dot x=x(\alpha-c\gamma) \\ \dot y=y(\gamma x -\delta) $$ On the next page, it is ...
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Modeling, Measuring, and Maximizing “Mixedness”

Possible key-terms: combinatorial optimization techniques; simulated annealing; genetic algorithms; Kirkman's schoolgirl problem; Steiner triple systems; orthogonal regrouping. Background: My class ...
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Choose Scaling for t

My question is the last part of the d) part of the exercise 1.17 in Mark Holms' Introduction to Applied Mathematics. The exercise is given below, where I have emphasized the part of it that is my ...
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1answer
33 views

linear or bilinear interpolation

I want to know how to use linear and bilinear interpolation in 2D. Specifically the pairs $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$, and $(x_4,y_4)$ are given in a quadrilateral. In this case how to ...
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32 views

Rain forecast model and least squares

Good evening everyone, I'm trying to create a rain forecast model, I have about 720 data, which correspond to monthly rainfall in 60 years during the 12 months of the year. I have a matrix ...
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1answer
28 views

Probability of agreeing to do some work depending on the payment

I am looking for several options of modeling the probability of people agreeing to do some work depending on the price/payment. The payment can only range between $p_1$ and $p_2$, $(p_1 < p_2)$. I ...
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13 views

Modeling reasons for minimizing the distance between parameters

In system identification, when new parameters are calculated, is there any reason for the parameters to be close to the original parameters ?
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reformulating an integer quadratic problem into a linear integer problem

I am trying to solve an optimization problem, in order to find an optimal runtime schedule for a machine. It involves one boolean variable $x_{t} \in \mathbb{\{0,1\}}$, that describes whetever the ...
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Calculating weighs in a model

I am creating an index related to walkability. For this I have sevaral factors like length of sidewalk available, user perception rating on various measures of performance, and many other factors. My ...
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16 views

Concatenated model for 2D?

I am looking for a way to perform 2D convolution through a concatenated model. I am not looking for a faster way of doing 2D convolution. My objective is to find a scheme where I can perform it in ...
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2answers
44 views

Laplace Transform of derivative squared

I'm trying to solve a problem while I'm studying Control Theory and I came up with a difficult question. $ \mathcal{L}\left[y'(t)^2 \right] $ Basically I need to find the Laplace Transform of this ...
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18 views

Finding ratio of four value factors

Before reading this i know the question i asked can be answered based on our strategies, but i'd like to know the methods of quantifying these strategies into numbers. I'm doing subscriber profiling ...
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30 views

How can I show that $x'(t) = - (1-x(t))'$ from $x(t)$'s functional form?

I have a differential equation modelling the concentration of vaccinators in a population. Here are a few assumptions. Assume we can write the concentration of vaccinators as $x$, and that we can ...
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Conversion of cylindrical harmonic field into space-harmonic field for plane waves

It is well known that a plane wave can be represented by an infinite sum of cylindrical wave function of the form $\varphi^i(\rho,\phi)=e^{\left(-j\beta \rho ...
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“Damping factor” for a set of non-linear ODEs

I am not sure if this question is on-topic here I have a set of four non-linear ODEs representing a negative feedback. I have done parameter variation by random sampling to study the sensitivity of ...
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42 views

Modelling a warehouse in optimization?

I am trying to model the following rather general optimization problem. Let $p_{t}$ be a given non time series of product prices. These are fixed points $p_{t}$ is not described as a random variable. ...
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35 views

nondimensionalisation for an ODE

I need help to understand 'nondimensionalisation' for ODEs better. I stacked how to deal with a constant input in a prey-predator model. I reproduced the following ODE system ...
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Averaging Models in Excel

I am working in Excel and have two sets of data points that come up with a percentage for the likelihood of a recession. I am wondering what the best strategy would be to combine these data points? ...
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1answer
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what is the influence of the specific statistical model selection in a practical project

I hope this is the right place to ask this question. But if it is not, please feel free to migrate. There is a famous quote, which is like "all models are wrong, but a few are useful". So, I was just ...
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22 views

Discrete sinusoidal to state space

I'm looking to apply an optimal LQR filter to a discrete signal of the form $x[n]=Asin(ω_0n+ϕ)+v[n]$ The amplitude $A$ and the phase $ϕ$ are unknown variables I want to estimate using the filter, ...
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1answer
33 views

modelling the behavior of a particle

I want to study the evolution of a particle as a function of time, then in dynamical systems, the usual thing to do would be to define the state of the particle. Usually we are able to do this by ...
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Methods for Extrapolating Data Close To Observations

I am aware of many different ways to go about interpolating between the values of known data points. However, whenever I come upon (I work in Quantitative Finance) the need to extrapolate data I find ...
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50 views

Mathematics of contamination [closed]

I want to know the distribution of residual material (contamination) in subsequent refills. For example, suppose a cup normally used for transferring salt is used, without cleaning, for transferring ...
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28 views

Solving 2nd order ODE with 2 independent parameters(over finite intervals), with bounds on solution

I have a 2nd order ODE of the form: $\ddot {x} + 2c \dot {x} + 39Ex = 0 $ $Initial$ conditions being: x(0) = 0 and $\dot {x}(0)$=0.1 Where c is in the interval [1,5] and E is in the interval ...
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30 views

Light attenuation through water at an angle

I know that light intensity decreases exponentially governed by \begin{equation*} \frac{dy}{dx} = -ky \end{equation*} where $y$ is the intensity and $x$ is the distance. Now what happens when light ...
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what is the meaning of Ricker model?

How can I interpret Ricker model? It is about population model but it has the term $e^{1-x}$ see: $$a_{t+1} = a_t e^{r\left(1-\frac{a_t}{k}\right)}.$$ http://www.dma.uvigo.es/~eliz/pdf/oman.pdf ...