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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Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
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178 views

What differential equation might model this almost-harmonic oscillator?

I need to precisely control the motion of a damped, driven (nearly) harmonic oscillator: $$ \ddot x(t) + \alpha\dot x(t) + \omega_0^2 x(t) \approx V(t) $$ I use the $\approx$ symbol because this is ...
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3k views

Mathematical Modeling of Real-World Situations

I was considering how to model the following problem mathematically and was wondering what you thought the best way to do it is. "A takes 1 minute to cross a bridge, B takes 2 minutes, C takes 5 ...
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171 views

Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
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42 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
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85 views

A mathematical abstraction of colours?

Does any formal system exist built upon the mechanics of Additive Colour Theory? Additive Colour Theory is the description of the behaviour of the visible spectrum of light as it combines-the ...
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46 views

What resources (books, videos, etc) to help develop math thinking skills?

I am a applied mathematics major and have taken basic undergraduate coursework up to multi-variable calculus, ordinary differential equations, and elementary linear algebra. I am currently taking ...
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88 views

How can I find a tranformation matrix/Mathematical relation between two 5th degree polynomial curves in space?

I have the equation of two 5th degree polynomials which they don`t intersect with each other .Each curve is made of 100 points and these two curves looks similar but there are small differences .I am ...
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48 views

Mathematical interpretation of pressure (gradient)

I'm having some problem with the following. Usually, the pressure of some mass on an area A is defined by $$P=\frac{F}{A}$$ where $F$ is the force of the mass exerted due to gravity. However, here ...
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139 views

How to solve the advection equation with spiral motion

The advection equation is : $$\frac{\partial f(x,y,t)}{\partial t} + \nabla_{(x,y)} \cdot (A f)= 0$$ With initial condition $f(x,y,0) = f_0(x,y)$. If the vector $A$ is constant, ie. $A = ...
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47 views

How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
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57 views

is possible to deduce a formula for vaccination coverage from Whittle threshold theorem?

I am reading the article Application of Whittle’s stochastic threshold theorem to a chickenpox outbreak and I can't understand the meaning of the term "intensity" in the Whittle threshold theorem. In ...
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81 views

Question regarding the projective models of the anti-de-Sitter spaces and good online references for learning them from the scratch? (Specifics below)

As my title says above, I am trying to find answers to and also good online reference where I can find complete description of projective models of hyperbolic space, de-Sitter space and anti-de-Sitter ...
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81 views

Boltzmann machines - motivation for the energy function

I've been studying Boltzmann machines lately and was wondering if anyone could give me a "high-level" explanation or motivation for the energy function used: $$E = -\sum_{i<j} w_{ij} \, s_i \, s_j ...
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106 views

How to model bending, folding of 2D figures?

2D shape can be folded in various ways. For example, trapezoid can have its sides (with the acute angles) folded, so that it will effectively become rectangle – with the difference, that part of the ...
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175 views

economic modelling asked for

I am putting together a proposal for a system of economic exchange which links a transaction of money through a period of time, and subjective relationship evaluation between two people. How can it be ...
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20 views

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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81 views

mathematical model of an assignment/scheduling problem

I am solving a scheduling problem and I am able to abstract it into an assignment problem of assigning 45 machines to 42 jobs. the assignment problem was given as having 14 jobs, each with 3 tasks and ...
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58 views

Predicting profit with price variation

I am currently working on a high school project that aims to predict profit from X amount of items to Y amount of profit based off a deviated sale price. For instance: I sale 10 cookies for 10 ...
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77 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
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101 views

Is it compulsory to make transformation to the econometric model in order to have only diagonal elements on variance-covariance matrix of errors?

I need some sharped and advanced advices for the following issue ... Model and its assumptions I'm working on the methodology of a two-way error component model. Here is the model: $y_{jis} = ...
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284 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
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173 views

A good book on convolutional neural networks

Good evening! Don't you know a good book on convolutional neural networks, where the next questions are highlighted: 1) How are the backpropagations for convolutional and pooling layers are ...
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64 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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69 views

Calculating heterozygosity of a population as size increases (combine growth and genetic drift equations)

I am working on a assignment to program a genetic drift simulator and include population growth. My program works fine as far as I can tell, and I have the not unexpected result that in the time I am ...
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189 views

Formalizing quantities that have units

This is a bit of a weird idea, so any advice on how to make it clearer would be welcome. Please leave a comment. Suppose we're using mathematics to study electronic circuits. We're probably ...
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77 views

How to define an objective function that conveys the concept of selecting the best elements in a set

Consider a set of tasks $\mathcal{T} = \{t_1, \ldots, t_I\}$. Consider also a set of workers $\mathcal{W} = \{w^1, \ldots, w^J\}$, where each worker $w^j \in \mathcal{W}$ is associated with a value ...
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103 views

Differential Equations & Sinusoidal Functions

I am developing a model for sales forecasting, the basic premise of which is that the rate of change of sales is proportional to the number of possible buyers. In developing this model, I came up with ...
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152 views

Considering the predator prey model to find the range of values to be a spiral

I have the following problem: Consider the predator-prey model: $$\frac{du}{dt}=u(1-\alpha(u)-v), \frac{dv}{dt}=\rho(-1-\alpha(v)+u),$$ where $\rho$ and $\alpha$ are positive parameters with ...
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78 views

Measuring Model Bias

If given the choice between two statistical models (for argument's sake, let's say Model 1 is $y = \beta_0 + \beta_1 x_1 + \epsilon$ and Model 2 is $y = \beta_0 + \beta_1 x^2_1 + \epsilon$), is there ...
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101 views

Modelling randomized cup stacking, animal behaviour

This question has no scientific relevance for me whatsoever, but is a real life question which left me puzzled for a while. Even though I am not going anywere with this, maybe there is still somebody ...
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322 views

Finding a model for multiple non-linear regression

I want to implement a regression analysis, but I have problems with finding a model for the given data. There are $149$ $(x,y,z)$-values. $y$ values are all positive, $x$ is between $[-10, 10]$ and ...
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146 views

Check my solution - Modelling of a spring with Differential Equation

I am doing some work with differential equations. I have solved the following problem but am uncertain if I'm doing it correctly. Could someone look over it for me and check if I'm doing something ...
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157 views

How to model server load?

I want to model the server under load. I'm using following assumptions: The server serves only one request at a time, and all requests take him exactly 100ms to process. All requests that came ...
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261 views

Legendre Polynomials

I was given a "generic" matrix that I was told was constructed using Legendre Polynomials. ...
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121 views

Transformation induced by a spherical mirror

This is at heart a mathematical problem, but is best motivated in physical terms. I'll introduce a very special case and move on to the general case later. Special case An object, taken for ...
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47 views

Deriving functions for empiracal distributions -very applied mathatics

First I am a new user of this site. Second my math background is very limited, although I do have a lot of experience in applied statistics. Component or piece part failures on high value parts($1000 ...
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35 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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33 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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19 views

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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11 views

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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14 views

reference for regime shifting models

I'm looking for a good introduction to regime shifting models. It would be nice to see things like simple example of regime shifting models, ways to detect a regime shift in data, fitting regime ...
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36 views

Drawing a phase diagram

I am working through an example to draw a phase diagram the DE used is $\frac{dx}{dt}=xy(x-1)(x-y)$ In the first step I have to identify the isoclines by setting $\frac{dx}{dt}=0$ having done this I ...
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19 views

How to model a coding problem with Poisson Distribution

I've met a problem in information theory that deals with probability and number of occurrence. It states that: The probability of a single bit being corrupted is p. Now I have an error-correction ...
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31 views

What is a bifurcation point?

Given a density dependent difference equation, $N_{n+1}=N_{n}e^{r[1-(N_{n}/K)]}=f(N_{n})$, with $r > 0$ and $K > 0$. I've found that the equilibria are at $N^*=K$ or $0$. Discussing their linear ...
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20 views

Discrete logistic model

Given a difference equation such as N_{n+1}=N_{n}exp^{r[1-(N_{n}/K]=f(N_{n}). What does it mean when they say density-dependent difference equation?
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116 views

Study the stability of the following ODE: $u'=u(1-u)-\alpha$

Given that $\alpha$ is real, I'm being asked to give a basic analysis for this nonlinear ODE. However the problem is that I'm having trouble understanding how to pick the conditions we need to study ...
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15 views

From kinetics rate to individual probabilities

I'm building an agent-based model for convection-reaction simulations. Basically my particles are moving at a certain speed in their environment and when they encounter receptors they can bind to them ...
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30 views

Regression analysis model vs mathematical model

Can anyone explain the difference between the equation generated from a regression analysis as opposed to a mathematical model such as $E = m \cdot {c^2}$ type models?
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39 views

Forming a differential equation from game

I was wondering if someone could help me form a differential equation from the following game: A population consists of two types of diets, fish and veg. People play a with every other person and the ...