# What is Mathematical modelling: Definition + 31 Threads

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). Mathematical models are also used in music, linguistics,philosophy (for example, intensively in analytic philosophy), and religion (for example, the recurring uses of the #7, 12 & 40 in the Bible).
A model may help to explain a system and to study the effects of different components, and to make predictions about behavior.

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1. ### Engineering Deriving the Cable Equation from Fundamental Physics Laws

> Note: I am using SageMath to do the manipulations, I will attach it with the post I modeled the problem as a cylinder of height ##\Delta z## and anisotropic conductivity: the conductivity along the axis is different from the one along the radius. Using ##J = \sigma E##, where ##\sigma## is a...
2. ### Modelling Guy Needing Refresher

Hi everybody. I like to model dynamical systems, but over the last few years, I've been busy implementing simulations, without actually deriving their equations of motions. I'm thus here to check with members whether some systems for which I wrote the equations of motions are actually corrects.
3. ### Multidimensional time simulation

If there are computer simulations of four-dimensional space are there any possibilities to digitally simulate a space -time with time having more than one dimension? Please, leave some related links, if possible.
4. ### I Feynmann's connection machine model

Lowly engineer here. I am struggling - I think like many - to develop intuition on DEs. From looking at the history and applications of DEs, general themes that come to mind are, conservation, energy (eg. isochrone problem), causality, feedback (control systems), etc. However, I can't seem to...
5. ### Help Evaluating Mathematical Modelling of Physical Problems

I am really struggling with these problems and do not really know where to begin. In most cases I have just defined what the modelling means, e.g A rough surface is one upon which friction acts etc. I would really appreciate some help with suitably answering these questions comprehensively, and...
6. ### What research designs used on mathematical modelling?

I am currently conducting a study that proposes a mathematical model. "mathematical model (n): a representation in mathematical terms of the behavior of real devices and objects."[1] The study composes of: AIM of the study: Create a mathematical model that represents a phenomena or happening...
7. ### Partial Differential Equation Mathematical Modelling

Salutations, I have been trying to approach a modelling case about organism propagation which reproducing with velocity $$\alpha$$ spreading randomly according these equations: \frac{du(x,t)}{dt}=k\frac{d^2u}{dx^2} +\alpha u(x,t)\\\ \\ u(x,0)=\delta(x)\\\ \lim\limits_{x \to \pm\infty}...
8. ### What is the solution for calculating population growth with mice?

Homework Statement Hey guys I'm struggling to find much information of modelling single species population dynamics that relates to this question. A question like this is going to be coming up in my final exam and I need to be able to solve it. I'm struggling to even know where to start. I'm...
9. ### Finding the Zeros of Damped Harmonic Motion Equations

Homework Statement Solve the damped harmonic motion system \ddot{x} + 2k\dot{x} + \omega^2 x = 0 with initial conditions \dot{x}=V at x = 0 in the cases (i) \, \omega^2 = 10k^2 (ii) \omega^2 = k^2 (iii) \omega^2 = 5, k = 3 Identify the type of damping, sketch the curve of x versus t>0 in...
10. ### Fluid solid interaction boundary condition problem

I have come across the paper attached in which a 1D fluid piston is modeled. I have question on the boundary conditions (BCs) of the system. Essentially, the problem consists of a fluid chamber in contact with a spring (a mass -spring system). ALE is used to move the mesh. I am not certain...
11. ### Scientific Computing vs Applied Math at UMN

I'm graduating this year with a B.S in Computational Physics (the difference is the second semester upper division physics courses aren't required, and are replaced with a year of numerical analysis and a CS minor. But I took the 2nd semester physics back when I was a physics major anyways) and...
12. ### Mathematical Modelling An Object for a System

In order for me to be able to run a simulation I need to write an equation which calculates the distance from a point inside a circle of radius 'r' to any point along the circle's circumference using a point a distance 0<=d<=r from its center. The ultimate system to be simulated is a radially...
13. ### Mathematical Modelling, Vectors and Parametric Equations

Homework Statement Sorry to disappoint the math fanatics but no this is not a question that integrates all three topics at once but individual ones. I still need assistance though with the following more so in the reasoning behind them as I feel my logic is flawed...
14. ### Mathematical modelling of Electric-Thermal-Structuralphysics

Hi i am working on a research paper for which i need very good citation for the analytic analysis coupling Electric - Thermal-Structural physics(via Joule Thomson effect & Thermal stress/strain). Please provide any good source of mathematical relations describing the above complete or in part...
15. ### Master degree - Mathematical modelling or Astro?

I'm an udergrad, 2nd year physics. I recently got interested in solar physics - one reason being, that I was offered to cooperate on a project, where I'll be doing some sunspot simulations. I really like mathematics and I kinda like the mathematical modelling curriculum. However the...
16. ### Engineer who wants to do Mathematical Modelling.

Hello! I am on my last year of study for my bachelor degree in Mechatronics. Looking back at my courses I can say that what I want to do with my life is mathematical modelling of systems (Be they technical, financial, whatever). My favorite courses so far were the mathematical ones and the...
17. ### Mathematical Modelling question

Though this question is about medicine, the actual question has little to do with medicine and more to do with modelling .. Homework Statement A patient is put on an intravenous drip at time t=0, the drip supplies a drug into the patients bloodstream at a constant rate λ. At the same time...
18. ### Equilibrium solutions in mathematical modelling

Hi, I don't want to list the exact problem I have to solve, as I would rather do it myself, all I would like is some guidance. The problem is a function like: Pk+1=a (Pk-1) with a few more constants and some brackets thrown about on the right hand side. I need to find all the equilibrium...
19. ### Time dependent PDEs - mathematical modelling - diffusion equation

Homework Statement Porous membranes are used to separate mixtures in industry, because smaller compounds permeate through them more easily than larger ones. KnoGas Pty Ltd are trialling an experimental separation process, using a membrane to sep- arate compounds A and B: compound A...
20. ### Interested in Mathematical Modelling? How Can You Specialize in Energy Systems?

Hi I will like some advice. I intend to know more about mathematical modelling. Can anyone recommend any useful books, websites of software? How does one develop an interest in it? I will like to specialise in the modelling of energy systems and not sure how to do it. Please advise
21. ### A good book on Mathematical modelling

i want to learn how to use experimental data to produce effective mathematical model for good prediction of any phenomenon. my mathematical background is : i know about single and multivariable calculus,college algebra,introductory probability theory,trigonometry,vector algebra and calculus,and...
22. ### Solving for Car Depreciation: Linear, Quadratic, and Exponential Models

Homework Statement A car depreciates over time. x(years) y (\$) 1 14000 2 9100 3 6200 4 4000 5 3000 i) determine the linear model (1 mark) ii) determine the quadratic model (1 mark) iii) determine the...
23. ### Quick one about first steps in mathematical modelling of nuclear stuff

Hi, I am looking to get some good information sources on modelling nuclear power in power plants and related fields. Anyone got any good starting points ? P.S. I am a biomedical engineer looking into different fields.
24. ### Computer graphic mathematical modelling question

Hi, I am just finished my Calc II class and a programming class and I am trying to write a computer graphics shader... My goal is to model this scenario: "Imagine a brick wall standing on a plane --- a shadow will be cast depending on the light source" ---my goal is to model the dispersion of...
25. ### Help in mathematical modelling phase diagrams

Help in mathematical modelling phase diagrams! :( Mathematical modelling question on predator-prey models logistic prey-predator model with prey logistic growth dx/dt= ax - bx^2 -cy dy/dt= -ey + fxy ax = growth rate of prey in the absence of predation -cxy = the death rate per...
26. ### Mathematical modelling question on predator-prey models

logistic prey-predator model with prey logistic growth dx/dt= ax - bx^2 -cy dy/dt= -ey + fxy ax = growth rate of prey in the absence of predation -cxy = the death rate per encounter due to predation -cy = the natural death rate of predators in the absence of prey fxy = is the prey's...
27. ### Mathematica Math Modelling: Calculating Equilibrium Position X0

Homework Statement A particle of mass m moves along the positive x-axis with a potential energy given by V(x)=C+4/x^2+x^2 where C is a postive constant. Calulate the equilibrium position X0 of the particle. Homework Equations None. The Attempt at a Solution I realize...
28. ### Mathematica Math Modelling with Differential Equations for Physics

hi guys, i am an 11th grade student who loves physics and i have been doing lots of advanced problems from books like irodov,etc. I recently came across something called mathmatical modelling via differential equations. And my teacher once mentioned that u can solve most of problems of...
29. ### Mathematica Mathematical modelling - Fishery - Harvest equation

A logistic function has formula U(n+1)=rUn This models the growth in the fish population from year n to year n+1. If you now decided to harvest H fish, your equation looks like this: U(n+1)=rUn-H Now, they want me to find the maximum H for which the population stays constant (growth factor...
30. ### Mathematica Mathematical Modelling Question

HELP: Mathematical Modelling Question Hi Given X_1 \ldots X_n be stochastic independent variables with the distribution functions F_X_{1}, \ldots ,F_X_{n} . U = min(X_1 \ldots X_n) and V = min(X_1 \ldots X_n). F_{U} and F_{V} for U and V, and let F_{U,V} be simultaneously distribution...
31. ### Mathematica Mathematical modelling question

Hey, So, In a question about finding volume in a dome we were Given that V = pi.k(k^2/r - k^2/3r^3 - r/8) And K = m/2pi.p.t Firstly we are asked to obtain an expression for the value of r that maximises the volume of air and rearrange to obtain an equation of the form ar^4 + br^2 + c =...