What is Mathematical modeling: Definition and 46 Discussions

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. Codezero

    I Modeling Asteroid Rotation Using Quaternions: Seeking Guidance on Init

    Hello everyone, I am an International Baccalaureate (IB) student working on my extended essay, which is a mandated 4,000-word research paper. My chosen topic is Quaternions, a mathematical concept I find highly intriguing. The primary aim of my paper is to model the rotation of an asteroid...
  2. V

    Ts = temperature of steamModel Boiler: Negative Rate of Change of Enthalpy

    hello, I have dynamically modeled a drum boiler, but when i am solving the equation i am getting an negative rate of change of enthalpythe reason i find is the enthalpy of the steam is very higher than the enthalpy of water. can someone please verify the model and help me with this...
  3. O

    Analytical mathematical modeling of the torque caused by the laundry

    Hello my dear physicists, I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor...
  4. V

    Mathematical Modeling of an evaporator for evaporating water

    I am trying to model an evaporator which evaporates water to steam in Matlab/simulink. Are there any governing equations i need to know and follow when modelling the evaporator mathematically? Please let me know.
  5. V

    Mathematical modeling of a screw compressor

    I am trying to design a compressor in simulink. the mathematical equations has been modeled. but i just need, is there any relation to find the rate of change of volume with respect to time in compressor. Are there any equations or relations to find the rate of change in volume. As its a...
  6. T

    How to characterize mathematical models for comparison

    I am reviewing and comparing a wide range of mathematical models that are being applied to a specific realm of wildlife biology. For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model. As I do...
  7. M

    Do physicists really need to master mathematical modeling?

    Summary: Do physicists really need to master mathematical modeling? Do physicists really need to master mathematical modeling? As far as I know Mathematical modeling is a separate discipline form Physics?
  8. P

    How to calculate the voltage induced in a coil by an AC magnetic field?

    So, as it says in the title, I am trying to calculate overall voltage induced in a coreless coil in the cases of it being stationary and moving in an alternating magnetic field. To go more into detail, I would like to create a mathematical model of a coil in an alternating magnetic field that...
  9. K

    Mathematical modeling of driveline impact test of an automobile

    I am in a process of making a mathematical model of an automobile driveline validation procedure called "Driveline impact". In this test, after the engine in cranked, first gear is selected. While clutch pedal is still pressed, engine rpm is raised unto its max. torque deliverable speed. In this...
  10. mollwollfumble

    I Connection between entropy and time travel?

    My background is that I'm an applied mathematician and engineer, self-taught in GR and QFT. It's an old idea, in some dozen or so SciFi books. But I'm looking for a mathematical framework for handling it. The second law of thermodynamics, that entropy always increases in a closed system, can be...
  11. P

    Mathematical Modeling of an articulated vehicle (trailer)

    Hello, I have an problem with mathematical modelling of a special kind of articulated trailer (please have a look at the images: 1st image is the yaw plane and the second is the ZX plane). I have two methods of deriving equations of motion namely Lagrange and Newton-euler to analyse their...
  12. Nikhil N

    Dynamic modeling of a system and transients of the system

    Consider, I have a dynamic system model for air compressor. Which means I have modeled the system by including its physics. Does this means I also included the transients of the system? What I think is, when i modeled any system with equations, I think that includes the transients. Is it...
  13. patrickmoloney

    How Does a Bungee Jumper's Energy Change During a Jump?

    Homework Statement A bungee jumper of mass m attaches a light elastic string to his foot, and the other end to railing of a bridge on which he stands. The string has natural length l_0 and modulus of elasticity \lambda. Write down the energy equation. use conservation of energy to find the...
  14. levadny

    Mathematica Books on mathematical modeling

    Hello for All! Please recommend English-language books on mathematical modeling. Interested in a general theory. In Russian I know these books, but I would like to get acquainted with English. Thank you.
  15. ZenSerpent

    Relating Transformer Parameter I2 to V1 (Non-ideal) Updated

    ≪ mod note: thread moved from technical forum so template is missing ≫ Homework Statement Relate secondary current to primary voltage in a single-phase transformer having resistive load for non-ideal situation. Homework Equations KVL, Voltage across resistor and inductor, ac voltage as a sine...
  16. Y

    Where there is a mathematical modeling plate

    I'm going to take part in the International Mathematical Modeling Contest, I would like to ask you where the forum thank you!
  17. U

    Engineering Getting An Internship after getting B.S. in mathematics

    A few years ago, I graduated from Wheaton College with a B.S. in Mathematics; my objective is to be a mathematician in engineering that helps mechanical engineers with their mathematical/statistical modeling. Since I graduated, I have been looking for internships in Chicago: Unfortunately, I...
  18. CK328

    Mathematical modeling of a mountain bike rear shock

    Evening all, I've recently undertaken a project where my roll is to analyse the suspension of a mountain bike. The suspension unit in question is a Rock Shox Monarch RT3. To give a brief summary: The shock uses compressed air as the spring, the pressure is adjustable via an air valve. The shock...
  19. M

    Mathematical Modeling Question using a 2-cycle

    Homework Statement a. Use algebra and calculus to find the positive fixed point p(c) (in terms of c) and identify its exact interval of stability. b. Use algebra and calculus to find the exact interval of stability of this fixed point c. Use algebra to find the point p1(c), p2(c) of the 2-cycle...
  20. W

    Exploring the Cutting-Edge Topics of Mathematical Modeling and Physics

    I'm really interested in mathematical modeling and I've seen a lot of interesting topics about math and physics, so I hope that I can participate in the exchange with everyone here.
  21. ckyborg4

    Is there any relationship between light intensity and angle

    Homework Statement I'm working on a project right now, which uses laser beams and part of the project requires me to find a mathematical model which relates angle of projection to the intensity of the light. Does anyone know of an equation(s) which relates the intensity and angle together...
  22. FritoTaco

    Mathematical Modeling: Regression

    Homework Statement Restaurant Reservations for a given week were: Monday - 34 Tuesday - 27 (minimum value) Wednesday - 33 Thursday - 47 Friday - 58 Saturday - 61 (maximum value) Sunday - 42 Homework Equations I don't think you need these equations to help me solve what I'm stuck on Amplitude...
  23. M

    Undergraduate Senior Physics Research Topic (Theory)

    Hello all, This is most likely a question for those who have experience/knowledge of theoretical/mathematical physics at the graduate level and can provide recommendations following my criteria. Here is some background about me: I am a senior majoring in math and physics at a small...
  24. dandy_stepper

    Mathematical Modeling Textbook

    Hello all, I have recently started a course at my University called Introduction to Mathematical Modeling. However, the course does not require/recommend a textbook, and I am someone who really depends on having a textbook in order to learn. I have asked the professor to recommend me some...
  25. ZenSerpent

    Single Phase Transformer Losses -- Hysteresis, Eddy Current Constants

    Hi. My colleagues and I are doing a research on transformers (single-phase) and we stumbled across the following equations involving hysteresis and eddy current losses: Wh = ηBmaxxfV where Wh = hysteresis losses η = Steinmetz hysteresis constant Bmax = maximum flux density x = constant...
  26. Chrono G. Xay

    Calculate the 'Feel' of a Drumhead?

    As another of my personal music projects, I have wondered if it would not be possible to calculate the 'feel' of a drumhead (i.e. the amount of 'give' expressed as transverse displacement 'z' that an equally pre-tensioned circular membrane of radius 'r' experiences when struck on its plane at a...
  27. T

    Mathematical modeling in particle physics

    So my university offers two programs focused on particle physics. One is simply masters in nuclear/particle physics, the other is masters in mathematical modelling with focus on particle physics. I want to go into mathematical modelling and I'm choosing what I will focus on. I'm not really...
  28. H

    How Does Doubling the Slope Affect Velocity and Mass Data?

    Homework Statement Below is a table for some experiment data: m(kg) - v(m/s) 0.1 - 3.16 0.2 - 2.24 0.3 - 1.83 0.4 - 1.58 0.5 - 1.41 0.6 - 1.29 0.7 - 1.20 0.8 - 1.12 As the mathematical model for these data, I put v^2 (m^2/s^2) = 1.00 (kgm^2/S^2)/m(kg). Another set of experiments finds for the...
  29. B

    Mathematical modeling of the deflection of a rod

    A rod is radially mounted on a motor shaft and provided with a flat end plate. By turning movement, the end plate will touch a pointed object, and the angle turned is measured.By the torque of the motor during acceleration and deceleration, a vibration and deflection happens on the rod. The...
  30. W

    Axial eccentric loading on self-weight deflected cantileaver

    Homework Statement Hello, I am trying to model an arm mounted perpendicular to the straight mechanical column. An arm can be translated in horizontal direction by a gear which engages with the bottom of an arm such that it applies no force in vertical direction to the arm. And finally there is...
  31. F

    Can Higher Strain Rates Be Modeled from Existing Stress/Strain Curves?

    I want to create stress/strain curves for Higher Strain Rates from an available stress/strain curve? I am interested on the mathematical formulation aspect to generate a Dyna Material card.
  32. N

    How do I accurately model and calculate costs for different data plans?

    Re: Are my answers correct? Quadratic and logarithmic modeling I actually have a few more things that i'd like you to check for me please. Answers: Appetizer: {0<=x<=10 y=7 x>10 y=2(x-10)+7 or y=2x-13 Quest: {0<=x<=40 y=40 x>40 y=1(x-40)+40 or y=x) Voyager: {0<=x<=60 y=60 x>60...
  33. E

    Anyone know of good Mathematical Modeling classes/books?

    I've recently gotten into Mathematics more and more, and I wanted to do some mathematical modeling just to see where I stand on it and maybe try to get better at it. I've looked around as well as I could, and I didn't really find much, so I was wondering if anyone here knew of any good...
  34. S

    Part 2 of mathematical modeling question

    Okay so after tearing my face off trying to find a 2-cycle, I've managed to make significant process. I divided an enormous polynomial with another polynomial and got a god awful mess which incidentally was correct. Now I'm having trouble solving this equation with x in terms of c...
  35. S

    Need Help with a mathematical modeling question

    This question deals with a 1-parameter equation: fc(x)= (4/x)+(x/2)-c for 0≤c≤ 2.3 a.) Use algebra to find the positive fixed point p(c) of fc(x) (in terms of c) and identify its exact interval of existence a.) Ok so for the fixed point I got p(c)= -c+√(c2+8) I'm not sure if this is...
  36. V

    Mathematical modeling: physics degree or math degree

    I am currently a double major in biology and math, interested in mathematical modeling of ecosystems and physiological systems. The math portion involves modeling and pure math, but there isn't a lot of concentration on knowing physical laws. I'm not sure if I would miss all the knowledge...
  37. B

    How can I effectively learn mathematical modeling for social science research?

    Hi All, Just wanted to know, what is a good way to learn mathematical modeling? I'm a social scientist working with simulation and data, and would like approach the issue more formally. Before trying modeling textbooks, what should I know beyond calculus? Any suggestions (books, tutorials...
  38. R

    Linear Algebra Vs Mathematical Modeling -Importance in relation to physics

    Hey as part of my Physics undergrad in second year I have to take a module in either Mathematical Modelling or Linear Algebra (both course descriptions below) In first year I preferred Linear Algebra ( a very basic intro course) but apparently in second year its just all proof and no...
  39. H

    Mathematical Modeling of an Elevator System

    Hi, I'm a physics major working an internship for an engineering company at present. I have been trying to model the energy consumption and/or power for an elevator system. The goal is to be able to input different variables (cab weight, capacity, counterweight percentages, motor types...
  40. D

    Mathematical modeling of a feedback control system

    My system is a compound pendulum hinged at some distance from one end and have a propeller mounted dc motor at the other end. I wish to position the pendulum with the help of motor propeller system. I tried but i am unable to get a mathematical model for it. I am getting a non linear model...
  41. D

    What makes one type of mathematical modeling more difficult than the other?

    I'm guessing it depends on how many factors/how unpredictable a subject is, what is it really? What makes mathematical finance so rigorous- requiring a phd in math/finance- while something like systems biology or pharmacokinetics only requires knowledge up to linear algebra?
  42. J

    How Do You Model Viral Growth with Differential Equations?

    Homework Statement When certain viral particles enter the bdoy, the replicate to 160% every four hours and the immune system eliminates these particular viral particles at the rate of 50000 viral particles per hour. Find an equation modeling this viral growth. Homework Equations N/A...
  43. U

    Vehicle Mathematical modeling and dynamics

    i am working on the vehicle full suspension model. I am in modeling phase , i am electrical student and i am facing some difficulty in the dynamic results . When i am giving road disturbance to the vehicle the pessanger seat is getting more bounce and oscillations as compared to body to which...
  44. E

    How do Scientists Translate Physical Systems into Mathematical Models?

    Hello, In engineering, for instance, we set up the problem mathematically, and solve it mathematically. The question is: How did scientists interpret the physical systems into mathematical systems? and based on what? Did all come from experiments? Regards
  45. C

    Mathematical Modeling of Population

    This is a bit of a general question, but does anyone happen to know a good book, resource, or author in the field of accurate population growth and decline modeling? I'd like to find a good academic (non-website) source to get a general idea of the main things a population ecologist looks at...
  46. K

    Mathematica Mathematical Modeling Cube: Static & Dynamic Energy Conservation

    How can we Mathematicaly model(Mechanical) a system which is in the form of cube...like a box ...what are energy conservation equations set up for static and dynamic analysi.s...