What is Models: Definition and 400 Discussions

A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, a measure.
Representational models can be broadly divided into the concrete (e.g. physical form) and the abstract (e.g. behavioural patterns, especially as expressed in mathematical form). Of particular importance in the modern context, conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere.
In commerce, a model might instead reference a specific version or configuration of a product offering, rather than functioning as a representation of something else.
In taxonomic settings (e.g. biology, architecture, art) a model is sometimes a particular instance of a set of related entities (species, built structures, artistic compositions) chosen as a convenient reference point around which to build discourse; such a model is almost always chosen to typify some central tendency of the group, exemplify the group's defining characteristic, or reify the group's historical lineage.
Kinds of models include:

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  1. T

    Exploring Hartle-Hawking & Hawking-Turok Models for a Flat Universe

    Hi there! I'm new here and am currently looking into the Hartle-Hawking and Hawking-Turok Quantum creation models. What I've read about the Hartle-Hawking model is that it predicted a Closed Universe. But isn't that the opposite of what we have learned? The WMAP sattelite has confirmed the...
  2. A

    Open and Closed Models in Cosmology

    Let us consider the cosmological metric: {ds}^{2}{=}{dt}^{2}{-}{[}{a}{(}{t}{)}{]}^{2}{[}\frac{{dr}^{2}}{{1}{-}{k}{r}^{2}}{+}{r}^{2}{(}{d}{\theta}^{2}{+}{sin}^{2}{(}{\theta}{)}{d}{\phi}^{2}{]} -------------- (1) For closed models k is positive We shall consider here a closed one: We write...
  3. R

    Unraveling Linear Models: Solving n*Sum(XiYi) - Sum(XiYi)

    Linear models is the topic And i believe my professor wrote this n*Sum(XiYi) - Sum(XiYi) = Sum(Xi - Xbar)(Yi - Ybar) i was hoping if some one could tell me if this is true of if it is my bad in typing down. If it is true then can some one please tell me how? I've attached an image...
  4. C

    Collisional Astrophysics Models: A Guide for Computer Scientists

    I would like find references to collisional astrophysics models. I am a computer scientist interested in developing discrete event n body algorithms and would like any help that I can get. I have developed a direct n body algorithm for systems without collisions which seems to work well and...
  5. J

    How accurate are simple models of the solar system?

    How accurate are "simple" models of the solar system? Exactly how much effect does the perturbation of other planets have on planetary orbits? That is, if we were to take a naive model of the solar system, just applying Kepler's laws to each planet individually, with no planet-planet...
  6. A

    Guy pushing girl on a swing models h.displacement with function

    1,2,3. Homework Statement , and work done. After Lee gives his little sister Kara a big push on a swing, her horizontal position as a function of time is given by the equation x(t) = 3cost(t)*e^{-0.05t} , where x(t) is her horizontal displacement, in metres, from the lowest point of her swing...
  7. C

    Cosmological Models Predicting Heat Death of the Universe

    I have read that some cosmological models predict a heat death of the universe. Eventually all matter (beggining with superclusters, clusters, then galaxies, then stars) will lose all energy and separate (due to expansion which will eventually occur even on a galactically local level) so that...
  8. K

    Understanding the Concept: Unchangeable Models

    Anyone can briefly tell me about this concept? Did it is a undeformable model?
  9. K

    This problem has plagued me for years: finding SPICE models for real components.

    For years I have mastered the art of simulation and testing, but I almost never seem to be able to find SPICE models for real devices. For example, the TI OPA548. It's a high-current power op-amp. I would love to run some simulations...but I can't find a model of it anywhere to use in...
  10. C

    Cosmological Inflationary Models

    I am doing a project in school and am looking up different cosmological models to research. I have found Steinhardt Turok Model, Kaluza Klein. I know these are not the best models, so I was wondering if there are any more specific models that I can look into.
  11. P

    What Physical Models could these ODES represent?

    Homework Statement (2xy-5)dx+(x^2+y^2)dy=0, y(3)=1 (2x+y^2)dx+4xy dy=0, y(1)=1 x^3y'+xy=x, y(1)=2 y'(t)=-4y+6y^3 We're doing these in 2nd yr engineering Math and I have heard the Lecturer say they are useful across all disciplines. I've heard him suggest RLC circuits, springs with...
  12. R

    Is Physics More About Models Than Reality in Explaining Phenomena Like Gravity?

    So physics is about measurements and following models that can explain stuff even if they don't correlate with reality? For example. General Relativity is believed even if space doesn't really curve. Only spacetime curves but not space. Since space is empty and doesn't have structure. It is not...
  13. R

    Exploring the Complexity of Physics Models

    Are the mathematical models which describe the laws of physics considered simple or complex?
  14. B

    Mathematical models, the 'real world' and quantum mechanics

    A mathematical model may show that there are two possible states for something in the real world, let's say a coin, that may be either heads or tails; make a computer program to simulate coin flipping and you soon discover that the odds of heads or tails is 50/50. In the real world however...
  15. Pythagorean

    Spiking neuron models (ion current models)

    Models like the Hodgkin-Huxley and Morris-Lecar include a current term: applied current. http://cropsci.illinois.edu/faculty/gca/bioengin/Top/Lit/GENESIS_book/iBoGpdf/chapt4.pdf From what I understand, experimentally, this is the injected current, applied by the experimenter. But what is it...
  16. L

    Which model of the Universe is most accurate according to Alan Watts?

    I know there are three models of the universe: closed, flat and open. But which one of these models is the most accepted by scientists and why? I read that the WMAP satellite discovered that the universe is flat. But other observations have shown that, from 7.5 billion years after the Big...
  17. nomadreid

    L and inaccessibles as models of ZFC

    Three facts: (1)The constructible universe L is the minimal model for ZFC; (2) L is a model of "there exists an inaccessible cardinal \kappa"; and (3) if V=L, an inaccessible cardinal \kappa with the membership relation \epsilon is a model of ZFC. So, what is confusing me is: if...
  18. A

    Help Growth Models - Derivates

    Hi! I am amateur in mathemathicals growth models but I am doing my graduated work in adjust five differents models in some growth parameters in onion, [PLAIN]http://img820.imageshack.us/img820/2929/models.png So my doubt is basically in a derivate for gauss model, i can't derivate this model...
  19. nomadreid

    Confused about inner models and On

    I do not understand how On, the class of ordinals, can be included in the universe of an inner model of ZFC such as < V\kappa, epsilon>, where \kappa is the first inaccessible ordinal. My confused attempts to do so have led me to believe that I am getting off on the wrong foot in my analysis...
  20. Saladsamurai

    Ideal Gas Mixtures: Dalton vs Amagat Models

    Hello all! :smile: You know, I thought I knew something about ideal gas mixtures, but now I am not so sure. I am reading through a section of a text that discusses the Dalton and the Agamat models of ideal gas mixtures. I will briefly describe each: Dalton Model: The underlying assumption...
  21. A

    Discovering Kinematic Models: Help Identify Our Collection | School Project

    Hey guy, I'm working at my school to ID our collection of kinematic models and make signs for explaining them. I have them almost done, but there are a few I can't find in any of the books, can you guys take a look at the attached and linked pictures and see if you can ID them?
  22. I

    C - graphics library for physical models

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  23. P

    How relevant are solvable models such as 2D Ising to real systems?

    It surprises me how much mathematics is needed to solve the innocent-looking 2D Ising model, and the Heisenberg model is quite an exercise even in 1D. I begin to doubt whether solving these models is really worth the effort, given that these systems don't look very realistic, and computer...
  24. R

    What is the Angle of Repose for Granular Materials?

    For my coursework, i am investigating the angle of repose of granular materials. However, for my coursework to be. . . successful i need to prove or disprove a theory or an empirical equation which i can test. So far from my research i have not found a simple... or appropriate complexity theory...
  25. MTd2

    Why do matrix models fail to be The M-Theory?

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  26. S

    Systems and Signals Models - population model

    Homework Statement At the beginning of the year 2000, country A had a population p of 100 million people. The birth rate is 4%/year and the death rate is 2%/year, compounded daily. Every day, 275 immigrants enter country A. Neglect leap-year effects. Write a difference equation for the...
  27. 0

    Solving General Linear Model: Part (C) - 95% CI for Recovery Time

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  28. P

    Can Matter Shape the Metric in Analog Models of Gravity?

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  29. P

    Finding 3D Models: A Resource Guide

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  30. J

    (newbie question) Useful mental models for the flow of electricity?

    Hi all I'm a complete newbie to the subject of electricity and trying to wrap my head round it. To be more precise, I'm trying to build a mental model for myself that accurately predicts what goes on in circuits. I've read several accounts that suggest a model based on the flow of...
  31. E

    Can Supersymmetry be harmonized with technicolor/topcolor models?

    Suppose the LHC discovers that EW is dynamically broken by technicolor, topcolor, top quark condensate models. Can these be harmonized with SUSY? If new strongly interacting dyanmics breaks EW, how would that modify SUSY, including SUSY particle content? Or, would discovery of technicolor/top...
  32. L

    Equivalent Models: Hybrid-pi vs. T-model for FETs

    Hi, When it comes to the hybrid-pi model and the T-model for the AC equivalents of an FET, what's the exact difference? For example I know that in a BJT circuit, the hybrid-pi includes the resistance r_\pi in the base while the t-model includes the resistance r_e = \frac{r_\pi}{1+...
  33. J

    Nuclear models: excited states of 182Ta

    Hi all, I'm doing some test prep for a Nuclear Physics course and working on a past paper. I've attached a photo of the question. The diagram is 3.19 in Krane. The course is based on Krane, and so the relevant chapter is Chp 5: Nuclear Models. Problem description The problem is to explain...
  34. K

    Cosmological Models: Exploring Common Models

    Which of the common cosmological models do you prefer and why? Assume we don't know which if any of the models is the actual one that matches the universe.
  35. A

    Models for Trajectory Simulation.

    Homework Statement I have an assignment in which i need to employ the practice of 'Crowd Sourcing' to get the answers to problem statements. I can have my own answer but i also need the answers collected from various sources. *Kindly help ur answers* The problem statement is ...
  36. S

    Past eternal universe in inflationary models

    Assuming inflation is true, we have this paper by Guth, Valenkin and Borde: http://cdsweb.cern.ch/record/521154 which says that inflation can't be past eternal and then we have this paper saying it can be made past eternal: http://arxiv.org/abs/gr-qc/0301042 Can anyone explain to me the...
  37. W

    Models versus sufficient reason

    While I know next to nothing about the philosophy of science, I would think about scientific models and explore whether there are features of these models that should be required in order to say they make a good theory or whether any model that predicts the data is as good as any other. From...
  38. A

    Solving Differential Equations: Linear Models Homework

    Homework Statement An Archer on top of a 50-ft high cliff shoots a 4-oz arrow straight up in the air. The bow is strung so that it can achieve maximum initial velocity of 128 feet per second. If the air resistance causes a drag constant of 1/1024 lb/fps, what is the maximum elevation reached...
  39. A

    Differential Equations: Linear Models

    Homework Statement A 500-gallon tank originally contains 350 gallons of pure water. A 2-pound per gallon brine solution is pumped into the tank at 10 gallons per minute and the well-stirred mixture is pumped out at one-half that rate. How much salt is in the tank at th emoment of overflow...
  40. F

    When will the alligator population in the swamp reach four dozen?

    Working on some DE homework and need a tad bit of guidance. I got fairly far, I'm just wondering what the next step is. Homework Statement The rate of change of an alligator population P is proportional to the square of P. The swamp contained a dozen alligators in 1988, two dozen in 1998...
  41. cepheid

    Thermodynamics in Friedman World Models

    Hi there, I have a question regarding thermodynamics in the expanding universe. I'm specifically looking at section 7.1 of Galaxy Formation by Malcolm S. Longair. In this section, he sets out to show that the dynamical equations for the scale factor automatically incorporate the first law of...
  42. 2

    The real reason why I care about mathematical models for flirting

    Hopefully you don't mind me saying this, I get the impression PhysicsForums is trying to tell me to turn my mind into a vegetable because all thoughts/feelings are automatically found in a book no matter what and so you have to purge all your feelings. I wonder if coming up with some...
  43. 2

    What are the popular/very useful mathematical models for principles in economics?

    I have a question for those who are cognisant with the study of economics. I've heard in economic classes they teach all sorts of mathematical models to describe/predict all the "laws" in the field, or at least approximations. I'm trying to hunt down the popular and useful economics...
  44. L

    Looking for visual models or discriptions of bullet vs. shape charge

    Hello, I'm creating a slide-show presentation that describes how a shape charge explosion (namely that of an improvised explosive formed projectile) is more effective than that of a bullet projectile. I would like to include visuals and equations which describe how the initial explosion...
  45. S

    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...
  46. R

    Connectedness of Discrete Space-Time Models

    Been enjoying Physics Forums and this is my first question so before I ask I should I applaud everyone for the helpful friendly atmosphere. I'm trying to understand the concepts of continuity and connectedness. I have no set theory background nor physics backgrounds so I just read online...
  47. J

    Solving for ground temperature using atmospheric layer models and energy budgets

    Homework Statement Imagine that our simple single layer atmosphere model derived in class now has 2 atmospheric layers. It is transparent to visible light but a blackbody for IR a) Write the energy budgets for both atmospheric layers, for the ground, and for the Earth as a whole. b)...
  48. G

    Are closed time like curves an inherent feature of rotating universe models?

    This is a follow up to my previous question, as they appear that in both the Godel Metric and the Van Stockum dust Perhaps a better way to put this is, could there be a model where you had rotation (maybe around a non-symmetrical axis?) and not get these CTCs?
  49. G

    Mathematical impact of outliers on accuracy of models

    Is there a general approach to calculating the impact outliers have on the accuracy of one's (predictive) model?
  50. D

    Finite Models of ZF - Infinity

    Is there a finite model of ZF - Infinity?
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