What is Model: Definition and 1000 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

    Maximum likelihood of a statistical model

    Homework Statement I look at the distribution ##(Y_1,Y_2,...,Y_n)## where ##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1. I need to find the the maximum likelihood estimator for μ and...
  2. Poliona

    Understanding the Hard Sphere Model of Crystallography

    I am currently studying C Hammond's "Basics of Crystallography and Diffraction" (third ed.). In the first chapter ,concerning hard sphere model, I have found the following statement: There are, in fact, no examples of elements with this structure because, as the model building shows,the atoms...
  3. smodak

    Particle The Standard Model in a Nutshell - Goldberg

    Just found this new book on amazon. Looks interesting. I purchased. https://www.amazon.com/dp/0691167591/?tag=pfamazon01-20 The TOC, Preface, and intro could be found here http://press.princeton.edu/titles/11050.html I wish they included a sample chapter as well (the book in not cheap), but I...
  4. Eclair_de_XII

    How to create a mathematical model of investment?

    Homework Statement "Someone with no initial capital ##S_0=0## invests ##k \frac{dollar}{year}## at an annual rate of return ##r##. Assume that investments are made continuously and that the return is compounded continuously." Find the solution ##S## that solves the differential equation...
  5. C

    B Standard model particle properties

    In the Standard Model, for any particle, I have only found properties related to electromagnetic and gravitational (in fact mass does not necessarily mean it is a property related to gravity, but to emergy)forces like charge and mass. Why there isn't anything about the other two interactions...
  6. J

    B Raisin bread model of space-time

    The impact of a bowling ball on the shape of a stretched gridded sheet is often used as a tool to help some of us to better visualize how the presence of a mass influences the curvature of spacetime? However, while this kind of diagram is helpful, I think that it is misleading because it...
  7. H

    Scaling Rotational Inertia - from Model to Full Size

    Homework Statement If we multiply all the design dimensions of an object by a scaling factor (f), its volume and mass will be multiplied by f^3. a) By what factor will its moment of inertia be multiplied? b) IF a 1/48 scale model has rotational kinetic energy of 2.5 Joules, what will be the...
  8. F

    Trying to model mutual inductance with losses

    So as a learning project I am trying to solve a transformer with losses but I am stuck. 1 coil L1 with N1 turns is excited by a sinusoidal voltage V1 with a resistor R1 in series. Wound around a common core with a second coil L2 with N2 turns and a resistor R2 also in series...
  9. Jenab2

    I Structure of Earth, pressure and density model

    I created interpolative curvefits to the graph of Earth's density as a function of radius, shown here: (Image from Wikipedia) Earth is assumed to be a sphere of radius 6371 kilometers. The independent variable r is the geocentric distance as a fraction of the Earth's radius; i.e. the range of...
  10. Q

    Unruh Effect for Standard Model Fields

    I have seen the derivation for Unruh radiation for a massless, non-interacting scalar field (Carroll). Are there interesting differences that arise for more realistic standard model cases. For example, what does QCD look like for an accelerating observer? Any papers that detail this would be...
  11. essil

    I Attractive Kronig-Penney Potential Dispersion Relation Confirmation

    Hi all! Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice): $$cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 +...
  12. Demystifier

    A A need for an exactly solvable model

    Consider a Hamiltonian of the form $$H=\frac{p_x^2}{2m}+\frac{p_y^2}{2M}+\frac{k(y)x^2}{2}$$ where ##k(y)## is some free function which I can choose at will. For ##k(y)=k=constant##, the Hamiltonian is a trivial combination of a free particle with position ##y## and a harmonic oscillator with...
  13. R

    Model reaction diffusion brusselator 2d matlab

    Hello, I have a project (model reaction diffusion brusselator 2d) ∂u/∂t=A+u^2v-(B−1)u+D1((∂^2)u/∂(x^2)+(∂^2)u/∂(y^2)) ∂v/∂t=Bu−u^2v+D2((∂^2)v/∂(x^2)+(∂^2)v/∂(y^2)) initial conditions: u(x,y,0) = 0.5 + y, v(x,y,0) = 1 + 5x. boundary conditions: ∂u/∂n = 0, ∂v/∂t = 0 n-external normal to the...
  14. wolram

    B Beyond the standard model through 'mini spirals'

    https://www.sciencedaily.com/releases/2016/12/161215080856.htm Can anyone provide the origin of this article.
  15. J

    Max altitude of a model rocket

    Homework Statement Hello all, I have to determine the maximum height of a model rocket. The rocket is launched at an 45 degree angle The finale velocity is 15,69 m/s (v) the extutevelocety is 14,23 m/s (c) The total mass is 180 gram (m) or m0) The emty mass is 52 grams (mf) The mass pr sek is...
  16. farolero

    Futurama: How plausible is the cyclic model, is it mainstream?

    https://en.wikipedia.org/wiki/Cyclic_model it brings to mind as well the many worlds theory the cyclic model is shown in a futuruma episode where the professor builds a only forward time machine(consistent with relativity) but he goes so far into the future that he ends in the past of the...
  17. Jules Winnfield

    I How do I compare a model to logarithmic data?

    I have a model which is quadratic (e.g. ##y = k x^2##). I'm comparing it against a large set of data (galaxy cluster masses) which spans several Log10 decades (e.g. ##10^{11}## to ##10^{15}## solar masses). What is the right way to say how good the data fits the model? Obviously the errors in...
  18. P

    Damping coefficient in RLC model (piezoelectric transducer)

    Hello! I am a university student working on a project regarding a piezoelectric patch transducer, and RLC modelling of said transducer. Edit: After reading the rule post i think i should clarify this is not coursework homework, this is a thesis project. The short version of my question is how...
  19. G

    Resistance: Dissipated power in collision model

    Hi. A simple model explains resistance in metals with collisions of the electrons with the stationary atomic cores. So I assume more collisions result in a higher resistance? But for the dissipated power we have ##P=U^2/R## , which is large for small resistance. I have difficulties combining...
  20. V

    A What is first and Second order Dependence?

    Can someone please explain to me what it means what they say a model is "first and second order dependence?"
  21. F

    Software to model magnetic fields in a core

    Hi I am looking around for some way to model magnetic fields through a simple core with an air gap similar to this image : I was thinking Comsol... but Comsol is so hard to figure out, their documentation is terrible... I was looking at FEMM, but its only on windows. Does anyone know how to...
  22. T

    I Dispersion relation in tight binding model

    Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}} where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}} where \vec{b} is a nearest...
  23. Euler2718

    MATLAB "Linear Model" of a Pendulum via Euler's Method

    In my problem the linear modal is defined as the first term in the series expansion of \sin(x) so: \sin(x) = x - \frac{x^{3}}{3!}+\dots \sin(x) = x is the linear modal. So with this, I then have to write \frac{d^{2}x}{dt^{2}} = -\sin(x) as a system of x^{\prime} and y^{\prime}, so...
  24. M

    Lattice Models for Fluids - Regular Solution Model

    1. Problem Statement: For the regular solution model, develop the equations for the compositions of the coexisting phases in a binary system and plot the phase boundary as a function of χ/RT.2. This question stems from Sandler's Introduction to Applied Statistical Thermodynamics. The Attempt...
  25. K

    I Bohr model, Why do we assume a standing wave?

    Hi, I wonder why we assume the matter wave of an electron is standing wave. Is there any reason why it has to be standing wave?Is it because standing wave is the right "wave equation solution" that satisfies integer multiple behaviour of bohr model?
  26. M

    I Realistic coasting cosmology from the Milne model

    In the past few months, there appear some observational results supporting the linear coasting models for the universe. http://www.nature.com/articles/srep35596 http://iopscience.iop.org/article/10.3847/0004-637X/828/1/35/meta This brings the coasting models again to the centre-stage of...
  27. VishalSharma

    I Harper-Hofstader Model: Butterfly & Landau Levels Relationship

    How are Hofstader's Butterfly and Landau Levels in 2-Dimesnions related to each other, if at all ?
  28. J

    Standard Database Model for Academic Management

    I am the database administrator of my university, so I have to build up the database from scratch. I am just wondering if there exists already some predefined database model for academic management which focuses on entities such as students, grades, courses, teachers and faculty buildings.
  29. wolram

    B Does antimatter fit into the standard model

    AFAIK antimatter was produced equality in the big bang, and in the matter antimatter fight the matter won . Does antimatter react to gravity the same as matter, surly if it does then the antimatter will be annihilated due to matter antimatter mixing IF matter repels antimatter how did the...
  30. L

    A Ising model and Hamilton function

    In case of Ising model we are working with effective Hamiltonian. So let's look to spins which interact. In a case of feromagnet energy function is defined by ## H=-JS_1S_2 ## We have two possibilities. ##S_1## and ##S_2## has different values. And ##S_1## and ##S_2## has the same value. In...
  31. G

    Water model for electric circuits: Pipe diameter?

    Hi. There's this nice water circuit model for electric circuits where pressure corresponds to electric potential and the (mass or volume) flow rate to electric current. In the water model, we can vary the pipe diameter along the circuit. Since water is practically incompressible, the flow rate...
  32. S

    Simulink model of a hybrid vehicle (replace battery with fuel cell)

    greetings, here I found a Simulink model on mathswork, I want to replace the battery with a fuel cell, so I'm stuck at the level of the energy management block. here is the link of the model: https://www.mathworks.com/matlabcentral/fileexchange/28441-hybrid-electric-vehicle-model-in-simulink...
  33. M

    A Tree-level unitarity constraints in Two-Higgs Doublet Model

    Hi, I'm looking at the unitarity constraints for the Two-Higgs Doublet Model and I'm trying to follow what they do in the attached article, which can also be found here: https://arxiv.org/pdf/hep-ph/0312374v1.pdf. However I do not know how to get the scattering matrices in eq. (7). They say...
  34. adamaero

    Bohr Model applied to Excitons

    An exciton is a bound electron-hole pair (in a semiconductor). For this problem, think of an exciton as a hydrogen-like atom, with a negatively charged electron and positively charged hole orbiting each other. The permittivity of free space (ε0) is replaced with permittivity of the...
  35. lep11

    MATLAB Data Analysis: Observation Model Problem

    The observation model will be ##z=H\theta+v##, where ##z## is column vector containing the results, ##H## is the observation matrix, ##\theta## is the parameter vector and ##v## is a vector containing random additive noise. b.) In this case ##z##=[1 1 0; 1 0 1; 0 1 1; 1 1 1]*[##m_1## ##m_2##...
  36. L

    B Is wave a physical object or its just a model?

    Is wave a physical object or its just a model?
  37. L

    I Chernobyl Dose Model & Estimates

    Hello all, I've been tasked with developing a model for dose received from the Chernobyl Accident. I'm struggling a little to find dose estimates from which I can extrapolate back to find the initial dose received. Does anyone have any references that they can point me towards? I believe there...
  38. Vitani11

    How do you modify the Bohr model equation for Li++?

    Homework Statement Consider an electron in the n = 4 level of Li ++. According to the Bohr model, what is the radius of the orbit of the electron? Homework Equations r = .0529 nm r(n) = (.0529 nm) x (n2) The Attempt at a Solution I thought this was pretty obvious? We want to know the radius...
  39. V

    Find a Small, Low RPM Generator for Your DIY Turbine - 100-300RPM!

    Hi all, Does anyone know of, or can anyone point me in the right direction for where to find a small, low rpm generator? RPM can be anywhere in the range of 100-300RPM, and size would be around 50mm long. To put this into context, I am building a small turbine (~300mm diameter), which will...
  40. EdColider

    Mathematical model of a phenomenon

    I want to know how can I begin to exercise the representation of a phenomenon in a mathematical model.
  41. Urs Schreiber

    Insights Spectral Standard Model and String Compactifications - Comments

    Urs Schreiber submitted a new PF Insights post Spectral Standard Model and String Compactifications Continue reading the Original PF Insights Post.
  42. K

    I Why the energy inversely propotional to n^2 in Bohr model

    After reading some materials on Bohr model, I understand the model is more or less incorrect, especially in terms of "orbital". I just wonder if the energy expression is also wrong or not. In my text for general quantum theory, the energy about two neighboring level is given as ##\Delta E =...
  43. I

    I How to turn model of Schrödinger's Equation 2D?

    Hi, I am a student in the Netherlands, currently 17 years old and at the end of my 'middelbare school', meaning that next year I'll be a bachelor student at a university. I am doing an extended essay/research thing that is custom you do in your last year, with a friend of mine. We picked the...
  44. R

    De Broglie wavelength and energy levels

    Homework Statement In the earliest circular planetary model of the atom the electron and proton orbited a common centre. The electrostatic forces alone provided the force field. However an accelerating charged body will send out electromagnetic waves and the orbiting charges would consequently...
  45. D

    Model Heat Transfer with COMSOL

    Does anyone here have experience with COMSOL? I want to model a system where i have a fluidic channel containing warm fluid running through a block and I want to analyze the heat transfer from the channel into the block . To establish the warm fluid I put an initial temperature condition at...
  46. Paul Colby

    B Toy GW Detector Model: "Hook Law Force

    A simple harmonic oscillator model consisting of two masses connected with a massless spring is provided in [edit] I hate cut and past on the mac. Always seems broken Slide 30 http://webs.um.es/bussons/GW_lecture_KG.pdf The left hand side of the equation of motion is simply the classical one...
  47. Luca_Mantani

    A Custodial Symmetry in the Standard Model

    Hi, I am reading about this symmetry but I'm struggling to have a deep understanding of it. Would somebody please explain this symmetry to me from a conceptual point of view? Thanks in advance, Luca
  48. W

    Axisymmetric FEA model for magnetic flux distortion

    Why do axisymmetric FEA models of magnets and their fields make the field farther from the axis appear denser than it really is when the flux line mode is enabled? I'm using the F.E.M.M. system at the moment. All integrals and graphs give correct values, but the depicted lines of flux appear...
  49. A

    Current flow model through a resistance field

    Hey everyone. I thought about this problem the other day, but I don't know what theory I need to solve this problem. Given a 2D rectangle with a known, varying resistance, and a known voltage drop across the length, how would one calculate the current density at each point on the surface. By...
  50. R

    Filament lamp model (derivation)

    Homework Statement State and use simple assumptions to show that ' Power is proportional to V^5' is the expected relationship for a pure tungsten filament bulb. Homework Equations V=IR I=dq/dt Q=mcT The Attempt at a Solution I tried to use a simple model where the rate of heat loss is...
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