Model Workshop

  • There is nothing without reason. (Leibniz)          
  • One mathematical model says more than thousand words. (Dylan)
  • Nature’s great book is written in mathematics. (Galileo) 
  • With four parameters I can fit an elephant, and with five I can make him     wiggle his trunk. (von Neumann)

Model Workshop opens to a problem based approach to learning, where tools and methods are collected as they are needed to handle specific cases of significance, rather than teaching  generalities first. For the young mind particularities can be more captivating than generalities and generalisation can come at a later stage by discovering similarities of particularities.

Model Workshop invites to an answer – question form of learning, where the student after having explored a simulation gets incentive to answer the questions: How is it done? What elements are included? What does the code express? How can I expand the simulation? It is like watching a magician showing a trick and then seeking to find out how it was done and how to repeat/modify it. This gives the student an active role in an open search for information on the web, to be compared with a the passive role in the traditional form of question – answer directed by teacher and book.

Explanation is thus kept sparse to give incentive to explore models by trial and error computation with inspiration from reality and web in learning-by-computing. Watch out: Can be Addictive!

You can enter Model Workshop with a minimal preparation of Basic Mathematics 16-29 assuming basic knowledge of decimal numbers and return to binary numbers later.

Check code to find explanation of model if not given directly. The models are carefully selected to be as simple as possible yet open windows to a complex world of many phenomena. Be confident that in retrospect you will see the scientific wealth buried in these (seemingly simple) models.

Add to Game Workshop using the physics of Model Workshop.

Run code by clicking arrow on upper left corner. Modify code, test and have fun!

(Sometimes restart is needed to activate mouse interaction).

List of topics: 

  1. Start: Space-Position Time-Motion
  2. Population Dynamics
  3. Mass-Spring Systems
  4. Electrical Circuits
  5. Resonance
  6. Elastic Mechanics
  7. Convection-Diffusion
  8. Reaction-Diffusion
  9. Fluid Mechanics
  10. Coupled Fluid-Elastic Mechanics
  11. Waves in Elastic Bodies
  12. Waves in Fluids
  13. Heat Conduction
  14. ElectroMagnetics
  15. Chemical Reactions
  16. Chaos
  17. Fractals and Representation
  18. Parameter Identification
  19. Music
  20. Image
  21. Cosmology
  22. Atom Physics

1. Start: Space-Position Time-Motion

  1. Fireworks (see also Fireworks Many + with sound)
  2. Harmonic Oscillator (with music) (with damping) (soft-stiff spring) (double)
  3. Journey to the Center of Earth
  4. Stop Watch
  5. Bouncing Block: Single (with click sound)  (3d version)
  6. Bouncing Block: Many    (3d version)
  7. Lawn Mower Robot: Ergodic?
  8. Newton’s Cradle
  9. Elastic Collision
  10. Walking Boy Animation     Running Caveman Animation
  11. Variants of sin cos: BesselFunction V2 V3  V4 V5  V6  V7
  12. Zeno’s Paradoxes
  13. Brachistochrone Problem
  14. Leibniz Subnormal Problem

2. Population-Reaction Dynamics

  1. Logistics Function: Population Growth
  2. National Economy
  3. Gumpertz Function: Corona Virus 
  4. SIR Corona Model
  5. Spread of Pandemi 2d (compare with this article)
  6. Corona: Keep Distance Stay Together
  7. Rabbits and Foxes
  8. Crash Model
  9. Battle Between Red and Blue Team
  10. Nerve Signal: FitzHugh-Nagumo Model
  11. Reproduction Advantage Model (see Enflo Model)

3. Mass – Spring Systems

  1. Two Body Gravitational Problem 
  2. Sun-Planet-Moon System
  3. Rubber Band Model
  4. String Models
  5. Single Pendulum
  6. Double Pendulum
  7. Multi Pendulum
  8. Constrained Motion along Curve  (alternative) (ellipse)
  9. Cosmic Interaction (stunning, compare with Lone Space Traveler)
  10. Elastic Body (compare Circus Cow1+Circus Cow2)
  11. Elastic Body as Particle-Spring System
  12. Build and Play with Elastic Body.
  13. Elastic String of Beads (variant)
  14. Vibrating String
  15. Plucking String
  16. Colliding Elastic Balls(with Sliders)
  17. Gravitational World Model 
  18. Newton’s Nightmare
  19. Compare 13 with Lone Space Traveler+Many Space Travelers
  20. Real Quantum Mechanics

4. Electrical Circuits

5. Resonance

  1. Forced Oscillator
  2. Resonance

6. Elastic Mechanics

  1. Elastic Bar
  2. Erecting a Circus Tent
  3. Elastic Web
  4. Elastic Truss
  5. Elastic Membrane (compare HD version)
  6. Plane Elastic Body under Impulse Load
  7. Plane Elastic Cantilever under Gravity
  8. Elastic Beam (clamped) (clamped/free)
  9. Euler Beam Buckling
  10. Bridge Updated Lagrangian  (see MST chap 132)
  11. Earth Quake
  12. Pulsating Sea Tulip
  13. Elasto-Visco-Plastic Plate under Gravity
  14. Elasto-Visco-Plastic Plate under Distributed Load
  15. Obstacle Problem: Free Boundary Problem

7. Convection – Diffusion

8. Reaction – Diffusion

9. Fluid Mechanics

  1. Inspiration:The Secret of Flight, Incorrect Theories of Flight, D’Alembert’s Paradox, Potential Flow
  2. Potential Flow around Square (1st type) (variant) (skew variant) (read me)
  3. Potential Flow around Disc (2nd type) (with pressure) (around square)
  4. Potential Flow around Disc as Real Part of z + 1/z (two discs)
  5. Potential Flow around Elliptical Wing (2nd type)
  6. Cauchy-Riemann Equations
  7. Analytic Functions
  8. Archimedes Principle
  9. Meteorology: Wind-Pressure Map (compare with real global wind map)
  10. Meteorology: Air Pollution
  11. Titanic Ship Stability (catastrophical)
  12. Compressible Flow: Burgers equation (zero pressure) 2d
  13. Compressible Flow: Small velocity + viscosity (Stokes equations)
  14. Incompressible Flow: Lid Driven Cavity 2d (variant) (see Computational Turbulent Incompressible Flow)
  15. Incompressible Flow: Lid Driven Cavity 3d  (HD version)
  16. Incompressible Flow: Variable Density Lid Driven Cavity 2d
  17. Incompressible Flow: Ventilation
  18. Incompressible Flow: Bluff Body No-Slip (Slip) (HD version)
  19. Incompressible Flow Bluff Body Slip: Drag and Lift
  20. Incompressible Box/Flat Plate Slip Density Check
  21. Incompressible Flow: Periodic 2d
  22. Incompressible Flow: Atmospheric Inversion
  23. Compressible Flow: Euler equations for Ideal Gas (see Computational Thermodynamics)
  24. Compressible Flow: Riemann Problem
  25. Compressible Flow: Periodic boundary conditions + forcing
  26. Compressible Flow: 3d
  27. Compressible Flow: Bluff Body (HD-version)
  28. Compressible Flow: Low Mach
  29. Compressible Flow: Refrigerator1: Cooling by Expansion (see book)
  30. Compressible Flow: Refrigerator2: Compression
  31. Compressible Flow: Decay from Initial Random Momentum
  32. Compressible vs Incompressible Flow
  33. Compressible vs Incompressible Flow: Ventilation
  34. Compressible vs Incompressible Flow: Decay from Random
  35. Unified Compressible-Incompressible Bluff Body Flow (compare with std pressure equation for incompressible flow with slip and passive density check and with force)
  36. Compressible Bluff Body Slip (Skew)
  37. Unified Compressible-Incompressible Flow II: Compressible (HD and Skew) vs Incompressible (HD)
  38. Flat Plate Wing (slip): Incompressible 1:6 (HD 1:10). 
  39. Compressible Flow: Joule’s Experiment  (HD) (see Computational Thermodynamics p. 29)

10. Coupled Fluid – Elastic Mechanics

  1. Fluid vs Structure 1d
  2. Fluid vs Structure 2d
  3. Coupled Fluid-Structure 1d
  4. Coupled Fluid-Structure 2d
  5. Elastic Structure – Viscous Linear Fluid 2d
  6. Elastic Structure – Nonlinear Fluid 2d
  7. Water Fall

11. Waves in Elastic Media

  1. Eigenvalue Problem: Vibrating Membrane: Basic mode
  2. Vibrating Membrane: Higher modes
  3. Traveling and Standing Waves
  4. Elastic Waves 2d
  5. Drop Stone in Pond 
  6. Double Slit Experiment
  7. Broad Casting 2d Wave
  8. Diffraction (Variant)
  9. Cancellation in Superposition of random/uniform de-synchronised waves 
  10. Synchronisation by Common Bridge

12. Waves in Fluids

  1. Traffic Model as Conservation Law with Shock Formation (see also this)
  2. Breaking Wave Model (1d Burgers equation
  3. Shallow Water: Linearized Small Deviation (with periodic boundary cond)
  4. Shallow Water: Full Nonlinear (see also 3d plot)
  5. Shallow Water: Coriolis Force + Periodic
  6. Shallow Water: Ship Waves (HD version)
  7. Tsunamis and Solitons (compare with this)

13. Heat Conduction

  1. Heat Conduction 1d
  2. Heat Conduction through Wall
  3. Heat Conduction 1d: Forward Euler vs Midpoint Euler
  4. Fourier Method for Heat Equation
  5. Heat Conduction: Surface vs Ground Temperature 
  6. Heat Conduction 2d Hot Spot
  7. Reconstruction after Smoothing (test sharpening of smoothed jump)
  8. Sensitivity by Duality (heat eq)

14. ElectroMagnetics

  1. Electric Potential (compare: different data and  Solar Flare Eruptions? )
  2. Faraday’s Cage
  3. Magnetic Field/Scalar Magnetic Potential
  4. Maxwell’s Equations Plane Wave 1d
  5. Maxwell’s Equations Plane Wave Energy Transfer
  6. Maxwell’s Equations Plane Standing Wave
  7. Maxwell’s Equations Plane Standing Wave 2
  8. Maxwell’s Equations 3d 1-way Plane Traveling Wave
  9. Maxwell’s Eq. 3d 1-way Plane Non-Polarised Traveling Wave
  10. Maxwell’s Equations 3d 2-way Plane Traveling Wave
  11. Maxwell’s Equations 3d Vacuum
  12. Maxwell’s Equations 3d Given Current
  13. Mawell’s Equations 3d Vacuum/Conducting Medium
  14. Maxwell’s Equations 3d Vacuum: Ampere’s Law

15. Chemical Reactions

  1. Flame Front (The G Equation)

16. Chaos

17. Fractals and Representation

  1. Fractal Binary Tree by Recursion  (see also Fractal Binary Forest)
  2. Trigonometric Series
  3. Fourier Series 
  4. Discrete Sine-Transform
  5. Stock Market with Haar Basis

18. Parameter Identification

19. Music

  1. Music: Pythagorean Scale (Compare sinus wave with square wave) Combine with Frequency Sound Generator
  2. Play Tone
  3. Play Something

20. Image

  1. Image Resolution
  2. Build Image Pixel by Pixel
  3. Image Compression (explanation: Image Representation/Compression)
  4. Webcam Shader

21. Cosmology

  1. Gravitational Collapse into Black Hole (scary)
  2. Cosmology: Big Bang (compare with 14 and this post)
  3. Cosmology: Spiral Galaxy
  4. Cosmology:  3d Expansion – Contraction
  5. Dark Energy: Repellation of galaxies with mass of different sign (compare with Attraction of galaxies with mass of same sign)
  6. Unphysical Gravitational Collapse
  7. Physical Gravitational Collapse  (see this post)

22. Atom Physics

  1. Check out Real Quantum Mechanics (web site+book) and RealQM (page)
  2. Atom Secret (deep and colourful). Compare with this analysis and this.
  3. Hydrogen Atom Ground State Spherical Symmetry
  4. 2d 1-Electron Atom Ground State Eigenmode 
  5. 2d 1-Electron Atom 1st + 2nd Eigenmode
  6. 2d 1-Electron Atom Ground State: Wave Function
  7. 2d 1-Electron Atom Exited State Wave Function
  8. 2d 1-Electron Radiating Atom
  9. 3d Hydrogen Ground State
  10. 3d H2+ Ground State
  11. 1d 2-Electron Atom Model
  12. Helium Atom Model
  13. Helium 3d Overlaying Electrons
  14. RealQM Helium SpherSym
  15. RealQM Helium (finer resolution) (global variant)
  16. Real QM He+
  17. RealQM H2
  18. RealQM H2+
  19. Real QM Lithium+
  20. RealQM Beryllium2+
  21. RealQM Carbon4+
  22. RealQM Lithium SpherSym
  23. RealQM Beryllium SpherSym
  24. RealQM Helium 1S2S SpherSym
  25. RealQM 2d Model Bernoulli
  26. RealQM Atom Simulator: Ground States+Ions (see Atom Secret)
  27. RealQM Atom Simulator: ElectroNegativity
  28. Quantum String Model 1
  29. Quantum String Eigenvalue
Who is this guy? What has he got to do with atoms?

  • Originally I viewed it as the function of the abstract machine to provide a truthful picture of the physical reality. Later, however, I learned to consider the abstract machine as the true one, because that is the only one we can think ; it is the physical machine’s purpose to supply a working model, a (hopefully) sufficiently accurate physical simulation of the true, abstract machine. (Dijkstra)