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!

List of topics: 

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

Compare alternative list of models.

Start: Space-Position Time-Motion

  1. Fireworks (see also Fireworks Many + with sound)
  2. Harmonic Oscillator   (with music)
  3. Stop Watch
  4. Bouncing Block: Single (with click sound)  (3d version)
  5. Bouncing Block: Many    (3d version)
  6. Newton’s Cradle
  7. Elastic Collision
  8. Walking Boy Animation     Running Caveman Animation
  9. Variants of sin cos: BesselFunction V2 V3  V4 V5  V6  V7

Population-Reaction Dynamics

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

Mass – Spring Systems

  1. Sun-Planet-Moon System
  2. Single Pendulum
  3. Double Pendulum
  4. Multi Pendulum
  5. Cosmic Interaction (stunning, compare with Lone Space Traveler)
  6. Elastic Body (compare Circus Cow1+Circus Cow2)
  7. Elastic Body as Particle-Spring System
  8. Play with Elastic Body.
  9. Elastic String of Beads
  10. Vibrating String
  11. Plucking String
  12. Colliding Elastic Balls(with Sliders)

Resonance

  1. Forced Oscillator
  2. Resonance

Solid Mechanics: Elastic Bodies

  1. Elastic Bar
  2. Elastic Web
  3. Elastic Membrane (compare HD version)
  4. Plane Elastic Body under Impulse Load
  5. Plane Elastic Cantilever under Gravity
  6. Elasto-Visco-Plastic Plate under Gravity
  7. Elasto-Visco-Plastic Plate under Distributed Load
  8. Obstacle Problem: Free Boundary Problem

Convection – Diffusion

Reaction – Diffusion

Fluid Mechanics

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

Coupled Fluid – Solid 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

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)

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)

Heat Conduction

  1. Heat Conduction 1d
  2. Heat Conduction 1d: Forward Euler vs Midpoint Euler
  3. Heat Conduction 2d Hot Spot
  4. Reconstruction after Smoothing (test sharpening of smoothed jump)
  5. Sensitivity by Duality (heat eq)

ElectroMagnetics

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

Chemical Reactions

  1. Flame Front (The G Equation)

Chaos

Fractals and Representation

  1. Fractal Binary Tree by Recursion  (see also Fractal Binary Forest)
  2. Trigonometric Series
  3. Stock Market with Haar Basis

Parameter Identification

Music

  1. Music: Pythagorean Scale (Compare sinus wave with square wave) Combine with Frequency Sound Generator

Image

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

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)

Atom Physics

  1.  Atom Secret (deep and colourful). Compare with this analysis and this.
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)