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mathtoys [2016/05/24 00:07] (current)
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 +====== Mathematical Toys ======
  
 +  * Develop toy mathematical models of physical phenomena
 +  * Focus on differential and difference equations
 +  * Each toy model accompanied by numerical and analytical insight
 +
 +===== Fluid Mechanics =====
 +
 +  * [[mathtoys:​brownian|From Brownian motion to diffusion]]
 +  * Spreading droplets
 +  * Dripping paint
 +  * A traffic jam (telegraph and Burger'​s)
 +  * Transition to turbulence (Orr-Sommerfeld)
 +  * Ship waves
 +  * Porous flow, oil extraction, and viscous fingering
 +  * Capillary and gravity waves on a stream
 +  * Shock waves
 +  * Flight, Kutta-Joukowski,​ conformal mapping
 +  * Coriolis effect
 +  * Non-dispersive water waves (Boussinesq)
 +
 +
 +===== Solid Mechanics =====
 +
 +  * Waves on a string
 +  * Wrinkling and buckling
 +  * Crack propogation
 +  * Earthquakes:​ P-waves and S-waves
 +  * Vibrational modes of a plate (biharmonic equation)
 +
 +===== Dynamics =====
 +  * [[mathtoys:​rotatinghoop|Rotating hoops and sliding beads]]
 +  * [[mathtoys:​eulerwobble|Euler wobble and free rotations]]
 +  * Tops
 +
 +===== Biology, chemistry, and ecology =====
 +  * The leopard and its spots (Gray-Scott)
 +  * Metastability (Allen-Cahn)
 +  * Chemical systems
 +  * Modeling the brain
 +  * Predator prey systems
 +  * Spinodal decomposition (Cahn-Hilliard)
 +===== Light and electromagnetism =====
 +  * Shortest distances and geodesics
 +  * Airy equation, rays, caustics
 +  * Scattering light and Helmholtz
 +  * Green'​s functions and method of images
 +  * Superconductivity (Ginzburg-Landau)
 +
 +===== Economics and finance =====
 +
 +  * [[:​mathtoys:​blackscholes|Black-Scholes model]]
 +
 +===== Sociology and psychology =====
 +
 +===== Computers and technology =====
 +  * Image sharpening (Backwards heat equation, Perona-Malik)