Differences

This shows you the differences between two versions of the page.

 — mathtoys [2016/05/24 00:07] (current) Line 1: Line 1: + ====== 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) 