7/21/2019 Diffusion, Advection homework

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Edgar Marca GA-041 — J. Karam 1

Question 1.  List a set of examples of mathematical concepts applied in areas like

Economy, Social Science, Engineering, etc.

Answer 1. Convection   is the collective motion of particles in a fluid and actually

encompass both diffusion and advection.

•   Advection  is the motion of particles along a bulk flow.

∂ψ

∂t  + ∇.(uψ) = 0

•   Diffusion   is the net movement of particles from high concentration to low

concentration.∂ψ

∂t  =  ∇. (D∇ψ)

D: Diffusion Coefficient.

In Economy, the Black-Scholes equation for option pricing is a diffusion-advection

equation. In Social Science, the spread of crime can be modeled by a reaction-

diffusion-advection system. In Ecology, the mathematical model for fish schools are

modeled by a ecological diffusion model like Fokker-Planck. Additionally, diffusion

models can be used for studying insect and animal dispersal and invasion. The

diffusion can be applied to model contamination spread in a lake. In Engineering,

the diffusion equation can be used to model the heat conduction. The idea of flow

can be applied to traffic problems.

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