[Fick's law] Fick's laws of diffusion

From the mass conservation, the Fick's law is derived. 

Hence, for a random walk in inhomogeneous media (diffusion coefficient depends on space), we need an additional term in the diffusion equation.

밀도n의 시간t에 따른 변화는 외부로부터 유입되는 net-flux로 계산된다 (mass conservation).

${\displaystyle {\frac {\partial n}{\partial t}}+\nabla \cdot \mathbf {J} =0}$

따라서, 다음과 같은 식을 얻는다.

${\displaystyle {\frac {\partial n}{\partial t}}(x)=\nabla \cdot (D(x)\nabla n(x))}$

[Ref]

https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion

https://ko.wikipedia.org/wiki/%ED%94%BD%EC%9D%98_%ED%99%95%EC%82%B0_%EB%B2%95%EC%B9%99

https://arxiv.org/pdf/1512.07428.pdf

https://link.springer.com/article/10.1007%2FBF02634100

https://www.sciencedirect.com/science/article/pii/0022369788901990