The Diffusion Equation

  • Richard Ghez


We begin with a model for diffusion: the isotropic one-dimensional random walk.1–4 It is so simple that the basic physical processes cannot elude us. It also has a continuum limit, the diffusion equation, whose solutions are our main concern here and some of whose properties we then examine. Conversely, this model forms the basis for numerical methods of solution. We then discuss the diffusion equation’s form in higher dimensions and other physical instances where that equation offers a realistic description. This chapter ends with a brief account of the origin of conservation principles and constitutive relations that pervade transport phenomena.


Diffusion Equation Constitutive Relation Explicit Scheme Adjacent Site Jump Distance 
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© Springer Science+Business Media New York 2001

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  • Richard Ghez

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