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2016
In this chapter, the random walk model of a particle is used to drive a better understanding of what diffusion is. The probability density function for the limiting form of the probability distribution of the random walk is shown to be a solution to a diffusion model.
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In this chapter, the random walk model of a particle is used to drive a better understanding of what diffusion is. The probability density function for the limiting form of the probability distribution of the random walk is shown to be a solution to a diffusion model.
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2001
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.
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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.
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1991
Diffusion is a process by which matter is transported as a result of random molecular motion. If in a system a substance is not distributed homogeneously, a net transfer of that substance takes place in the direction of lower concentration.
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Diffusion is a process by which matter is transported as a result of random molecular motion. If in a system a substance is not distributed homogeneously, a net transfer of that substance takes place in the direction of lower concentration.
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1984
For a » 1 and s » 1 we have obtained accurate estimates of the equilibrium joint distribution when \(\kappa = {{\left( {s - a} \right)} \mathord{\left/ {\vphantom {{\left( {s - a} \right)} {\sqrt s }}} \right. \kern-\nulldelimiterspace} {\sqrt s }}\) is either large and positive or large and negative.
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For a » 1 and s » 1 we have obtained accurate estimates of the equilibrium joint distribution when \(\kappa = {{\left( {s - a} \right)} \mathord{\left/ {\vphantom {{\left( {s - a} \right)} {\sqrt s }}} \right. \kern-\nulldelimiterspace} {\sqrt s }}\) is either large and positive or large and negative.
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