MARKOV CHAIN THEORY OF FREE-MOLECULE FLOW,
Abstract
The motion of molecules can be described by a stochastic process if and only if one chooses a stochastic boundary condition in which the properties of reflected molecule is not uniquely determined by the properties of the incident molecule, but depends only on the properties of the local surface condition (e.g. the diffuse reflection law is a stochastic boundary condition). In this paper, a mathematical model has been proposed which describes the motion of each molecule by probability function in a multi-reflection system (such as internal flow or external flow with nonconvex body) in terms of its initial probability function and successive transition probabilities in a discrete sample space. The successive transition probability functions are determined from the diffuse reflection law and the geometry of the system, and are independent of time. Such a mathematical model is equivalent to a stationary Markov chain process in probability theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1964
- Accession Number
- AD0622566
Entities
People
- Yau Wu
Organizations
- Princeton University