Accession Number : AD0633861

Title :   QUADRATIC DIFFERENTIAL SYSTEMS FOR MATHEMATICAL MODELS,

Corporate Author : ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

Personal Author(s) : JENKS,Richard D.

Report Date : MAY 1966

Pagination or Media Count : 139

Abstract : This study is concerned with a set of n coupled non-linear differential equations. Such systems suggest mathematical models in almost every branch of the physical sciences where collisions of entities are involved. This paper is essentially in three parts. The first part concerns general n-dimensional systems. Results concerning the existence, uniqueness, and stability of critical points of the above system are given. Certain 'connectedness' concepts are introduced for classification purposes. The second part deals with lower dimensional systems, n=2 and n=3. For n=3, a geometric theory of 'completely positive' systems uncovers a large class of systems which have unique critical points in the interior of the first orthant and which are asymptotically stable in the large. The third part considers a mathematical model for the collision of molecules in a uniform gas. The classical Boltzmann model is discretized by considering the velocity space to be partitioned into a finite number of mutually exclusive regions called 'bins,' each with its own distribution function. This assumption not only greatly simplifies the Boltzmann integro-differential equation but also suggests quadrature methods for numerical evaluation of the Boltzmann integral. (Author)

Descriptors :   (*MATHEMATICAL MODELS, (*NONLINEAR DIFFERENTIAL EQUATIONS), BIOLOGY, MOLECULAR BEAMS, KINETIC THEORY, GASES, MATRICES(MATHEMATICS)

Subject Categories : Biology
      Operations Research
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE