Hybrid Methods in Engineering Modeling, Programming, Analysis, Animation

ISSN for PRINT: 1099-2391

For Online Access

Best Paper Award Selection - Editorial Board Site

1999, Volume1

Issue 4

138 pages

Issue price - $125.00

F. C. Peixoto
Institute de Pesquisa e Desenvolvimento (IPD), Grupo de Quimica, Rio de Janeiro, Brazil, and Escola de Quimica, Centro de Tecnologia, UFRJ, Cidade Universitdria, Rio de Janeiro, Brazil

Cell cultures can be thought as a continuum of organisms, each of which goes through a cycle that includes birth, aging, reproduction, and death. The properties of each organism change during this cycle and one (or more) of these properties can be used to continuously characterize the individuals present in the culture, using a frequency distribution function. Rigorous models for this kind of mixture are called population balance equations. Due to their integro-partial differential form, these equations are considered difficult to solve analytically, and approximations or numerical approaches are usually employed. In the present work, an explicit solution to this kind of equation is found, with minimum loss of generality, using a perturbational procedure. Once the recurrence is obtained, the terms are expanded in an orthonormal basis to calculate the time evolution of the distributions.

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