Browsing by Author "Wake, Graeme C."

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    A cell growth model revisited
    (Research Institute, College of Judea and Samaria,, 2012) Derfel, G; Van Brunt, B; Wake, Graeme C.
    In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This probabilistic approach gives straightforward proof of the existence of the steady-size distribution and a simple derivation of the functional-differential equation for it. The latter one is the celebrated pantograph equation (of advanced type). This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework.