We have attempted to explain the concepts which have been used and
developed to model the stochastic dynamics of natural and biological systems.
While the theory of stochastic differential equations and stochastic processes
provide an attractive framework with an intuitive appeal to many problems
with naturally induced variations, the solutions to such models are an active
area of research, which is in its infancy. Therefore, this book should provide
a large number of areas to research further.
Unstructured modelling growth of Lactobacillus acidophilus
as a function of the temperature: We present modelling software developed under MATLAB in which parameter estimations are obtained by using non-linear regression techniques. The different parameters appear in a set of non-linear algebraic and differential equations representing the model of the process. From experimental data obtained in discontinuous cultures a representative mathematical model (unstructured kinetic model) of the macroscopic behaviour of Lactobacillus acidophilus has been developed.
The increasing demand on ultra miniturized electronic devices for ever improving
performances has led to the necessity of a deep and detailed understanding
of the mathematical theory of charge transport in semiconductors.
The end of the 1970s saw the idea of fractal geometry spread into numerous
areas of physics. Indeed, the concept of fractal geometry, introduced by B.
Mandelbrot, provides a solid framework for the analysis of natural phenomena
in various scientific domains. As Roger Pynn wrote in Nature, “If this opinion
continues to spread, we won’t have to wait long before the study of fractals
becomes an obligatory part of the university curriculum.”