English | PDF | 2009 | 165 Pages | ISBN : 0387876820 | 2.17 MB
This book gives a user friendly tut08rial to Fronts in R4ndom Media, an interdisciplinary research topic, to seni08r undergraduates 4nd graduate students in the mathematical sciences, physical sciences 4nd engineering.
Fronts 08r interface motion occur in a wide range of scientific areas w6eere the physical 4nd chemical laws are expressed in terms of differential equations. Heterogeneities are always present in natural environments: fluid convection in combustion, p08rous structures, noise effects in material manufacturing to name a few.
Stochastic models hence become natural due to the often lack of complete data in applications.
The transition from seeking deterministic solutions to stochastic solutions is both a conceptual change of thinking 4nd a technical change of tools. The book explains ideas 4nd results systematically in a motivating manner. It covers multi-scale 4nd r4ndom fronts in three fundamental equations (Burgers, Hamilton-Jacobi, 4nd reaction-diffusion-advection equations) 4nd expl08res their connections 4nd mechanical analogies. It discusses representation f08rmulas, Laplace methods, homogenization, ergodic the08ry, central limit the08rems, large-deviation principles, variational 4nd maximum principles.
It shows how to combine these tools to solve concrete problems.
Students 4nd researchers will find the step by step approach 4nd the open problems in the book particularly useful.