Variational and Extremum Principles in Macroscopic Systems

Recent years have seen a growing trend to derive models of macroscopic phenomena encountered in the fields of engineering, physics, chemistry, ecology, self-organisation theory and econophysics from various variational or extremum principles. Through the link between the integral extremum of a functional and the local extremum of a function (explicit, for example, in the Pontryagin's maximum principle variational and extremum principles are mutually related. Thus it makes sense to consider them within a common context. The main goal of the present book is to collect various mathematical formulations and examples of physical reasoning that involve both basic theoretical aspects and applications of variational and extremum approaches to systems of the macroscopic world. The first part of the book is focused on the theory, whereas the second focuses on applications. The unifying variational approach is used to derive the balance or conservation equations, phenomenological equations linking fluxes and forces, equations of change for processes with coupled transfer of energy and substance, and optimal conditions for energy management.* A unique multidisciplinary synthesis of variational and extremum principles in theory and application. *A comprehensive review of current and past achievements in variational formulations for macroscopic processes. *Uses Lagrangian and Hamiltonian formalisms as a basis for the exposition of novel approaches to transfer and conversion of thermal, solar and chemical energy.

Table of Contents:
Part I: Theory Variational Principles in Macroscopic Systems Part II: Applications Statistical Physics and Thermodynamics, Hydrodynamics and Continuum Mechanics, Transport Phenomena and Energy Conversion, Ecology, Selforganization and Econophysics Glossary of principal symbols Index

About the Author :
Stanislaw Sieniutycz is a former member of the Committee of Engineering at the Polish Academy of Sciences and also a professor of chemical engineering at the Warsaw University of Technology, Poland. His research focuses on problems of chemical, environmental, ecological, and biomechanical engineering with emphasis on analysis, control, and optimization of these systems. He is a former member of the Editorial Board of Open System and Information Dynamics and an honorary editor of the Journal of Non-Equilibrium Thermodynamics. He has served as an associate editor of Advances in Thermodynamics Series and Energy & Conversion Management. He has published 12 books, 250 articles, and 152 conference papers. He has been a visiting professor at the University of Budapest, University of Bern, University of San Diego, University of Delaware, and University of Chicago.

Review :
"This book will be valuable for mathematicians, physicists, chemists, and engineers, in particular those involoved in the application of the mathematical and thermodynamic knowledge to systems with energy generation and transport, solar radiation, chemical waves, liquid crystals, thermo-elastic media, composites, multiphase flows, porous media, membrane transfer, microeconomics, etc." -INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2006