Variational and Extremum Principles in Macroscopic Systems

9780080972299: 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.

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About the Author:

Stanislaw Sieniutycz is Professor of Chemical Engineering at the Institute of Chemical and Process Engineering at the Warsaw University of Technology in Poland. His research focuses on thermal and chemical engineering with special emphasis on the control, stability and optimization of chemical and electrochemical reaction systems. He published 10 books with international scientific publishers and 224 articles in international scientific journals, and 140 conference and invited papers. He is Associate Editor and Member of Editorial Board of the Journal of Non-Equilibrium Thermodynamics, Associate Editor and Member of Editorial Board of the Journal: Open Systems and Information Dynamics, Associate Editor and Member of Editorial Board of the Journal: International Journal of Applied Thermodynamics, Member of Editorial Board of the Journal: Energy & Conversion Management, Associate Editor of Advances in Thermodynamics Series, Member of Committee of Chemical Engineering at Polish Academy of Sciences. He received 7 awards.

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

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