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| VARIATIONAL AND EXTREMUM PRINCIPLES IN MACROSCOPIC SYSTEMS
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By
Stanislaw Sieniutycz, Warsaw University of Technology, Faculty of Chemical and Process Engineering, Poland
Henrik Farkas, Budapest University of Technology and Economics
Description
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.
Audience
Readership is extremely broad and includes applied mathematicians, mathematical physicists, applied physicists, chemists, geologists,
ecologists, mechanical engineers, chemical engineers, economists and system theorists, undergraduates, graduates and instructors, both
from academia and industry.
Contents
List of contributors
Preface
Part I: Theory
I.1. Progress
in Variational Formulations for Macroscopic Processes
I.2. Lagrange-Formalism and Thermodynamics of Irreversible Processes: The 2nd Law
of Thermodynamics and the Principle of Least Entropy Production as Straightforward Structures in Lagrange-Formalism
I.3. Fundamental
Problems of Variational Principles: Objectivity, Symmetries and Construction
I.4. Semi-Inverse Method for Establishment of Variational
Principles for Incremental Thermoelasticity with Voids
I.5. Variational Formulations of Relativistic Elasticity and Thermo-Elasticity
I.6. The Geometric Variational Framework for Entropy in General Relativity
I.7. Translational and Rotational Motion of a Unaxial Liquid
Crystal as Derived Using Hamilton?s Principle of Least Action
I.8. An Introduction to Variational Derivation of the Pseudo-Momentum Conservation
in Thermo-Hydrodynamics
I.9. Towards a Variational Mechanics of Dissipative Continua?
I.10. On the Principle of Least Action and its
Role in the Alternative Theory of Non-Equilibrium Processes
I.11. Variational Principles for the Linearly Damped Flow of Barotropic and
Madelung-Type Fluids
I.12. Least Action Principle for Dissipative Processes
I.13. Hamiltonian Formulation as a Basis of Quantized Thermal
Processes
I.14. Conservation Laws and Variational Conditions for Wave Propagation in Planarly-Stratified Media
I.15. Master Equations
and Path-Integral Formulation of Variational Principles for Reactions
I.16. Variational Principles for the Speed of Traveling Fronts
of Reaction-Diffusion Equations
I.17. The Fermat Principle and Chemical Waves
Part II: Applications
Statistical Physics and Thermodynamics
II.1. Fisher Variational Principle and Thermodynamics
II.2. Generalized
Entropy and the Hamiltonian Structure of Statistical Mechanics
Hydrodynamics and Continuum Mechanics
II.3.
Some Observations of Entropy Extrema in Physical Processes
II.4. A Variational Principle for the Drag in Linear Hydrodynamics
II.5. A
Variational Principle for the Impinging Streams Problem
II.6. Variational Principles in Stability Analysis of Composite Structures
Transport Phenomena and Energy Conversion
II.7. Field Variational Principles for Irreversible Energy and
Mass Transfer
II.8. Variational Principles for Irreversible Hyperbolic Transport
II.9. A Variational Principle for Transport Processes
in Continuous Systems: Derivation and Application
II.10. Do the Navier-Stokes Equations Admit a Variational Formulation?
II.11. Entropy
Generation Minimization in Steady State Heat Conduction
II.12. The Nonequilibrium Thermodynamics of Radiation Interaction
II.13. Optimal
Finite-Time Endoreversible Processes- General Theory and Applications
II.14. Evolutionary Energy Method (EEM) – An Aerothermoservoelectrostatic
Application
Ecology
II.15. Maximization of Eco-Exergy in Ecosystems
Selforganization and Econophysics
II.16. Self-Organized Criticality within the Framework of Variational Principle
II.17. Extremum Criteria for Nonequilibrium States of
Dissipative Macroeconomic systems
II.18. Extremal Principles and Limiting Possibilities of Open Thermodynamic and Economic Systems
Glossary of principal symbols
Index
| Bibliographic details |
Hardbound, 810 pages, publication date: MAR-2005
ISBN-13: 978-0-08-044488-8
ISBN-10: 0-08-044488-1
Imprint: ELSEVIER
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| Price and Ordering |
Price:
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USD 305
EUR 237.95
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Last update: 5 Sep 2009
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