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Variational and Extremum Principles in Macroscopic Systems
- 1st Edition - March 30, 2005
- Authors: Stanislaw Sieniutycz, Henrik Farkas
- Language: English
- Hardback ISBN:9 7 8 - 0 - 0 8 - 0 4 4 4 8 8 - 8
- Paperback ISBN:9 7 8 - 0 - 0 8 - 0 9 7 2 2 9 - 9
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 4 5 6 1 4 - 0
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 an… Read more
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Request a sales quoteRecent 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 Variational and Extremum Principles in Macroscopic Systems 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
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.
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
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
- No. of pages: 810
- Language: English
- Edition: 1
- Published: March 30, 2005
- Imprint: Elsevier Science
- Hardback ISBN: 9780080444888
- Paperback ISBN: 9780080972299
- eBook ISBN: 9780080456140
SS
Stanislaw Sieniutycz
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.
Affiliations and expertise
Professor of Chemical Engineering, Warsaw University of Technology, Faculty of Chemical and Process Engineering, PolandHF
Henrik Farkas
Affiliations and expertise
Budapest University of Technology and Economics