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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

**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**

- No. of pages: 810
- Language: English
- Edition: 1
- Published: March 30, 2005
- Imprint: Elsevier Science
- Hardback ISBN: 9780080444888
- Paperback ISBN: 9780080972299
- eBook ISBN: 9780080456140

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### Stanislaw Sieniutycz

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