The Thermomechanics Of Nonlinear Irreversible Behaviours
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The Thermomechanics Of Nonlinear Irreversible Behaviours
In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of “irreversible thermodynamics” behaviors which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework.The book is intended for all students and researchers whose main concern is the rational modeling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, fracture, nonlinear-diffusion, and phase-transformation phenomena.
Extended Irreversible Thermodynamics
Author: David Jou
language: en
Publisher: Springer Science & Business Media
Release Date: 2001
I. General Theory.- 1 Classical and Rational Formulations of Non-equilibrium Thermodynamics.- 1.1 The General Balance Laws of Continuum Physics.- 1.2 The Law of Balance of Entropy.- 1.3 Classical Irreversible Thermodynamics.- 1.4 Rational Thermodynamics.- Problems.- 2 Extended Irreversible Thermodynamics: Evolution Equations.- 2.1 Heat Conduction.- 2.2 One-component Viscous Fluid.- 2.3 The Generalised Entropy Flux and Entropy Production.- 2.4 Linearized Evolution Equations of the Fluxes.- 2.5 Rational Extended Thermodynamics.- 2.6 Some Comments and Perspectives.- 2.7 Entropy Evolution in an Isolated System: An Illustrative Example.- Problems.- 3 Extended Irreversible Thermodynamics: Non-equilibrium Equations of State.- 3.1 Physical Interpretation of the Non-equilibrium Entropy.- 3.2 Non-equilibrium Equations of State: Temperature.- 3.3 Non-equilibrium Equations of State: Thermodynamic Pressure.- 3.4 Convexity Requirements and Stability.- Problems.- 4 Hamiltonian Formulations.- 4.1 GENERIC Formulation.- 4.2 Reversible and Irreversible Kinematics.- 4.3 Governing Equations of EIT.- Problems.- II. Microscopic Foundations.- 5 The Kinetic Theory of Gases.- 5.1 The Basic Concepts of Kinetic Theory.- 5.2 Non-equilibrium Entropy and the Entropy Flux.- 5.3 Grad' Solution.- 5.4 The Relaxation-Time Approximation.- 5.5 Dilute Non-ideal Gases.- 5.6 Non-linear Transport.- 5.7 Beyond the Thirteen-Moment Approximation: Continued-Fraction Expansions of Transport Coefficients.- Problems.- 6 Fluctuation Theory.- 6.1 Einstein' Formula. Second Moments of Equilibrium Fluctuations.- 6.2 Ideal Gases.- 6.3 Fluctuations and Hydrodynamic Stochastic Noise.- 6.4 The Entropy Flux.- 6.5 Application to a Radiative Gas.- 6.6 Onsager' Relations.- Problems.- 7 Information Theory.- 7.1 Basic Concepts.- 7.2 Ideal Gas Under Heat Flux and Viscous Pressure.- 7.3 Ideal Gas Under Shear Flow: Non-linear Analysis.- 7.4 Ideal Gas Submitted to a Heat Flux: Non-linear Analysis.- 7.5 Relativistic Ideal Gas Under an Energy Flow.- 7.6 Heat Flow in a Linear Harmonic Chain.- 7.7 Information Theory and Non-equilibrium Fluctuations.- Problems.- 8 Linear Response Theory.- 8.1 Projection Operator Methods.- 8.2 Evolution Equations for Simple Fluids.- 8.3 Continued-Fraction Expansions.- Problems.- 9 Computer Simulations.- 9.1 Computer Simulations of Non-equilibrium Steady States.- 9.2 Non-equilibrium Equations of State.- 9.3 Dependence of the Free Energy on the Shear Rate: Non-linear Approach.- 9.4 Shear-Induced Heat Flux and the Zeroth Law.- Problems.- III. Selected Applications.- 10 Hyperbolic Heat Conduction.- 10.1 The Finite Speed of Thermal Signals. Second Sound.- 10.2 Heat Pulses.- 10.3 Beyond the Maxwell-Cattaneo Equation.- 10.4 Second Sound Under a Heat Flow.- 10.5 Heat Conduction in a Rotating Rigid Cylinder.- 10.6 Non-linear Heat Transfer: Flux Limiters.- 10.7 Other Applications.- Problems.- 11 Waves in Fluids.- 11.1 Hydrodynamic Modes in Simple Fluids.- 11.2 Transverse Viscoelastic Waves.- 11.3 Ultrasound Propagation in Monatomic Gases.- 11.4 Shock Waves.- Problems.- 12 Generalised Hydrodynamics.- 12.1 Density and Current Correlation Functions.- 12.2 Spectral Density Correlation.- 12.3 The Transverse Velocity Correlation Function: the EIT Description.- 12.4 The Longitudinal Velocity Correlation Function: the EIT Description.- 12.5 Influence of Higher-order Fluxes.- Problems.- 13 Non-classical Diffusion.- 13.1 Extended Thermodynamics of Diffusion.- 13.2 Telegrapher' Equation and Stochastic Processes.- 13.3 Taylor' Dispersion.- 13.4 Non-Fickian Diffusion in Polymers.- 13.5 Hyperbolic Reaction-Diffusion Systems.- Problems.- 14 Electrical Systems.- 14.1 Electrical Systems: Evolution Equations.- 14.2 Cross Terms in Constitutive Equations: Onsager' Relations.- 14.3 Hydrodynamical Models of Transport in Semiconductors and Plasmas.- 14.4 Dielectric Relaxation of Polar Liquids.- Problems.- 15 Rheological Materials.- 15.1 Rheological Models.- 15.2 EIT Description of Linear Visc
Continuum Mechanics Through the Eighteenth and Nineteenth Centuries
Author: Gérard A. Maugin
language: en
Publisher: Springer Science & Business Media
Release Date: 2014-04-04
Conceived as a series of more or less autonomous essays, the present book critically exposes the initial developments of continuum thermo-mechanics in a post Newtonian period extending from the creative works of the Bernoullis to the First World war, i.e., roughly during first the “Age of reason” and next the “Birth of the modern world”. The emphasis is rightly placed on the original contributions from the “Continental” scientists (the Bernoulli family, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in competition with their British peers (Green, Kelvin, Stokes, Maxwell, Rayleigh, Love,..). It underlines the main breakthroughs as well as the secondary ones. It highlights the role of scientists who left essential prints in this history of scientific ideas. The book shows how the formidable developments that blossomed in the twentieth century (and perused in a previous book of the author in the same Springer Series: “Continuum Mechanics through the Twentieth Century”, Springer 2013) found rich compost in the constructive foundational achievements of the eighteenth and nineteenth centuries. The pre-WWI situation is well summarized by a thorough analysis of treatises (Appell, Hellinger) published at that time. English translations by the author of most critical texts in French or German are given to the benefit of the readers.