| Theory / Part I： |
| Introduction / Chapter 1： |
| Overview / 1.1： |
| The challenge of multiple time and length scales / 1.2： |
| The energy as the fundamental quantity / 1.3： |
| The generalized bracket approach / 1.4： |
| A simple application: The damped oscillator / 1.5： |
| Symplectic geometry in optics / Chapter 2： |
| Theories of optics / 2.1： |
| Symplectic structure / 2.3： |
| The symplectic vector space / 2.3.1： |
| The symplectic transformation / 2.3.2： |
| Gaussian and linear optics / 2.4： |
| Gaussian optics / 2.4.1： |
| Linear optics / 2.4.2： |
| Geometrical optics / 2.5： |
| The symplectic structure of geometrical optics / 2.5.1： |
| Fermat's principle / 2.5.2： |
| An overview of wave optics and electromagnetism / 2.6： |
| Hamiltonian mechanics of discrete particle systems / Chapter 3： |
| The calculus of variations / 3.1： |
| Hamilton's principle of least action / 3.2： |
| The Poisson bracket description of Hamilton's equations of motion / 3.3： |
| Properties of the Poisson bracket / 3.4： |
| The Liouville equation / 3.5： |
| The optical/mechanical analogy / 3.6： |
| A historical aside on the principle of least action / 3.7： |
| Fermat's reception / 3.7.1： |
| Maupertuis' contribution / 3.7.2： |
| Hamilton on the principle of least action / 3.7.3： |
| Equilibrium thermodynamics / Chapter 4： |
| The fundamental equation of thermodynamics / 4.1： |
| Other fundamental relationships of thermodynamics / 4.2： |
| The fundamental equation for a multicomponent system / 4.3： |
| Extensive variable formulation / 4.3.1： |
| Specific variable formulation / 4.3.2： |
| Density variable formulation / 4.3.3： |
| Equilibrium thermodynamics of a material with internal microstructure / 4.4： |
| Additivity in compound systems / 4.5： |
| Poisson brackets in continuous media / Chapter 5： |
| The material description of ideal fluid flow / 5.1： |
| The canonical Poisson bracket for ideal fluid flow / 5.2： |
| The calculus of functionals / 5.2.1： |
| The continuum Poisson bracket / 5.2.2： |
| The spatial description of ideal fluid flow / 5.3： |
| Ideal fluid flow with constraints: The incompressible fluid / 5.4： |
| Nonlinear elasticity / 5.5： |
| The material description of nonlinear elasticity / 5.5.1： |
| Spatial bracket derivation / 5.5.2： |
| Spatial bracket in terms of a tensor with unit trace / 5.5.3： |
| The relation between thermodynamics and hydrodynamics / 5.6： |
| The global system / 5.6.1： |
| The compound system / 5.6.2： |
| Non-equilibrium thermodynamics / Chapter 6： |
| Irreversibility and stability / 6.1： |
| Systems with internal variables / 6.2： |
| The Clausius inequality / 6.3： |
| Non-equilibrium thermodynamics of flowing systems / 6.4： |
| The entropy balance equation / 6.4.1： |
| The linear phenomenological relations / 6.4.2： |
| Frame indifference and material invariance / 6.4.3： |
| The principle of microscopic reversibility / 6.4.4： |
| The nature of affinities and fluxes / 6.4.5： |
| The Onsager/Casimir reciprocal relations / 6.5： |
| Einstein's fluctuation theory / 6.5.1： |
| Transformation properties of the reciprocal relations / 6.5.2： |
| Affinities and fluxes for continua / 6.6： |
| Density description of the entropy production rate / 6.6.1： |
| Description of the entropy production rate in terms of fluxes / 6.6.2： |
| The dissipation bracket / Chapter 7： |
| The general dissipation bracket / 7.1： |
| Definition and properties of the dissipation bracket / 7.1.1： |
| Equivalence of the energetic and entropic formalisms / 7.1.2： |
| The hydrodynamic equations for a single-component system / 7.2： |
| The general isotropic fluid / 7.2.1： |
| The incompressible Navier/Stokes equations / 7.2.2： |
| The hydrodynamic equations for a polar fluid / 7.2.3： |
| The hydrodynamic equations for a multicomponent fluid / 7.3： |
| Applications / Part II： |
| Incompressible viscoelastic fluids / Chapter 8： |
| Incompressible and isothermal viscoelastic fluid models in terms of a single conformation tensor / 8.1： |
| Simple phenomenological spring/dashpot-type models / 8.1.1： |
| Elastic dumbbell models of dilute polymer solutions arising through kinetic theory / 8.1.2： |
| Single internal variable models for concentrated polymer solutions and melts / 8.1.3： |
| Dissipation and admissibility criteria for single-mode viscoelastic fluids / 8.1.4： |
| The non-negative character of the conformation tensor for single-variable viscoelastic fluids / 8.1.5： |
| Evolutionary character of the governing equations of single-variable viscoelastic fluids / 8.1.6： |
| Incompressible viscoelastic fluid models in terms of multiple conformation tensors / 8.2： |
| Guidelines on multiple-variable viscoelastic fluid models from the perspective of linear viscoelasticity / 8.2.1： |
| Phenomenological multiple-variable models / 8.2.2： |
| The bead/spring-chain model of kinetic theory / 8.2.3： |
| Transport phenomena in viscoelastic fluids / Chapter 9： |
| Compressible and non-isothermal viscoelastic fluid models / 9.1： |
| Modeling of the rheology and flow-induced concentration changes in polymer solutions / 9.2： |
| Single-fluid model of polymer-solution hydro-dynamics allowing for concentration variations / 9.2.1： |
| Two-fluid model for polymer solutions / 9.2.2： |
| Comparison of various theories for polymer solution hydrodynamics / 9.2.3： |
| Surface effects on the microstructure and concentration in incompressible and isothermal viscoelastic fluid flows / 9.3： |
| Derivation of the governing equations in terms of the Hamiltonian / 9.3.1： |
| Determination of the Hamiltonian functional / 9.3.3： |
| Calculations with the resulting model equations / 9.3.4： |
| Comparison with available experimental data and previous theoretical work / 9.3.5： |
| Effects of surface adsorption / 9.3.6： |
| Non-conventional transport phenomena / Chapter 10： |
| Relaxational phenomena in heat and mass transfer / 10.1： |
| Flux-relaxation models / 10.1.1： |
| The bracket formulation of relaxational phenomena in heat conduction / 10.1.2： |
| The bracket description of relaxational phenomena in mass diffusion / 10.1.3： |
| Heat and mass flux relaxation in the kinetic theory of gases / 10.1.4： |
| Relaxational mass transfer in polymeric systems / 10.1.5： |
| Phase transitions in inhomogeneous media / 10.2： |
| The kinetics of phase transitions / 10.2.1： |
| The bracket description of the kinetics of phase transitions / 10.2.2： |
| The inertial description of incompressible viscoelastic fluids / 10.3： |
| The dynamical theory of liquid crystals / Chapter 11： |
| Introduction to liquid crystals / 11.1： |
| Thermodynamics of liquid crystals under static conditions / 11.2： |
| Equilibrium thermodynamics of homogeneous liquid crystals / 11.2.1： |
| The Oseen/Frank description of non-homogeneous nematic liquid crystals / 11.2.2： |
| The LE and Doi models for flowing liquidcrystalline systems / 11.3： |
| The Leslie/Ericksen theory / 11.3.1： |
| The scalar/vector theory / 11.3.2： |
| The Doi theory / 11.3.3： |
| The Leslie coefficients: Implications for flow behavior and molecular determination / 11.3.4： |
| The bracket description of the LE theory / 11.4： |
| The inertial form / 11.4.1： |
| The non-inertial form / 11.4.2： |
| The conformation tensor theory / 11.5： |
| Comparison of the conformation tensor theory to previous theories / 11.5.1： |
| Reduction to the Leslie/Ericksen theory / 11.6.1： |
| Reduction to the scalar-vector theory / 11.6.2： |
| Reduction to the original Doi theory / 11.6.3： |
| Reduction to the extended Doi theory / 11.6.4： |
| Equivalent Leslie coefficients for the general conformation tensor theory / 11.6.5： |
| Concluding remarks / 11.7： |
| Multi-fluid transport/reaction models with application in the modeling of weakly ionized plasma dynamics / Chapter 12： |
| Elements from the modeling of weakly ionized plasma dynamics / 12.1： |
| Multi-fluid descriptions of nonlinear kinetics / 12.1.2： |
| The non-dissipative multi-fluid system / 12.2： |
| The dissipative multi-fluid system / 12.3： |
| Chemical reactions in a multicomponent single-fluid system / 12.4： |
| Chemical reactions in multi-fluid systems / 12.5： |
| Weakly ionized plasma model / 12.6： |
| Conclusions / 12.7： |
| Epilogue |
| Introduction to differential manifolds / Appendix A： |
| Differential manifolds / A.1： |
| Curves / A.2： |
| Tangent spaces / A.3： |
| Differential forms / A.4： |
| Symplectic forms and symplectic transformations / A.5： |
| The Lagrangian manifold / A.6： |
| The Hamiltonian vector field / A.7： |
| The Poisson bracket / A.8： |
| The Legendre dual transformation / Appendix B： |
| Poisson brackets for arbitrary second-rank deformation tensors / Appendix C： |
| Calculations of the random-flight model / Appendix D： |
| Calculation of the end-to-end distribution function near a solid surface / D.1： |
| Calculation of the partition function / D.2： |
| Bibliography |
| Author Index |
| Subject Index |
| Theory / Part I： |
| Introduction / Chapter 1： |
| Overview / 1.1： |
ＥＢ
