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1.

図書

図書
Vladimir N. Pokrovskii
出版情報: Dordrecht : Kluwer Academic, c2000  xiii, 231 p.
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2.

図書

図書
V.D. Potapov
出版情報: Chichester : John Wiley, 1999  xi, 275 p. ; 25 cm
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3.

図書

図書
Weimin Han and Mircea Sofonea
出版情報: Providence : American Mathematical Society, c2002  xvii, 442 p. ; 26 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 30
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目次情報: 続きを見る
Nonlinear variational problems and numerical approximation: Preliminaries of functional analysis Function spaces and their properties
Introduction to finite difference and finite element approximations
Variational inequalities
Mathematical modelling in contact mechanics: Preliminaries of contact mechanics of continua
Constitutive relations in solid mechanics
Background on variational and numerical analysis in contact mechanics
Contact problems in elasticity Contact problems in viscoelasticity: A frictionless contact problem
Bilateral contact with slip dependent friction
Frictional contact with normal compliance
Frictional contact with normal damped response
Other viscoelastic contact problems
Contact problems in visocplasticity: A Signorini contact problem
Frictionless contact with dissipative potential
Frictionless contact between two viscoplastic bodies
Bilateral contact with Tresca's friction law
Bibliography
Index
Nonlinear variational problems and numerical approximation: Preliminaries of functional analysis Function spaces and their properties
Introduction to finite difference and finite element approximations
Variational inequalities
4.

図書

図書
edited by G.A.C. Graham & J.R. Walton
出版情報: Wien : Springer-Verlag, 1995  311 p. ; 24 cm
シリーズ名: CISM courses and lectures ; No. 356
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5.

図書

図書
Antony N. Beris, Brian J. Edwards
出版情報: New York : Oxford University Press, 1994  xx, 683 p. ; 24 cm
シリーズ名: The Oxford engineering science series ; 36
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目次情報: 続きを見る
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:
6.

図書

図書
by John D. Ferry
出版情報: New York : Wiley, c1961  xx, 482 p. ; 24 cm
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7.

図書

図書
Stefan Zahorski ; [translation Antoni Pol]
出版情報: The Hague ; Boston : M. Nijhoff : Distributors for the U.S. and Canada, Kluwer Boston, 1982  xiv, 321 p. ; 24 cm
シリーズ名: Mechanics of fluids and transport processes ; 2
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8.

図書

図書
R.M. Christensen
出版情報: New York ; Tokyo : Academic Press, 1982  xii, 364 p. ; 24 cm
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9.

図書

図書
Andrew J. Matheson
出版情報: London : Wiley-Interscience, c1971  [xvii], 290 p. ; 24 cm
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10.

図書

図書
[by] F.J. Lockett
出版情報: London ; New York : Academic Press, 1972  xi, 195 p. ; 24 cm
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