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Gurtin M.E. — Thermomechanics of evolving phase boundaries in the plane
Gurtin M.E. — Thermomechanics of evolving phase boundaries in the plane

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Название: Thermomechanics of evolving phase boundaries in the plane

Автор: Gurtin M.E.

Аннотация:

This is one of the few books on the subject of mathematical materials science. It discusses the dynamics of two-phase systems within the framework of modern continuum thermodynamics, stressing fundamentals. Two general theories are discussed: a mechanical theory that leads to a generalization of the classical curve-shortening equation and a theory of heat conduction that broadly generalizes the classical Stefan theory. This original survey includes simple solutions that demonstrate the instabilities inherent in two-phase problems. The free-boundary problems that form the basis of the subject should be of great interest to mathematicians and physical scientists.


Язык: en

Рубрика: Физика/Классическая физика/Упругие среды/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 148

Добавлена в каталог: 18.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Angle-set      7
Arc-length, description      14
Arc-length, map      6 14 21
Arc-length, trajectory      15
Area identity      10
Balance of energy      112 119
Balance of forces      32 33 105
Boundary conditions, thermodynamical theory      135
Boundary curve      7
Bounded curve      6
Capillary force      32 40 93 132
Closed curve      6
Compatibility theorem, mechanical theory      38
Compatibility theorem, regularized theory      108
Compatibility theorem, thermodynamical theory      115 126
Constitutive equations, mechanical theory      38
Constitutive equations, regularized theory      107
Constitutive equations, thermodynamical theory      114 124 126
Containment principle      75 99
Control volume      26-30
Convex curve      7-10
Convexification      42
Convexified energy      46
Convexity      42
Corner force      94
Corners      40 94
Crystalline motions      96
Curvature      7
Curve class $R$      8
Curve definition      6
Curve normal, tangent for      6 7
Curve parametrization of      6
Curve-shortening equation      1
Dissipation inequality, mechanical theory      35
Dissipation inequality, regularized theory      106
Energy, bulk      35
Energy, interfacial, crystalline      91
Energy, interfacial, definition      35
Energy, interfacial, nonsmooth      91
Energy, interfacial, regular      51
Energy, interfacial, stability of      50
Energy, interfacial, total      70
Energy, interfacial, unstable      78
Entropy production, bulk      113
Entropy production, interfacial      123
Entropy, bulk      112
Entropy, interfacial      119
Equilibrium equations      53
Evolving curve      14
Extended energy      42 45
Faceted curve      11 22 81
First law      112
Frank diagram      42 44
Frank potential      44
Free energy, bulk      114
Free energy, interfacial      120
Gibbs relation      127
Globally convex section      42
Globally stable angles and sections      50
Growth of entropy      112 119
Growth theorem, thermodynamical theory      135
Heat equation      117
Heat flux, apparent      119
Heat flux, bulk      112
Heat supply, bulk      112
Infinitesimally wrinkled curve      12-13 85 88 100
Interface, a level set      62
Interface, conditions for thermodynamical theory      130 131
Interface, evolving      14
Interface, stationary      64
Interface, steadily evolving      19 65-68 90
Interface, the graph of a function      62 84
Internal energy, bulk      112
Internal energy, interfacial      119
Jump in a function      27
Juncture, angle      21
Juncture, curvature      21
Juncture, definition of      21
Juncture, tangential endpoint velocities of      21
Kinetic coefficient      39 86
Latent heat      125
Localization lemma      30
Mullins - Sekerka equations      136 140
Normal angle      7
Normal interaction      36
Normal time derivative      15
Normal velocity      15
Perfect conductors      137
Phase region      26 118
Polar diagram      41
Power      33-34
PS curve      11
PS evolving curve, admissibility for      78
PS evolving curve, definition      20
Quasi-linear problem      131
Quasi-static problem      132
Reference region      7
Regular interfacial energy      51
Regularized theory      105
Second law, general discussion      1
Second law, mechanical theory      35
Second law, thermodynamical theory      112
Simple curve      6
Soner's solution      75
Spinodal decomposition      110
Stability, for a PS curve      47
Stability, local      49
Steadily evolving, bump      20
Steadily evolving, facet      20
Supercooling, superheating      125 139 141
Support function      8
Surface shear      32
Surface tension      32
Taylor's solution      99
Temperature      112
Thermodynamical laws, approximate      132 134
Transition temperature      125
Transport theorem, area and perimeter      18
Transport theorem, integrals      18 23
Unbounded curve      6
Variational lemmas      24-5
Wrinkled curve      11 22 81
Wulff problem      58
Wulff ratio      58
Wulff region      55 92
Wulff theorem      58
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