Ebook: Nonlocal Continuum Field Theories

Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.

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Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.

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Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.
Content:
Front Matter....Pages i-xvi
Motion and Deformation....Pages 1-14
Stress....Pages 15-29
Constitutive Equations....Pages 31-48
Nonlocal Electromagnetic Theory....Pages 49-59
Constitutive Equations of Nonlocal Electromagnetic Media....Pages 61-70
Nonlocal Linear Elasticity....Pages 71-176
Nonlocal Fluid Dynamics....Pages 177-192
Nonlocal Linear Electromagnetic Theory....Pages 193-222
Memory-Dependent Nonlocal Thermoelastic Solids....Pages 223-229
Memory-Dependent Nonlocal Fluids....Pages 231-235
Memory-Dependent Nonlocal Electromagnetic Elastic Solids....Pages 237-245
Memory-Dependent Nonlocal Electromagnetic Thermofluids....Pages 247-252
Nonlocal Microcontinua....Pages 253-324
Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids....Pages 325-336
Nonlocal Continuum Theory of Liquid Crystals....Pages 337-356
Back Matter....Pages 357-376

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Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.
Content:
Front Matter....Pages i-xvi
Motion and Deformation....Pages 1-14
Stress....Pages 15-29
Constitutive Equations....Pages 31-48
Nonlocal Electromagnetic Theory....Pages 49-59
Constitutive Equations of Nonlocal Electromagnetic Media....Pages 61-70
Nonlocal Linear Elasticity....Pages 71-176
Nonlocal Fluid Dynamics....Pages 177-192
Nonlocal Linear Electromagnetic Theory....Pages 193-222
Memory-Dependent Nonlocal Thermoelastic Solids....Pages 223-229
Memory-Dependent Nonlocal Fluids....Pages 231-235
Memory-Dependent Nonlocal Electromagnetic Elastic Solids....Pages 237-245
Memory-Dependent Nonlocal Electromagnetic Thermofluids....Pages 247-252
Nonlocal Microcontinua....Pages 253-324
Memory-Dependent Nonlocal Micropolar Electromagnetic Elastic Solids....Pages 325-336
Nonlocal Continuum Theory of Liquid Crystals....Pages 337-356
Back Matter....Pages 357-376
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