| Description |
xviii, 181 pages : illustrations ; 24 cm |
| Series |
Advances in Mechanics and Mathematics ; 15 |
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Advances in mechanics and mathematics ; 15
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| Contents |
Machine derived contents note: 1 A General Co nept of Dynamic Materials 1 -- 1.1 The idea and efinition of dynamic materias -- 1.2 Two types of ynamiiic materias 2 -- 1.3 Impren) tation of dynamic materials in ealectronics and optics 7 -- .1 .3. l Ferroelectric and ferr gnetic i -- 1.3.2 Nonline Ar optics 10 -- 1. Some applications of dynamic materials . -- 1.5 f Dyna.mic materials and virati onal maechanics 12 -- R e fere n ces 15 -- 2 An Actvatd Elastic Bar: Effective Properties 17 -- 2.1 Longitudinal vibrations of ac ivated elastic biar 17 -- 2.2 The effective p ar,menters o aictivated lam na,te 24 -- 2.3 The ede parm ters: homogezao a. 28 -- 2.4 The ective paramers: the Fiquet thor 31 -- 25 The effctiv parameters: discussion 33 -- 2.6 Balance of energy in longitudinal wave -- propagat on throuh an activated elastic bar 4 -- R e fe ren ces 9 -- Dynamitc 1Maeria s in Electrodynamics of Moving -- 3D 1 Prelim inary rem arks 51 -- 32i The basics of electrodynamics of moving -- d iele tri s 5 1 -- 3.3 Relativistic form of axwel' syste 5 -- .4 M teal tensor s: discussion. Two types f dynamic materitals 58 -- 3.5 An activted dielectric lamitate: -- one- imensiona wavi e propagation 5 -- 3:.6 A spatio-tempot poycrystallic laminate: -- one dimension l wa ve propaga tion 61 -- 3.7 A spaIt o-temporal polycrstallc laminate: -- the bounds 63 -- 3.8 An activtd dIielectric l laminat: -- 3.9 An activated dielectri la ninate: the energy -- considerations iaves of near nerg 75 -- 3.10 N eric a exaIples and dis'ussi on 8 -- 3.11 Effective Iro pe tis of activated lamina.t s ccula ted via -- Lorentz t rasforim. Cse of spacrlike inte rfae 7 -- to One-.Dimensional Wave Propagati on 91 -- 4.L Preliin iar F cu onsideatl io s. Trminology -- 12 Conserva tion o the \wav m pedan e throlugh -- one-dimnsiontal wave prop gation. A stable -- G-.closure of a single isotropic dielectric 93 -- 4 f3 A st-abl G-Ilosure of a set 7 of two isotopi -- tric wit t t o o:ne-diN mensioIn -- w ave p ) lopazation 3. 9 -- 4.4 The secnd i nvariant i a f as a: affine -- function; a Istbrle G-closre of an arbitrary s -- U of isotropi c dielect ics 97 -- 4[.5 A stable C1,.-cosure of a set U of two -- isotropic dielectr ics 102 -- L Comparison w Ith an elliptic case 102 -- R eferen ces 107 -- 5 Rectangular Microstructures in Space-Time i09 -- 5.1 Introductory rema rks 109 -- 5.2 State ent of a problem 110 -- 53 Case of separation of variab s 13 -- 5.4 ChAeckerboard Issmblage of nat-erias -- with e qual wave napeduane 116 -- 5.5 Energy transfirmation in the presence -- of limit cycles 127 -- 5r.6 Numeric al e at alysis of energy acumlta tion. 31 -- 5.7 Some remarks about d iscontiuous solutions -- i r lam in ates 33 -- e fe re n ces 13 -- 6 Some Applications of Dynami Materials in Electrical -- Engineering and Optimal Design -- 0.1 A 4lane electromaminei wave propagation thBlough an -- activated l miate in A3D -- .2 The hoImogen4ized euations Elimina ion of the cutoff -- frequencP i a plane waveguide 142 -- 6.3 Th e effective mateal tensor and honogenized -- Stromagnet,i field 143 -- Sj4 The transport of effective eergy 1 -- i.5 Oni t he aeces ar coditions of optnimaity i a. typical -- ihyprbolic control problcm with controls in the coefficients . -- j.5I 1 Introdi uction 146 -- 65.2 Statement of the pioble -- 6.53 The necessarv c onditions of optinmalit 149 -- . Tarar'sformation of the expression for AI : the strip test 1 3 -- .7 A oyyta in spce-tie 155 -- References 161 |
| Summary |
"This book gives a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials - that is, material substances whose properties are variable in space and time. Unlike conventional composites that are often found in nature, dynamic materials are mostly the products of modern technology developed to maintain the most effective control over dynamic processes. These materials have diverse applications: tunable left-handed dielectrics, optical pumping with high-energy pulse compression, and electromagnetic stealth technology, to name a few. Of special significance is the participation of dynamic materials in almost every optimal material design in dynamics." "This book is intended for applied mathematicians interested in optimal problems of material design for systems governed by hyperbolic differential equations. It will also be useful for researchers in the field of smart metamaterials and their applications to optimal material design in dynamics."--BOOK JACKET |
| Bibliography |
Includes index |
| Notes |
Print version record |
| Subject |
Composite materials.
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Differentiable dynamical systems.
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Differential equations, Partial.
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Electrodynamics.
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Materials science -- Mathematics.
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Materials.
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Mathematical optimization.
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Optical materials.
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Smart materials.
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Vibration.
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| LC no. |
2006940343 |
| ISBN |
038738278X (hbk.) |
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9780387382784 (hbk.) |
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