Vortices in nonlinear fields: from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings
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| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1999
|
| Series: | The international series of monographs on physics
100 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 290 S. Ill., graph. Darst. |
| ISBN: | 0198501676 |
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Record in the Search Index
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| adam_text | VORTICES IN NONLINEAR FIELDS FROM LIQUID CRYSTALS TO SUPERFLUIDS FROM
NON-EQUILIBRIUM PATTERNS TO COSMIC STRINGS L. M. PISMEN DEPARTMENT OF
CHEMICAL ENGINEERING TECHNION-ISRAEL INSTITUTE OF TECHNOLOGY CLARENDON
PRESS * OXFORD 1999 CONTENTS ORDERED MEDIA 1 1.1 BROKEN SYMMETRY 1 1.1.1
ORDER PARAMETER FIELDS 1 1.1.2 MINIMAL MANIFOLD 3 1.1.3 TEXTURES AND
TOPOLOGICAL DEFECTS 5 1.2 COMPLEX SCALAR FIELD 6 1.2.1 LAGRANGIAN AND
MINIMAL ORBIT 6 1.2.2 PHASE SINGULARITY 7 1.2.3 STATIC SOLUTIONS 9 1.2.4
VORTICES IN LINEAR FIELDS 11 1.3 TOPOLOGICAL THEORY OF DEFECTS 14 1.3.1
HOMOTOPY GROUPS 14 1.3.2 COMPUTATION OF THE FUNDAMENTAL GROUP 15 1.3.3
HIGHER HOMOTOPY GROUPS 17 1.4 ENERGY INTEGRAL AND EVOLUTION EQUATIONS 17
1.4.1 ENERGY VS. TOPOLOGY . . 17 1.4.2 GENERAL GL LAGRANGIAN 18 1.4.3
EVOLUTION EQUATIONS 20 1.5 MEDIA WITH BROKEN ROTATIONAL SYMMETRY 21
1.5.1 FERR OMAGNETS 21 1.5.2 UNIAXIAL NEMATICS 23 1.5.3 NEMATICS IN
EXTERNAL FIELDS 25 1.5.4 SMECTIC C 26 1.5.5 BIAXIAL NEMATICS . 27
DISSIPATIVE MOTION 30 2.1 FAR FIELD DYNAMICS 30 2.1.1 FAR FIELD
EQUATIONS 30 2.1.2 PHASE FIELD OF A MOVING VORTEX 32 2.1.3 DISSIPATION
INTEGRAL AND PEACH-KOHLER FORCE 33 2.2 MATCHED ASYMPTOTIC EXPANSIONS 37
2.2.1 MOTIVATION 37 2.2.2 CORE EXPANSION AND MATCHING 38 2.2.3
SOLVABILITY CONDITION 40 2.3 INHOMOGENEITIES AND PINNING 43 2.3.1
VARIABLE SUPERCRITICALITY 43 2.3.2 MOTION IN A SUPERCRITICALITY RAMP ,
43 2.3.3 QUENCHED DISORDER 45 2.4 VORTICES IN LIQUID CRYSTALS 48 XII
CONTENTS 2.4.1 DYNAMICS OF COARSENING IN THIN LAYERS 48 2.4.2
TWO-DIMENSIONAL NEMATICS AND SMECTICS C 51 2.4.3 NEMATICS IN EXTERNAL
FIELD : 51 2.5 DEFECTS IN THREE-DIMENSIONAL NEMATICS 54 2.5.1 STATIC
SOLUTIONS 54 2.5.2 MONOPOLES JOINED BY A STRING 55 2.5.3 MOTION OF
INTERACTING DEFECTS 57 2.5.4 ALTERNATIVE CORE STRUCTURES 59 3
DISLOCATIONS IN PATTERNS 61 3.1 STRIPED PATTERNS , 61 3.1.1 AMPLITUDE
EQUATIONS 61 3.1.2 PHASE DYNAMICS 63 3.1.3 SINGULARITIES OF THE PHASE
FIELD 66 3.2 MOTION OF DISLOCATIONS 67 3.2.1 THE NATURE OF THE DRIVING
FORCE . 67 3.2.2 ZIPPING TECHNIQUE 68 3.2.3 SELF-CONSISTENT SOLUTION .
72 3.2.4 PARTICLE-FIELD COMPUTATIONS 73 3.3 DISLOCATIONS IN AN ISOTROPIC
SYSTEM 76 3.3.1 SOLUTION OF NWS PHASE EQUATION 76 3.3.2 MOBILITY
ESTIMATES 78 3.4 DISLOCATIONS IN RESONANT PATTERNS 80 3.4.1 RESONANT
INTERACTIONS 80 3.4.2 DISLOCATIONS IN HEXAGONAL PATTERNS 83 3.4.3
RIGIDITY OF A RESONANT STRUCTURE 86 3.4.4 DISLOCATIONS IN 3D STRUCTURES
89 4 VORTICES IN SUPERFLUIDS 91 4.1 SUPERFLUID MODELS 91 4.1.1 NATURE OF
THE SUPERFLUID STATE 91 4.1.2 BASIC EQUATIONS 93 4.1.3 VORTEX STRUCTURE
. 94 4.1.4 THERMODYNAMIC STABILITY 95 4.2 CONSERVATIVE DYNAMICS , 97
4.2.1 MOTION OF POINT VORTICES 97 4.2.2 FLUID-MECHANICAL REPRESENTATION
99 4.2.3 INTEGRALS OF MOTION 100 4.3 VORTEX-SOUND INTERACTION * 102
4.3.1 SECOND SOUND 102 4.3.2 ACOUSTIC RADIATION BY MOVING VORTICES 104
4.3.3 ACOUSTIC DRAG 107 4.3.4 ACOUSTIC MAGNUS FORCE 110 4.4 DISSIPATION
AND INSTABILITIES 113 4.4.1 TWO-FLUID MODEL 113 CONTENTS XIII 4.4.2
DISSIPATIVE VORTEX DRIFT 114 4.4.3 STABILITY OF FLOW AND NUCLEATION OF
VORTICES 116 4.4.4 STABILITY OF NON-UNIFORM FLOW 118 4.5 MOTION ON AN
JNHOMOGENEOUS BACKGROUND 122 4.5.1 OPTICAL VORTEX IN A NON-UNIFORM BEAM
122 4.5.2 VORTEX DRIFT 123 4.5.3 INTERACTION OF VORTICES IN A CENTRAL
FIELD 125 5 MOTION OF LINE VORTICES 129 5.1 LOCALLY INDUCED MOTION 129
5.1.1 INTRINSIC EQUATIONS OF MOTION OF CURVES 129 5.1.2 BINORMAL MOTION
131 5.1.3 ALIGNED COORDINATE FRAME 134 5.1.4 NORMAL MOTION 136 5.2
CONSERVATIVE MOTION 137 5.2.1 BIOT-SAVART INTEGRAL , 1 3 7 5.2.2 CORE
EXPANSION AND MATCHING 140 5.2.3 ENERGY AND MOMENTUM OF FLOW FIELD 141
5.2.4 RING VORTEX 145 5.2.5 HELICES AND COAXIAL RINGS 146 5.3
OSCILLATIONS AND INSTABILITIES , 148 5.3.1 LIA SPECTRUM 148 5.3.2
PERTURBATIONS OF A STRAIGHT-LINE VORTEX 150 5.3.3 NONLOCAL FILAMENT
EQUATION 152 5.3.4 PERTURBATIONS OF PARALLEL VORTICES 155 5.3.5
OSCILLATIONS OF.A RING VORTEX 158 5.3.6 ACOUSTIC EFFECT OF OSCILLATIONS
161 5.4 DISSIPATION AND TURBULENCE 164 5.4.1 DISSIPATIVE INDUCTION , 164
5.4.2 LIA COMPUTATIONS ; : 166 5.4.3 VORTEX RECONNECTION 168 5.4.4
PINNING AND DEPINNING 171 6 VORTICES IN SUPERCONDUCTORS 173 6.1 STATIC
VORTICES 173 6.1.1 GINZBURG-LANDAU ENERGY . 173 6.1.2 BOGOMOLNY
EQUATIONS 176 6.1.3 VORTEX STRUCTURE IN TYPE II SUPERCONDUCTORS - *- 177
6.1.4 PEACH-KOHLER FORCE 179 6.1.5 ANISOTROPIC VORTEX STRUCTURE 180 6.2
CONSERVATIVE DYNAMICS 182 6.2.1 SPACETIME ACTION 182 6.2.2 HAMILTONIAN
DYNAMICS OF POINT VORTICES 184 6.2.3 CURVATURE-DRIVEN BINORMAL MOTION *
186 6.2.4 INDUCED ELECTRIC FIELD 187 CONTENTS 6.2.5 ELECTRIC MAGNUS
FORCE 189 6.3 DISSIPATIVE MOTION 191 6.3.1 GRADIENT FLOW 191 6.3.2
CURVATURE-DRIVEN NORMAL MOTION 193 6.3.3 GENERAL MOBILITY RELATION 194
6.3.4 INHOMOGENEITIES AND VORTEX PINNING 195 NON-POTENTIAL AND NONLOCAL
MODELS 200 7.1 , SPIRAL WAVES 200 7.1.1 COMPLEX GINZBURG-LANDAU EQUATION
200 7.1.2 PLANE WAVE SOLUTIONS 201 7.1.3 HAGAN S SOLUTION 202 7.1.4
ASYMPTOTIC RELATIONS 204 7.1.5 OPTICAL SPIRAL VORTICES 207 7.1.6 SPIRAL
WAVES IN SYSTEMS WITH SEPARATED SCALES 208 7.2 INSTABILITIES AND
INTERACTIONS 211 7.2.1 PHENOMENOLOGY OF SPIRAL WAVE PATTERNS 211 7.2.2
FAR FIELD AND CORE INSTABILITIES 213 7.2.3 INTERACTIONS OF SPIRAL
VORTICES 215 7.2.4 DYNAMICS OF SCROLL WAVES 218 7.3 MEAN FIELD MODELS
219 7.3.1 NONLOCAL NONLINEAR RESPONSE 219 7.3.2 VERTICAL VORTICITY IN
CONVECTIVE PATTERNS 221 7.3.3 MEAN FLOW NEAR THE THRESHOLD ** 223 7.3.4
INTERACTION OF A DISLOCATION WITH MEAN FLOW 225 7.3.5 DRIVEN AND
INTERACTING DEFECTS 227 7.3.6 DISLOCATION IN A SPIRAL WAVE . 229
ANISOTROPIC SUPERFLUIDS } 231 8.1 VORTICES IN COMPLEX VECTOR FIELDS 231
8.1.1 COUPLED GL EQUATIONS 231 8.1.2 MINIMAL ORBITS AND TOPOLOGICAL
DEFECTS 233 8.1.3 STRUCTURE OF VORTEX CORES 235 8.1.4 INSTABILITY OF THE
DARK CORE STRUCTURE 238 8.2 DYNAMICS OF COMPLEX VECTOR FIELDS 240 8.2.1
VORTEX INTERACTIONS 240 8.2.2 ACOUSTICS OF COMPLEX VECTOR FIELDS 242
8.2.3 VORTEX-KINK INTERACTION 242 8.2.4 SPIRAL VORTICES IN VECTOR FIELDS
N 247 8.3 VORTICES IN SUPERFLUID 3 HE 250 8.3.1 ORDER PARAMETER OF
SUPERFLUID 3 HE 250 8.3.2 TOPOLOGY OF B-PHASE 252 8.3.3 TOPOLOGY OF
A-PHASE 253 8.3.4 SUPERFLOW IN A-PHASE * 255 8.3.5 STRUCTURE OF VORTEX
CORES 257 CONTENTS XV 9 RELATIVISTIC VORTICES AND STRINGS 260 9.1 SCALAR
FIELDS IN SPACETIME 260 9.1.1 VACUUM AS A NONLINEAR MEDIUM 260 9.1.2
LORENTZ-INVARIANT LAGRANGIAN 261 9.1.3 GAUGE-INVARIANT LAGRANGIAN 262
9.1.4 NON-ABELIAN FIELD THEORIES 264 9.2 LOCALLY INDUCED MOTION 265
9.2.1 NAMBU STRINGS 265 9.2.2 COMOVING COORDINATE FRAME 267 9.2.3
ANALYTIC SOLUTIONS 269 9.3 NONLOCALLY INDUCED MOTION 272 9.3.1 FAR FIELD
SOLUTION 272 9.3.2 ASYMPTOTIC MATCHING 274 9.3.3 LARGE-SCALE DYNAMICS
276 REFERENCES 279 INDEX 286
|
| any_adam_object | 1 |
| author | Pisʹmen, Leonid Michajlovič ca. 20./21. Jh |
| author_GND | (DE-588)1051929032 |
| author_facet | Pisʹmen, Leonid Michajlovič ca. 20./21. Jh |
| author_role | aut |
| author_sort | Pisʹmen, Leonid Michajlovič ca. 20./21. Jh |
| author_variant | l m p lm lmp |
| building | Verbundindex |
| bvnumber | BV012564573 |
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| discipline | Physik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:29:46Z |
| institution | BVB |
| isbn | 0198501676 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008532324 |
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| physical | XV, 290 S. Ill., graph. Darst. |
| publishDate | 1999 |
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| series | The international series of monographs on physics |
| series2 | The international series of monographs on physics |
| spelling | Pisʹmen, Leonid Michajlovič ca. 20./21. Jh. Verfasser (DE-588)1051929032 aut Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings L. M. Pismen Oxford Clarendon Press 1999 XV, 290 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The international series of monographs on physics 100 Nichtlineare Feldtheorie (DE-588)4171752-1 gnd rswk-swf Wirbel Physik (DE-588)4128386-7 gnd rswk-swf Nichtlineare Feldtheorie (DE-588)4171752-1 s Wirbel Physik (DE-588)4128386-7 s DE-604 The international series of monographs on physics 100 (DE-604)BV000106406 100 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008532324&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pisʹmen, Leonid Michajlovič ca. 20./21. Jh Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings The international series of monographs on physics Nichtlineare Feldtheorie (DE-588)4171752-1 gnd Wirbel Physik (DE-588)4128386-7 gnd |
| subject_GND | (DE-588)4171752-1 (DE-588)4128386-7 |
| title | Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings |
| title_auth | Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings |
| title_exact_search | Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings |
| title_full | Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings L. M. Pismen |
| title_fullStr | Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings L. M. Pismen |
| title_full_unstemmed | Vortices in nonlinear fields from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings L. M. Pismen |
| title_short | Vortices in nonlinear fields |
| title_sort | vortices in nonlinear fields from liquid crystals to superfluids from non equilibrium patterns to cosmic strings |
| title_sub | from liquid crystals to superfluids ; from non-equilibrium patterns to cosmic strings |
| topic | Nichtlineare Feldtheorie (DE-588)4171752-1 gnd Wirbel Physik (DE-588)4128386-7 gnd |
| topic_facet | Nichtlineare Feldtheorie Wirbel Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008532324&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT pisʹmenleonidmichajlovic vorticesinnonlinearfieldsfromliquidcrystalstosuperfluidsfromnonequilibriumpatternstocosmicstrings |