Verfügbarkeit: The Frenkel-Kontorova model

The Frenkel-Kontorova model: concepts, methods, and applications

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Braun, Oleg M. 1949- (VerfasserIn), Kivšar, Juri S. (VerfasserIn)
Format:	Buch
Sprache:	German
Veröffentlicht:	Berlin [u.a.] Springer 2004
Schriftenreihe:	Texts and monographs in physics Physics and astronomy online library
Schlagworte:	Nonlinear theories Solid state physics Festkörper Sinus-Gordon-Gleichung Frenkel-Kontorova-Modell
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Literaturverz. S. 441 - 463
Beschreibung:	XVIII, 472 S. Ill., graph. Darst. : 24 cm
ISBN:	3540407715

Internformat

MARC


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245	1	0	\|a The Frenkel-Kontorova model \|b concepts, methods, and applications \|c Oleg M. Braun ; Yuri S. Kivshar
264		1	\|a Berlin [u.a.] \|b Springer \|c 2004
300			\|a XVIII, 472 S. \|b Ill., graph. Darst. : 24 cm
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Datensatz im Suchindex

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adam_text	TABLE OF CONTENTS 1 INTRODUCTION .............................................. 1 1.1 THE FRENKEL-KONTOROVA MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 THE SINE-GORDON EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 PHYSICAL MODELS .......................................... 9 2.1 GENERAL APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 A MECHANICAL MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 DISLOCATION DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 SURFACES AND ADSORBED ATOMIC LAYERS. . . . . . . . . . . . . . . . . . . . . 14 2.5 INCOMMENSURATE PHASES IN DIELECTRICS . . . . . . . . . . . . . . . . . . . . . 18 2.6 CROWDIONS AND LATTICE DEFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7 MAGNETIC CHAINS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.8 JOSEPHSON JUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.9 NONLINEAR MODELS OF THE DNA DYNAMICS . . . . . . . . . . . . . . . . . . 25 2.10 HYDROGEN-BONDED CHAINS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.11 MODELS OF INTERFACIAL SLIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3 KINKS ..................................................... 31 3.1 THE PEIERLS-NABARRO POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 DYNAMICS OF KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 EFFECTIVE EQUATION OF MOTION. . . . . . . . . . . . . . . . . . . . . . . 38 3.2.2 MOVING KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2.3 TRAPPED KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.4 MULTIPLE KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 GENERALIZED ON-SITE POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3.1 BASIC PROPERTIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.3.2 KINK INTERNAL MODES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3.3 NONSINUSOIDAL ON-SITE POTENTIAL . . . . . . . . . . . . . . . . . . . . 54 3.3.4 MULTIPLE-WELL POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3.5 MULTI-BARRIER POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.4 DISORDERED SUBSTRATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4.1 EFFECTIVE EQUATION OF MOTION. . . . . . . . . . . . . . . . . . . . . . . 68 3.4.2 POINT DEFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4.3 EXTERNAL INHOMOGENEOUS FORCE . . . . . . . . . . . . . . . . . . . . 73 XII TABLE OF CONTENTS 3.5 ANHARMONIC INTERATOMIC INTERACTION . . . . . . . . . . . . . . . . . . . . . . 75 3.5.1 SHORT-RANGE INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5.2 NONCONVEX INTERATOMIC POTENTIALS . . . . . . . . . . . . . . . . . . 82 3.5.3 KAC-BAKER INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.5.4 LONG-RANGE INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.5.5 COMPACTON KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4 BREATHERS ................................................. 99 4.1 PERTURBED SINE-GORDON BREATHERS. . . . . . . . . . . . . . . . . . . . . . . . . 99 4.1.1 LARGE-AMPLITUDE BREATHERS . . . . . . . . . . . . . . . . . . . . . . . . 99 4.1.2 SMALL-AMPLITUDE BREATHERS . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2 BREATHER COLLISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.2.1 MANY-SOLITON EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2.2 FRACTAL SCATTERING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.2.3 SOLITON COLD GAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.3 IMPURITY MODES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.3.1 STRUCTURE AND STABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.3.2 SOLITON INTERACTIONS WITH IMPURITIES. . . . . . . . . . . . . . . . . 116 4.4 DISCRETE BREATHERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.4.1 GENERAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.4.2 EXISTENCE AND STABILITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4.4.3 THE DISCRETE NLS EQUATION. . . . . . . . . . . . . . . . . . . . . . . . 125 4.4.4 DARK BREATHERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4.5 ROTOBREATHERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4.5 TWO-DIMENSIONAL BREATHERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.6 PHYSICAL SYSTEMS AND APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . 138 5 GROUND STATE ............................................. 141 5.1 BASIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.2 FIXED-DENSITY CHAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5.2.1 COMMENSURATE CONFIGURATIONS . . . . . . . . . . . . . . . . . . . . . 149 5.2.2 INCOMMENSURATE CONFIGURATIONS . . . . . . . . . . . . . . . . . . . 159 5.3 FREE-END CHAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 5.3.1 FRANK-VAN-DER-MERWE TRANSITION . . . . . . . . . . . . . . . . . . . 167 5.3.2 DEVILS STAIRCASE AND PHASE DIAGRAM . . . . . . . . . . . . . . . 171 5.4 GENERALIZATIONS OF THE FK MODEL . . . . . . . . . . . . . . . . . . . . . . . . . 174 5.4.1 ON-SITE POTENTIAL OF A GENERAL FORM . . . . . . . . . . . . . . . . 174 5.4.2 ANHARMONIC INTERATOMIC POTENTIAL . . . . . . . . . . . . . . . . . 177 5.4.3 NONCONVEX INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6 STATISTICAL MECHANICS ..................................... 195 6.1 INTRODUCTORY REMARKS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 6.2 GENERAL FORMALISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.3 WEAK-BOND LIMIT: GLASS-LIKE PROPERTIES . . . . . . . . . . . . . . . . . . 202 6.3.1 ISING-LIKE MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 TABLE OF CONTENTS XIII 6.3.2 CONFIGURATIONAL EXCITATIONS . . . . . . . . . . . . . . . . . . . . . . . 205 6.3.3 TWO-LEVEL SYSTEMS AND SPECIFIC HEAT . . . . . . . . . . . . . . 208 6.4 STRONG-BOND LIMIT: GAS OF QUASIPARTICLES . . . . . . . . . . . . . . . . . 211 6.4.1 SHARING OF THE PHASE SPACE AND BREATHERS . . . . . . . . . . . 214 6.4.2 KINK-PHONON INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . 215 6.4.3 KINK-KINK INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.4.4 DISCRETENESS EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.5 STATISTICAL MECHANICS OF THE FK CHAIN . . . . . . . . . . . . . . . . . . . . 220 6.5.1 TRANSFER-INTEGRAL METHOD . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.5.2 THE PSEUDO-SCHR¨ODINGER EQUATION . . . . . . . . . . . . . . . . . 225 6.5.3 SUSCEPTIBILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6.5.4 HIERARCHY OF SUPERKINK LATTICES . . . . . . . . . . . . . . . . . . . 233 6.5.5 EQUAL-TIME CORRELATION FUNCTIONS . . . . . . . . . . . . . . . . . 234 6.5.6 GENERALIZED FK MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 7 THERMALIZED DYNAMICS ................................... 243 7.1 BASIC CONCEPTS AND FORMALISM . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 7.1.1 BASIC FORMULAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 7.1.2 MORI TECHNIQUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 7.1.3 DIFFUSION COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 7.1.4 NONINTERACTING ATOMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 7.1.5 INTERACTING ATOMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 7.2 DIFFUSION OF A SINGLE KINK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 7.2.1 LANGEVIN EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 7.2.2 INTRINSIC VISCOSITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 7.2.3 ANOMALOUS DIFFUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 7.2.4 KINK DIFFUSION COEFFICIENT . . . . . . . . . . . . . . . . . . . . . . . . . 265 7.3 DYNAMIC CORRELATION FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 268 7.4 MASS TRANSPORT PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 7.4.1 DIFFUSION IN A HOMOGENEOUS GAS . . . . . . . . . . . . . . . . . . . 273 7.4.2 APPROXIMATE METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 7.4.3 PHENOMENOLOGICAL APPROACH . . . . . . . . . . . . . . . . . . . . . . 281 7.4.4 SELF-DIFFUSION COEFFICIENT . . . . . . . . . . . . . . . . . . . . . . . . . . 284 7.4.5 PROPERTIES OF THE DIFFUSION COEFFICIENTS . . . . . . . . . . . . . . 286 8 DRIVEN DYNAMICS ......................................... 291 8.1 INTRODUCTORY REMARKS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 8.2 NONLINEAR RESPONSE OF NONINTERACTING ATOMS . . . . . . . . . . . . . . 292 8.2.1 OVERDAMPED CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 8.2.2 UNDERDAMPED CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 8.3 OVERDAMPED FK MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 8.4 DRIVEN KINK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 8.5 INSTABILITY OF FAST KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 8.6 SUPERSONIC AND MULTIPLE KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . 316 8.7 LOCKED-TO-SLIDING TRANSITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 XIV TABLE OF CONTENTS 8.7.1 COMMENSURATE GROUND STATES . . . . . . . . . . . . . . . . . . . . . 323 8.7.2 COMPLEX GROUND STATES AND MULTISTEP TRANSITION . . . . 323 8.8 HYSTERESIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 8.9 TRAFFIC JAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 8.10 PERIODIC FORCES: DISSIPATIVE DYNAMICS . . . . . . . . . . . . . . . . . . . . 334 8.11 PERIODIC DRIVING OF UNDERDAMPED SYSTEMS . . . . . . . . . . . . . . . . 339 9 RATCHETS .................................................. 343 9.1 PRELIMINARY REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 9.2 DIFFERENT TYPES OF RATCHETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 9.2.1 SUPERSYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 9.2.2 DIFFUSIONAL RATCHETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 9.2.3 INERTIAL RATCHETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 9.3 SOLITONIC RATCHETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 9.3.1 SYMMETRY CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 9.3.2 ROCKED RATCHETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 9.3.3 PULSATING RATCHETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 9.4 EXPERIMENTAL REALIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 10 FINITE-LENGTH CHAIN ...................................... 365 10.1 GENERAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 10.2 GROUND STATE AND EXCITATION SPECTRUM . . . . . . . . . . . . . . . . . . . 366 10.2.1 STATIONARY STATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 10.2.2 CONTINUUM APPROXIMATION . . . . . . . . . . . . . . . . . . . . . . . . 369 10.2.3 DISCRETE CHAINS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 10.2.4 VIBRATIONAL SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 10.3 DYNAMICS OF A FINITE CHAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 10.3.1 CATERPILLAR-LIKE MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . 374 10.3.2 ADIABATIC TRAJECTORIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 10.3.3 DIFFUSION OF SHORT CHAINS . . . . . . . . . . . . . . . . . . . . . . . . . 379 10.3.4 STIMULATED DIFFUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 10.4 NONCONVEX POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 11 TWO-DIMENSIONAL MODELS ................................. 383 11.1 PRELIMINARY REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 11.2 SCALAR MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 11.2.1 STATISTICAL MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 11.2.2 DYNAMIC PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 11.3 ZIGZAG MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 11.3.1 GROUND STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 11.3.2 AUBRY TRANSITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 11.3.3 CLASSIFICATION OF KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 11.3.4 ZIGZAG KINKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 11.3.5 APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 11.4 SPRING-AND-BALL VECTOR 2D MODELS . . . . . . . . . . . . . . . . . . . . . . . 415 TABLE OF CONTENTS XV 11.4.1 THE GROUND STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 11.4.2 EXCITATION SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 11.4.3 DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 11.5 VECTOR 2D FK MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 11.5.1 LOCKED-TO-SLIDING TRANSITION . . . . . . . . . . . . . . . . . . . . . . 423 11.5.2 FUSE-SAFETY DEVICE* ON AN ATOMIC SCALE . . . . . . . . . . . 429 12 CONCLUSION ............................................... 431 13 HISTORICAL REMARKS ....................................... 435 REFERENCES .................................................... 441 INDEX ......................................................... 465
any_adam_object	1
author	Braun, Oleg M. 1949- Kivšar, Juri S.
author_GND	(DE-588)128686731
author_facet	Braun, Oleg M. 1949- Kivšar, Juri S.
author_role	aut aut
author_sort	Braun, Oleg M. 1949-
author_variant	o m b om omb j s k js jsk
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spelling	Braun, Oleg M. 1949- Verfasser (DE-588)128686731 aut The Frenkel-Kontorova model concepts, methods, and applications Oleg M. Braun ; Yuri S. Kivshar Berlin [u.a.] Springer 2004 XVIII, 472 S. Ill., graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Physics and astronomy online library Literaturverz. S. 441 - 463 Nonlinear theories Solid state physics Festkörper (DE-588)4016918-2 gnd rswk-swf Sinus-Gordon-Gleichung (DE-588)4329331-1 gnd rswk-swf Frenkel-Kontorova-Modell (DE-588)4530115-3 gnd rswk-swf Festkörper (DE-588)4016918-2 s Frenkel-Kontorova-Modell (DE-588)4530115-3 s Sinus-Gordon-Gleichung (DE-588)4329331-1 s DE-604 Kivšar, Juri S. Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537698&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Braun, Oleg M. 1949- Kivšar, Juri S. The Frenkel-Kontorova model concepts, methods, and applications Nonlinear theories Solid state physics Festkörper (DE-588)4016918-2 gnd Sinus-Gordon-Gleichung (DE-588)4329331-1 gnd Frenkel-Kontorova-Modell (DE-588)4530115-3 gnd
subject_GND	(DE-588)4016918-2 (DE-588)4329331-1 (DE-588)4530115-3
title	The Frenkel-Kontorova model concepts, methods, and applications
title_auth	The Frenkel-Kontorova model concepts, methods, and applications
title_exact_search	The Frenkel-Kontorova model concepts, methods, and applications
title_full	The Frenkel-Kontorova model concepts, methods, and applications Oleg M. Braun ; Yuri S. Kivshar
title_fullStr	The Frenkel-Kontorova model concepts, methods, and applications Oleg M. Braun ; Yuri S. Kivshar
title_full_unstemmed	The Frenkel-Kontorova model concepts, methods, and applications Oleg M. Braun ; Yuri S. Kivshar
title_short	The Frenkel-Kontorova model
title_sort	the frenkel kontorova model concepts methods and applications
title_sub	concepts, methods, and applications
topic	Nonlinear theories Solid state physics Festkörper (DE-588)4016918-2 gnd Sinus-Gordon-Gleichung (DE-588)4329331-1 gnd Frenkel-Kontorova-Modell (DE-588)4530115-3 gnd
topic_facet	Nonlinear theories Solid state physics Festkörper Sinus-Gordon-Gleichung Frenkel-Kontorova-Modell
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537698&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT braunolegm thefrenkelkontorovamodelconceptsmethodsandapplications AT kivsarjuris thefrenkelkontorovamodelconceptsmethodsandapplications

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