Found 95 Documents (Results 1–95)
Traveling waves for discrete reaction-diffusion equations in the general monostable case. (English) Zbl 1527.35118
Velocity diagram of traveling waves for discrete reaction-diffusion equations. (English) Zbl 1523.39001
Modulational stability brought by cubic-quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential. (English) Zbl 1497.35438
Heteroclinic solutions for a generalized Frenkel-Kontorova model by minimization methods of Rabinowitz and Stredulinsky. (English) Zbl 1433.37063
Blended force-based atomistic-continuum coupling method for the model adaptivity of a Frenkel-Kontorova model. (Chinese. English summary) Zbl 1449.65236
A simple counterexample to the Monge ansatz in multimarginal optimal transport, convex geometry of the set of Kantorovich plans, and the Frenkel-Kontorova model. (English) Zbl 1429.49048
Equilibrium configurations for generalized Frenkel-Kontorova models on quasicrystals. (English) Zbl 1433.35401
Reviewer: Eugene Postnikov (Kursk)
Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential. (English. French summary) Zbl 1419.37072
Reviewer: Utkir A. Rozikov (Tashkent)
A numerical investigation of the pinning phenomenon in quasi-periodic Frenkel Kontorova model under an external force. (A numerical investigation of the pinning phenomenon in quasi-periodic Frenkel Kontrova model under an external force.) (English) Zbl 1404.82038
Bäcklund transformation and quasi-integrable deformation of mixed Fermi-Pasta-Ulam and Frenkel-Kontorova models. (English) Zbl 1396.37077
Invariant circles and depinning transition. (English) Zbl 1390.37075
MSC:
37E40
37J45
Dynamics of incommensurate structures of the Frenkel-Kontorova model. (Chinese. English summary) Zbl 1499.37007
Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces. (English) Zbl 1510.82026
Calibrated configurations for Frenkel-Kontorova type models in almost periodic environments. (English) Zbl 1382.82025
Reviewer: Nasir N. Ganikhodjaev (Kuantan)
MSC:
82C20
Chaos and chaos control of the Frenkel-Kontorova model with dichotomous noise. (English) Zbl 1366.34089
A \(\mathcal{PT}\)-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling. (English) Zbl 1373.35195
Minimizers with bounded action for the high-dimensional Frenkel-Kontorova model. (English) Zbl 1321.37062
A dichotomy theorem for minimizers of monotone recurrence relations. (English) Zbl 1321.37063
Reviewer: William J. Satzer jun. (St. Paul)
Lubricated friction in Frenkel-Kontorova model between incommensurate surfaces. (English) Zbl 1498.76024
Saturation effects in ac+dc driven Frenkel-Kontorova model. (English) Zbl 1462.78008
Reviewer: Vicenţiu D. Rădulescu (Craiova)
Monotone gradient dynamics and the location of stationary \((p,q)\)-configurations. (English) Zbl 1291.37053
Reviewer: William J. Satzer jun. (St. Paul)
The Aubry-Mather theorem for driven generalized elastic chains. (English) Zbl 1293.34017
Reviewer: Caidi Zhao (Wenzhou)
Existence of dynamical hull functions with two variables for the ac-driven Frenkel-Kontorova model. (English) Zbl 1321.34022
Existence and uniqueness of traveling waves for fully overdamped Frenkel-Kontorova models. (English) Zbl 1285.82049
Reviewer: Vicenţiu D. Rădulescu (Craiova)
Existence of supersonic traveling waves for the Frenkel-Kontorova model. (English) Zbl 1289.34166
Reviewer: Aleksander Pankov (Baltimore)
Computer simulation study of thermal conduction in 1D chains of anharmonic oscillators. (English) Zbl 1264.82062
Synchronization and phase transition in the Frenkel-Kontorova-type model system. (English) Zbl 1267.82095
Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential. (English) Zbl 1221.37149
Reviewer: Utkir Rozikov (Tashkent)
Difference of directions between external driving force and movement direction of center of mass. (English) Zbl 1219.82145
Application of two-dimensional Frenkel-Kontorova model to nanotribology. (English) Zbl 1213.82124
MSC:
82D80
From the Frenkel-Kontorova model to Josephson junction arrays – Aubry’s transition as a Jamming-Glass transition –. (English) Zbl 1203.82143
Reviewer: Vicenţiu D. Rădulescu (Craiova)
Dynamics of the Frenkel-Kontorova model with irrational mean spacing. (English) Zbl 1201.37104
Reviewer: Guy Katriel (Haifa)
Rotating modes in the Frenkel-Kontorova model with periodic interaction potential. (English) Zbl 1208.34053
Reviewer: Antonio Cañada Villar (Granada)
Physics of solitons. Reprint of the 2006 original. (English) Zbl 1204.35141
Cambridge: Cambridge University Press (ISBN 978-0-521-14360-8/pbk; 978-0-521-85421-4/hbk). xii, 422 p. (2010).
Reviewer: Boris A. Malomed (Tel Aviv)
Dislocation dynamics: from microscopic models to macroscopic crystal plasticity. (English) Zbl 1178.35047
Nonlinear waves in two-dimensional (2D) square lattice Frenkel-Kontorova (FK) system. (English) Zbl 1177.35184
Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. (English) Zbl 1194.74012
Stability of single-wave-form solutions in the underdamped Frenkel-Kontorova model. (English) Zbl 1171.34036
Reviewer: Guy Katriel (Haifa)
Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. (English) Zbl 1160.82313
“Relativistic” characterisation of the energy of soliton-like defects in continuous media. (English) Zbl 1139.74005
Defects, singularities and waves. (English) Zbl 1131.82043
Bonilla, L. L. (ed.) et al., Recent advances in nonlinear partial differential equations and applications. Conference in honor of Peter D. Lax and Louis Nirenberg on their 80th birthdays, Toledo, Spain, June 7–10, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4211-9/hbk). Proceedings of Symposia in Applied Mathematics 65, 131-150 (2007).
MSC:
82D25
Ground states and critical points for generalized Frenkel-Kontorova models in \(\mathbb Z^d\). (English) Zbl 1206.82026
Heat conduction in a weakly anharmonic chain: an analytical approach. (English) Zbl 1107.82028
Reviewer: Hiroshi Tamura (Kanazawa)
Interaction of moving discrete breathers with vacancies. (English) Zbl 1104.82032
Reviewer: Piotr Garbaczewski (Opole)
Dynamics of quasi-1D topological soliton in 2D strongly anisotropic crystal. (English) Zbl 1108.82047
Spatially extended systems with monotone dynamics (continuous time). (English) Zbl 1111.34031
Chazottes, Jean-René (ed.) et al., Dynamics of coupled map lattices and of related spatially extended systems. Lectures delivered at the school-forum CML 2004, Paris, France, June 21 – July 2, 2004. Berlin: Springer (ISBN 3-540-24289-9/hbk). Lecture Notes in Physics 671, 241-263 (2005).
Reviewer: Gheorghe Moroşanu (Budapest)
Directed transport of modulated structures in the Frenkel-Kontorova model with a pulsating coupling. (English) Zbl 1098.82607
Lattice modelling of nonlinear waves in a bi-layer with delamination. (English) Zbl 1153.74384
MSC:
74S30
74J30
Interactions between impurities and breather-pairs in a nonlinear lattice. (English) Zbl 1098.70522
MSC:
70K30
On the existence of moving breathers in one-dimensional anharmonic lattices. (English) Zbl 1027.82025
Generic uniqueness of a minimal solution for variational problems on a torus. (English) Zbl 1001.49001
Multistable spatiotemporal dynamics in the driven Frenkel–Kontorova lattice. (English) Zbl 1164.37349
MSC:
37K60
Friction and complex dynamics at solid surfaces. (English) Zbl 1042.74038
MSC:
74M10
74S30
Modeling of an edge dislocation and estimate of the dislocation core for a close-packed atomic layer. (Russian) Zbl 0973.74058
Prikl. Mekh. Tekh. Fiz. 41, No. 5, 211-216 (2000); translation in J. Appl. Mech. Tech. Phys. 41, No. 5, 950-954 (2000).
Reviewer: N.I.Alexandrova (Novosibirsk)
Ground-states and growth structures for one-dimensional models with periodic to quasiperiodic transitions. (English) Zbl 1001.74089
Belin-Ferré, Esther (ed.) et al., Quasicrystals. Current topics. Proceedings of the Spring School on quasicrystals, Aussois, France, May 16-21, 1999. Singapore: World Scientific. 187-211 (2000).
Dry friction: Modeling and energy flow. (English) Zbl 0961.74044
MSC:
74M10
Traffic jams in a lattice-gas model. (English) Zbl 0963.82030
MSC:
82C20
Frenkel-Kontorova model with pinning cusps. (English) Zbl 0937.37038
MSC:
37K05
37E45
The Frenkel-Kontorova model: classical generalizations and quantum glimpses. (English) Zbl 0903.58038
Feng, Da Hsuan (ed.) et al., Quantum classical correspondence. Proceedings of the 4th Drexel symposium on quantum nonintegrability, Philadelphia, PA, USA, September 8–11, 1994. Cambridge, MA: International Press. 445-452 (1997).
“Critical” phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams. (English) Zbl 0894.58063
On the study of KAM tori in a class of generalized FK model. (English) Zbl 0812.58055
Research Report. Mathematical Sciences. 63. Chengdu: Academia Sinica, 14 p. (1994).
Reviewer: R.Cowen (Nairobi)
MSC:
37A99
Dynamical structures in 2D lattices. (English) Zbl 0900.35357
Christiansen, P. L. (ed.) et al., Future directions of nonlinear dynamics in physical and biological systems. Proceedings of a NATO Advanced Study Institute in honour of Alwyn Scott’s 60th birthday, Lyngby, Denmark, July 23–August 1, 1992. New York, NY: Plenum. NATO ASI Ser., Ser. B, Phys. 312, 195-201 (1993).
Solitary waves in a Frenkel-Kontorova model with non-convex interactions. (English) Zbl 0693.76032
MSC:
76B25
Metric properties of minimal solutions of discrete periodical variational problems. (English) Zbl 0676.49001
Mather sets for twist maps and geodesics on tori. (English) Zbl 0664.53021
Dyn. Rep. 1, 1-56 (1988).
Reviewer: A.M.Pastore
Ground states in a model of Frenkel-Kontorova type. (English. Russian original) Zbl 0646.58040
Math. USSR, Izv. 29, 323-354 (1987); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 50, No. 5, 969-999 (1986).
Structure of the spectrum of the Schrödinger difference operator with almost-periodic potential in the vicinity of its left edge. (English) Zbl 0585.39003
On the structure of the spectrum of a Schrödinger difference operator with almost periodic potential close to the left-hand border. (Russian) Zbl 0574.39004
Reviewer: A.D.Mednych
A new computable criterion for the non-existence of invariant circles. (English) Zbl 0585.58038
Fluctuations and sensitivity in non-equilibrium systems, Proc. Int. Conf., Austin/Tex. 1984, Springer Proc. Phys. 1, 260-264 (1984).
Reviewer: A.Stone
MSC:
37-XX
Percival variational principle for invariant measures and commensurate- incommensurate phase transitions in one-dimensional chains. (English) Zbl 0564.58015
Reviewer: E.P.Parker
The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states. (English) Zbl 1237.37059
The twist map, the extended Frenkel-Kontorova model and the devil’s staircase. (English) Zbl 0559.58013
Order in chaos, Proc. int. Conf., Los Alamos/N.M. 1982, Physica 7D, 240-258 (1983).
Reviewer: F.Przytycki
Solitons in crystals. (English) Zbl 0555.73007
Continuum models of discrete systems, Proc. 3rd int. Symp., Freudenstadt/Ger. 1979, SM Stud. Ser. 15, 253-328 (1980).
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