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Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equation with the quasi-Riesz derivative.
Phys Rev E
July 2024
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its Lévy index (LI). This FDNLS equation represents a novel discrete system, in which the nearest-neighbor coupling is combined with long-range interactions, that decay as the inverse square of the separation between lattice sites. The system may be realized as an array of parallel quasi-one-dimensional Bose-Einstein condensates composed of atoms or small molecules carrying, respectively, a permanent magnetic or electric dipole moment.
View Article and Find Full Text PDFComparing modeling predictions of aluminum edge dislocations: semidiscrete variational Peierls-Nabarro versus atomistics.
JOM (1989)
January 2018
Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 USA.
Multiple computational methods for modeling dislocations are implemented within a high-throughput calculation framework allowing for rigorous investigations comparing the methodologies. Focusing on aluminum edge dislocations, twenty-one classical aluminum interatomic potentials are used to directly model dislocation core structures using molecular dynamics, as well as provide input data for solving the semidiscrete variational Peierls-Nabarro dislocation model. The predicted dislocation core spreading obtained from both computational methods show similar trends across the potentials.
View Article and Find Full Text PDFKink-antikink asymmetry and impurity interactions in topological mechanical chains.
Phys Rev E
February 2017
Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands.
We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models.
View Article and Find Full Text PDFSoliton mobility in disordered lattices.
Phys Rev E Stat Nonlin Soft Matter Phys
October 2015
Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854, USA.
We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schrödinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from a deviation from integrability, which is due to randomness for the AL model, and both randomness and lattice discreteness for the NLS lattice. The statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size.
View Article and Find Full Text PDFFluxon mobility in an array of asymmetric superconducting quantum interference devices.
Phys Rev E Stat Nonlin Soft Matter Phys
January 2015
Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, vul. Metrologichna 14B, 03680 Kyiv, Ukraine.
Fluxon dynamics in the dc-biased array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) is investigated. The array of SQUIDs is described by the discrete double sine-Gordon equation. It appears that this equation possesses a finite set of velocities at which the fluxon propagates with the constant shape and without radiation.
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