scispace - formally typeset
Open AccessJournal ArticleDOI

Non-linear waves in lattices: past, present, future

Reads0
Chats0
TLDR
In this paper, a brief summary of various areas where non-linear waves have been emerging in the phenomenology of lattice dynamical systems is presented, including nonlinear optics, atomic physics, mechanical systems, electrical lattices, nonlinear metamaterials, plasma dynamics and granular crystals.
Abstract
In the present work, we attempt a brief summary of various areas where non-linear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include non-linear optics, atomic physics, mechanical systems, electrical lattices, non-linear metamaterials, plasma dynamics and granular crystals. We give some of the recent developments in each one of these areas and speculate on some of the potentially interesting directions for future study.

read more

Citations
More filters
Journal ArticleDOI

Wave propagation in single column woodpile phononic crystals: Formation of tunable band gaps

TL;DR: In this article, the formation of frequency band gaps in single column woodpile phononic crystals composed of orthogonally stacked slender cylinders is investigated. But the authors focus on investigating the effect of the cylinders' local vibrations on the dispersion of elastic waves along the stacking direction of the woodpiles phononic crystal.
Book ChapterDOI

Nonlinear Periodic Phononic Structures and Granular Crystals

TL;DR: In this paper, the authors describe the dynamic behavior of nonlinear periodic phononic structures, along with how such structures can be utilized to affect the propagation of mechanical waves, and discuss several possible future directions relating to granular crystals.
Journal ArticleDOI

Solitary waves in a chain of repelling magnets

TL;DR: In this paper, the dynamics of a one dimensional array of repelling magnets were studied experimentally, numerically, and theoretically, and it was shown that such systems support solitary waves with a profile and propagation speed that depend on the amplitude.
Journal ArticleDOI

Traveling waves in 2D hexagonal granular crystal lattices.

TL;DR: This study describes the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings, and provides scaling relations that characterize the directional power law decay of the wave velocity for various angles of impact.
Journal ArticleDOI

Traveling waves and their tails in locally resonant granular systems

TL;DR: In this paper, the authors revisited the theme of wave propagation in locally resonant granular crystal systems, referred to as mass-in-mass systems, and used three distinct approaches to identify relevant traveling waves.
References
More filters
Journal ArticleDOI

Absence of Diffusion in Certain Random Lattices

TL;DR: In this article, a simple model for spin diffusion or conduction in the "impurity band" is presented, which involves transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites.
Journal ArticleDOI

Solitons in polyacetylene

TL;DR: In this paper, the authors present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion.
Journal ArticleDOI

Solitons in conducting polymers

TL;DR: In this article, the authors review the theoretical models that have been developed to describe the physics of polyacetylene and related conducting polymers and summarize the relevant experimental results obtained for these materials.
Journal ArticleDOI

Solution of the One‐Dimensional N‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials

TL;DR: In this paper, the quantum-mechanical problems of N 1-dimensional equal particles of mass m interacting pairwise via quadratic (harmonical) and/or inverse (centrifugal) potentials is solved.
Journal ArticleDOI

Transport and Anderson localization in disordered two-dimensional photonic lattices

TL;DR: The experimental observation of Anderson localization in a perturbed periodic potential is reported: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice, demonstrating how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder.
Related Papers (5)