Related papers: Nonlinear Lattices Generated from Harmonic Lattice…
We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model along with cubic Klein-Gordon type nonlinearity. We investigate the long-time dynamics of the nonlinear edge states, which are obtained by nonlinear continuation of…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…
We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…
Geometrical dimensionality plays a fundamentally important role in the topological effects arising in discrete lattices. While direct experiments are limited by three spatial dimensions, the research topic of synthetic dimensions…
We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular,…
Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…
We construct a nonlinear lattice that has a particular symmetry in its potential function consisting of long-range pairwise interactions. The symmetry enhances smooth propagation of discrete breathers, and it is defined by an invariance of…
We analyze two-color spatially localized modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi-2) nonlinear interfaces embedded into a linear layered structure --- a quasi-one-dimensional…
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique…
The squeezing in a nonlinear system with chaotic dynamics is considered. The model describing interaction of collection of two-level atoms with a single-mode of self-consistent field and an external field is analyzed. It is shown that in…
Frames, or lattices consisting of mass points connected by rigid bonds or central force springs, are important model constructs that have applications in such diverse fields as structural engineering, architecture, and materials science.…
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…
Second harmonic generation is a powerful tool directly connected to the symmetry of materials. Phase transitions, lattice rotations or electromagnetic coupling in multiferroic compounds can be revealed by using second harmonic…
Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an…
Sponges were recently proposed as a generalization of lattices, focussing on joins/meets of sets, while letting go of associativity/transitivity. In this work we provide tools for characterizing and constructing sponges on metric spaces and…
In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of…
High-harmonic generation (HHG) in solids has rapidly emerged as a promising platform for creating compact attosecond sources and probing ultrafast electron dynamics. Resonant metasurfaces are essential for enhancement of the otherwise small…
This work investigates the effect of nonlinearities on topologically protected edge states in one and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are…