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Nonlinear localized excitations in one-dimensional diatomic lattices with cubic and quartic nonlinearity are considered analytically by a quasi-discreteness approach. The criteria for the occurence of asymmetric gap solitons (with vibrating…
We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a lattice-based algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is…
The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at the nodes to obtain energetically consistent models providing accurate descriptions of the acoustic behavior of the discrete system. The…
Controlling dopant transport with high spatial precision is crucial for improving the semiconductor functionality, reliability, and scalability. Although prior models of noise-assisted diffusion have been largely confined to idealized one…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We demonstrate that a flat-band state in a quasi-one-dimensional rhombic lattice is robust in the presence of external drivings along the lattice axis. The lattice was formed by periodic arrays of evanescently coupled optical waveguides,…
We investigate the impact of harmonic confinement in a finite optical superlattice and reveal the different mechanisms that can lead to the emergence of localized states. The optical superlattice, with odd or even number of unit cells, can…
Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of…
We examine quantum decay of localized vibrations in anharmonic crystal lattice. The theory which describes two-phonon anharmonic relaxation can be applied both to local modes associated with substitutional impurity and to intrinsic local…
The engineering of localised modes in photonic structures is one of the main targets of modern photonics. An efficient strategy to design these modes is to use the interplay of constructive and destructive interference in periodic photonic…
We investigate internal localized eigenmodes of the linearized equation around spin discrete breathers in 1D antiferromagnets with on-site easy axis anisotropy. The threshold of occurrence of the internal localized eigenmodes has a typical…
An analytical work on intrinsic localized modes in a two-dimensional Heisenberg ferromagnet on the checkerboard lattice is presented. Taking advantage of an asymptotic method, the governing lattice dynamical equations are reduced to one…
Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently, the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and…
We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially-decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the…
Intrinsic Localized Modes (ILM) (or Discrete Breathers, DB) are localized oscillatory modes known to occur in atomic or molecular chains characterized by coupling and/or on-site potential nonlinearity. Quasi-crystals of charged mesoscopic…
In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…
We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We prove the unique solvability of an initial-boundary value…
Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce…
We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally…
We analyze the existence and stability of nonlinear localized waves described by the Kronig-Penney model with a nonlinear impurity. We study the properties of such waves in a homogeneous medium, and then analyze new effects introduced by…