Related papers: Localized structures in dispersive and doubly reso…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
Spatially localized oscillations in periodically forced systems are intriguing phenomena. They may occur in spatially homogeneous media (oscillons), but quite often emerge in heterogeneous media, such as the auditory system, where localized…
We consider localised states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localised states is made possible by…
We study spin-polarized states and their stability in anti-ferromagnetic states of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…
An investigation is undertaken of coupled reaction-diffusion systems in one spatial dimension that are able to support, in different regions of their parameter space, either an isolated spike solution, or stable localized patterns with an…
We introduce a subclass of Lie symmetries, called parameter-state symmetries, to analyse the local structural identifiability and observability of mechanistic models consisting of state-dependent ODEs with observed outputs. These symmetries…
We study the turbulence transition of plane Couette flow in large domains where localised perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary between laminar and turbulent dynamics we…
Motivated by the increasing interest in the properties of multimode optomechanical devices, here we study a system in which a driven mode of a large-area optical cavity is despersively coupled to a deformable mechanical element. Two…
We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…
In this work we consider the dynamics of a chain of many coupled kicked rotors with dissipation. We map a rich phase diagram with many dynamical regimes. We focus mainly on a regime where the system shows period doubling, and forms patterns…
In a tight binding framework, we analyze the characteristics of electronic states in strongly disordered materials (hopping sites are placed randomly with no local order) with tunneling matrix elements decaying exponentially in the atomic…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of the nature in the…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and…
We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system…
It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the…
We extend a special kind of localized state trapped at the intersection due to the geometric confinement, first proposed in a three-terminal-opening T-shaped structure [Euro. Phys. Lett. {\bf 55}, 539 (2001)], into a ring geometry with a…