斑图形成与孤子
Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In addition the cellular automaton constructed by this procedure preserves the essential properties of the original equation,…
It is well known that one-dimensional Klein-Gordon lattices with nearest-neighbor interactions can support multibreathers with phase differences between the successive "central" oscillators $\phi_i=0\ \mbox{or}\ \pi$ (standard…
Acellular slime mould Physarum polycephalum is a monstrously large single cell visible by an unaided eye. It shows sophisticated behavioural traits in foraging for nutrients and developing an optimal transport network of protoplasmic tubes…
When (robotic) Automated Fibre Placement (AFP) is used to manufacture aerospace components with complex three dimensional geometries, gaps between fibre tows can occur. This paper is the first to explore the interaction under compressive…
If carbon fibre layers are prevented from slipping over one another as they consolidate onto a non-trivial geometry, they can be particularly susceptible to wrinkling/buckling instabilities. A one dimensional model for wrinkling during…
We investigate numerically and experimentally the influence of coupling disorder on the self-trapping dynamics in nonlinear one-dimensional optical waveguide arrays. The existence of a lower and upper bound of the effective average…
Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be…
As a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in…
We describe the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. After the initial impact strikes the system, a characteristic wave structure emerges…
In this work we explore how nonlinear modes described by a dispersive wave equation (in our example, the nonlinear Schrodinger equation) and localized in a few wells of a periodic potential can act analogously to a chain of coupled…
We consider an array of fiber lasers coupled through the nearest neighbors. The model is a generalized nonlinear Schroedinger equation where the usual Laplacian is replaced by the graph Laplacian. For a graph with no symmetries, we show…
We study the relationship between the partially synchronous state and the coupling structure in general dynamical systems. Our results show that, on the contrary to the widely accepted concept, topological symmetry in a coupling structure…
We study the statistical mechanics of the one-dimensional discrete nonlinear Schr\"odinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the…
We introduce a system of two parallel-coupled discrete nonlinear Schroedinger (DNLS) inhomogeneous chains. Each one favors the unidirectional transmission of incident packets, in the opposite directions with respect to each other. Two…
We propose an algorithm for the detection of recurrence domains of complex dynamical systems from time series. Our approach exploits the characteristic checkerboard texture of recurrence domains exhibited in recurrence plots (RP). In phase…
There exist two versions of the Kadomtsev-Petviashvili equation, related to the Cartesian and cylindrical geometries of the waves. In this paper we derive and study a new version, related to the elliptic cylindrical geometry. The derivation…
Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…
We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg--de Vries, equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave…
We study the occurrence of modulational instabilities in lattices with non-local, power-law hoppings and interactions. Choosing as a case study the discrete nonlinear Schr\"odinger equation, we consider one-dimensional chains with power-law…
Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We…