Related papers: Discrete Wave Turbulence
We investigate the asymmetric integrable turbulence and rogue waves (RWs) emerging from the modulation instability (MI) of plane waves for the DNLS equation. The \(n\)-th moments and ensemble-averaged kinetic and potential energy exhibit…
We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
The direct numerical simulation (DNS) of the Taylor--Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio & Luchini (Eur. J. Mech. B / Fluids, v.21, pp.413--427, 2002), and is based on a…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
The chaotic dynamics of small-scale vorticity plays a key role in understanding and controlling turbulence, with direct implications for energy transfer, mixing, and coherent structure evolution. However, measuring or controlling its…
It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly…
Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements. When the relative abundances of types can be measured well, we often observe heavy-tailed…
Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking place on a discrete half-space. All operators are represented graphically. The expressions…
The assemblies of either quantum dots or magnetic nanoclusters are studied. It is shown that such assemblies can produce coherent radiation. A method is developed for solving the systems of nonlinear equations describing the dynamics of…
Recent experimental and computational studies indicate that near wall turbulent flows can be characterized by universal small scale autonomous dynamics that are modulated by large scale structures. We formulate numerical simulations of near…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…
Drifting pattern domains (DPDs), moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this…
The pair density wave (PDW) exemplifies intertwined orders in strongly correlated systems. A recent discovery of superconductivity in a quarter-metal state offers the first experimental system where a pure PDW without uniform…
The interplay between quantum and thermal fluctuations in the presence of quenched random disorder is a long-standing open theoretical problem which has been made more urgent by advances in modern experimental techniques. The fragility of…
Formation of turbulence of capillary waves is studied in laboratory experiments. The spectra show multiple exponentially decreasing harmonics of the parametrically excited wave which nonlinearly broaden with the increase in forcing.…
The coherent dynamics of bubble clusters in liquid are of fundamental and industrial importance and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate unsupervised learning of…
Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group…
The complex interplay of magnetohydrodynamics, gravity, and supersonic turbulence in the interstellar medium (ISM) introduces non-Gaussian structure that can complicate comparison between theory and observation. We show that the Wavelet…
The Weak Turbulence Theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we…