Related papers: Wavenumber selection in coupled transport equation…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
We study the chaos of travelling waves (TW) in unidirectional chains of bistable maps. Previous numerical results suggested that this property is selective, {\sl viz.}\ given the parameters, there is at most a single (non-trivial) velocity…
The statistical properties of a large number of weakly nonlinear waves can be described in the framework of the Weak Turbulence Theory. The theory is based on the hypothesis of an asymptotically large system. In experiments, the systems…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically.…
Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior amongst the simplest…
Active turbulence is a paradigmatic and fascinating example of self-organized motion at large scales occurring in active matter. We employ massive hydrodynamic simulations of suspensions of resolved model microswimmers to tackle the…
The pattern selection problem in binary-mixture convection in an extended channel with a lateral through-flow is presented. The through-flow breaks left--right parity and changes pattern dynamics dramatically. The problem is studied based…
Many organisms navigate gradients by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles whenever attractant signal increases. This induces a functional coupling between movement and…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
We analyze a simplistic model for run-and-tumble dynamics, motivated by observations of complex spatio-temporal patterns in colonies of myxobacteria. In our model, agents run with fixed speed either left or right, and agents turn with a…
The problem of describing optical turbulent structures, arising in resonant media with high Fresnel numbers, is reviewed. The consideration is based on the probabilistic approach to pattern selection, ascribing a probability distribution of…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a statistically steady state of elastic wave turbulence. The analytical representation of the nonlinear frequency is obtained by evaluating the extended self-nonlinear…
During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows.…
The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…
The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate…