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The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
This work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual.…
The random energy landscapes developed by speckle fields can be used to confine and manipulate a large number of micro-particles with a single laser beam. By means of molecular dynamics simulations, we investigate the static and dynamic…
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially-varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
The physical mechanism behind the spontaneous formation of metachronal waves in microtubule arrays in a low Reynolds number fluid has been of interest for the past several years, yet is still not well understood. We present a model…
Peritrichous bacteria synchronize and bundle their flagella to actively swim while disruption of the bundle leads to tumbling. It is still not known whether the number of flagella represents an evolutionary adaptation towards optimizing…
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic…
The existence of travelling waves for a coupled system of hyperbolic/ parabolic equations is established in the case of a finite number of velocities in the kinetic equation. This finds application in collective motion of chemotactic…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
The existence of traveling and standing waves is investigated for chains of coupled pendula with periodic boundary conditions. The results are proven by applying topological methods to subspaces of symmetric solutions. The main advantage of…
We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random-…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…
A novel mechanism for the transport of microscale particles in viscous fluids is demonstrated. The mechanism exploits the trapping of such particles by rotational streaming cells established in the vicinity of an oscillating cylinder,…