Related papers: Dynamical cascade generation as basic mechanism of…
We consider a phenomenological continuum model for an active nematic fluid and show a universal, model independent, instability which renders the homogeneous nematic state unstable to order fluctuations. Using numerical and analytic tools…
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The…
We analyze the Benney model for interaction of short and long waves in resonant water wave interactions. Our particular interest is in the periodic traveling waves, which we construct and study in detail. The main results are that, for all…
We study abrupt changes in the dynamics and/or steady state of fermionic dissipative systems produced by small changes of the system parameters. Specifically, we consider open fermionic systems whose dynamics is described by master…
We explore the dynamical stabilities of a quasi-one dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed $N$ atoms with time-independent external potential. For the stationary states with zero flow density the general…
Considered herein is a particular nonlinear dispersive stochastic equation. It was introduced recently in [3], as a model describing surface water waves under location uncertainty. The corresponding noise term is introduced through a…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also…
A new concept called biased derivative is proposed. It has a potential to better understand and model some aspects of dynamical systems associated with creating bubbles.
Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a…
We establish a mathematically rigorous, general and quantitative framework to describe currents of non- (or weakly) interacting, indistinguishable particles driven far from equilibrium. We derive tight upper and lower bounds for the…
We consider Bose-Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length…
The Kelvin-Helmholtz instability in an ionized plasma is considered with a focus on the generation of magnetic field via the Biermann battery mechanisms. The problem is studied through direct numerical simulations of two counter-directed…
This announcement describes a probabilistic approach to cascades which, in addition to providing an entirely probabilistic proof of the Kahane-Peyri\`ere theorem for independent cascades, readily applies to general dependent cascades.…
Many new models of wave turbulence -- frozen, mesoscopic, laminated, decaying, sand-pile, etc. -- have been developed in the last decade aiming to solve problems seemingly not solvable in the framework of the existing wave turbulence theory…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is…
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…