Related papers: Linear and nonlinear information flow in spatially…
The Lyapunov spectrum describes the exponential growth, or decay, of infinitesimal phase-space perturbations. The perturbation associated with the maximum Lyapunov exponent is strongly localized in space, and only a small fraction of all…
The exponential growth in the rate at which information can be communicated through an optical fiber is a key element in the so called information revolution. However, like all exponential growth laws, there are physical limits to be…
Amplitude expansions are used to determine steady states of a semi-infinite solid subject to the Grinfeld instability in systems with a fixed (wave)length. We present two methods to obtain high-order weakly nonlinear results. Using the…
This paper is on the effect of nonlinearity in the equations for propagation of disturbances on transition in the class of Spiral Poiseuille Flows. The problem is approached from the fundamental point of view of following the growth of…
Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant…
Inertial waves transport energy and momentum in rotating fluids and are a major contributor to mixing and tidal dissipation in Earth's oceans, gaseous planets, and stellar interiors. However, their stability and breakdown mechanisms are not…
A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some---the ephemeral information---is dissipated and some---the bound information---is actively stored and so affects future behavior. We derive…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
The dynamics of the system is investigated when one part of the system initially behaves in a regular manner and the other in a chaotic one. The propagation of the chaos is considered as the motion of a region with the maximal Lyapunov…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…
Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite amplitude perturbations is studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales is studied. The analytic tool of pole expansion in the complex plane is emloyed to address the interaction of the unstable growth…
Mobility causes network structures to change. In PSNs where underlying network structure is changing rapidly, we are interested in studying how information dissemination can be enhanced in a sparse disconnected network where nodes lack the…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Non-equilibrium dissipative systems usually exhibit multistability, leading to the presence of propagative domain between steady states. We investigate the front propagation into an unstable state in discrete media. Based on a paradigmatic…