Related papers: Defect-Mediated Stability: An Effective Hydrodynam…
The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small…
A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which…
All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…
Infinitesimal perturbations in various systems showing spatiotemporal chaos (STC) evolve following the power laws of the Kardar-Parisi-Zhang (KPZ) universality class. While universal properties beyond the power-law exponents, such as…
We examine the differences between the driven turbulence described by the Kuramoto-Sivashinsky (KS) equation and the second law of thermodynamics. A general velocity and entropy density system is analyzed with the unified thermodynamic…
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as…
We study the nature of chaos in finite and infinite dimensional systems through a comparison between the Kuramoto Sivashinsky (KS) equation, the Lorenz system, and a Lorenz type reduction of the KS equation proposed by Wilczak. Numerical…
We study a noisy Kuramoto-Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by…
We study in this paper boundary stabilization, in the L2 sense, of the perturbed Kuramoto-Sivashinsky (KS) equation subject to intermittent sensing. We assume that we measure the state on a given spatial subdomain during certain time…
There are many subtle issues associated with solving the Navier-Stokes equations. In this paper, several of these issues, which have been observed previously in research involving the Navier-Stokes equations, are studied within the…
Recent work on the dynamics of a crystal surface [T.Frisch and A.Verga, Phys. Rev. Lett. 96, 166104 (2006)] has focused the attention on the conserved Kuramoto-Sivashinsky (CKS) equation: \partial_t u = -\partial_{xx}(u+u_{xx}+u_x^2), which…
By computing 254 unstable stationary solutions of the Kuramoto-Sivashinsky equation in the extensive chaos regime (Lyapunov fractal dimension D=8.8), we find that 30% satisfy the symmetry of the time-average pattern of the spatiotemporal…
Chaotic pattern dynamics in many experimental systems show structured time averages. We suggest that simple universal boundary effects underly this phenomenon and exemplify them with the Kuramoto-Sivashinsky equation in a finite domain. As…
We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and conjecture a scaling form for the structure…
We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of…
Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model describes, e.g., a two-layer liquid film…
We develop a Melnikov framework for the Kuramoto Sivashinsky (KS) equation under weak deterministic and stochastic forcing. By treating KS as an infinite dimensional dynamical system, we derive a Melnikov functional that measures splitting…
The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaotic dynamics. The continuous spatial translation symmetry…
We study the emergence of pattern formation and chaotic dynamics in the one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means of a time-series analysis, in particular a nonlinear forecasting method which is based on…
The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems.…