We report the observation of defects with fractional topological charges (disclinations) in square and hexagonal patterns as numerical solutions of several generic equations describing many pattern-forming systems: Swift-Hohenberg equation, damped Kuramoto-Sivashinsky equation, as well as nonlinear evolution equations describing large-scale Rayleigh-Benard and Marangoni convection in systems wi...

Noise-induced transition in the solutions of the Kuramoto–Sivashinsky (K–S) equation is investigated using the minimum action method derived from the large deviation theory. This is then used as a starting point for exploring the configuration space of the K–S equation. The particular example considered here is the transition between a stable fixed point and a stable travelling wave. Five saddl...

Abstract It is shown that an oblique projection-based feedback control able to stabilize the state of Kuramoto–Sivashinsky equation, evolving in rectangular domains, a given time-dependent trajectory. The actuators consist finite number indicator functions supported small subdomains. Simulations are presented, one-dimensional case under periodic boundary conditions and two-dimensional Neumann c...

We study the effects of multiplicative noise on a spatio-temporal pattern forming nonlinear Partial Differential Equation (PDE) model for premixed flame instability, known as the Kuramoto-Sivashinsky equation, in a circular domain. Modifications of a previously developed numerical integration scheme allow for longer time integration in the presence of noise. In order to gain additional insight,...

Phase transitions can be modeled by the motion of an interface between two locally stable phases. A modiied Kuramoto-Sivashinsky equation, h t + r 2 h + r 4 h = (1 ?)jrhj 2 (r 2 h) 2 + (h xx h yy ? h 2 xy); describes near planar interfaces which are marginally long-wave unstable. We study the question of nite-time singularity formation in this equation in one and two space dimensions on a perio...

Phase transitions can be modeled by the motion of an interface between two locally stable phases. A modified Kuramoto-Sivashinsky equation, h, + 72h + Wh = (1 a)lVhl ~ ± X(V~h): + ~A(hx~hyy h~y) , describes near planar interfaces which are marginally long-wave unstable. We study the question of finite-time singularity formation in this equation in one and two space dimensions on a periodic doma...

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative...