Nanofine spatial dissipative structures with azimutal lattice curvation

Emergence of Macro Spatial Structures in Dissipative Cellular Automata

Imperfect Bifurcations and Spatial Structures in Dissipative Systems

One-dimensional reaction-diffusion equations associated with the trimolecular model of Prigogine and Lefever ("Brusselator") are analyzed. A physical description of possibilities of keeping concentrations of initial components constant is discussed. It is shown that the problem considering diffusion of initial components gives rise to an imperfect bifurcation problem. The diffusion equations ha...

Midband dissipative spatial solitons.

We show dissipative spatial solitons in nonlinear optical microresonators in which the refractive index is laterally modulated. In addition to "normal" and "staggered" dissipative solitons, similar to those in spatially modulated conservative systems, a narrow "midband" soliton is shown, having no counterparts in conservative systems.

Simplicial Complexes with Lattice Structures

If L is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex ∆(L) (definition recalled below). Lattice-theoretically, the resulting object is a subdirect product of copies of L. We note properties of this construction and of some variants, and pose several questions. For M3 the 5-element nondistributive modular lattice...

Instabilities of localized structures in dissipative systems with delayed feedback.

We report on a novel behavior of solitary localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to nontrivial instabilities resulting in the formation of oscillons, soliton rings, labyrinth patterns, or moving structures. We provide a bifurcation analysis of the delay...