Pattern formation

The proposed material is a review of the results of the study of the dynamics of roll domains of parametrically excited waves on the surface of the liquid. The processes of establishing regular wave patterns and structures from heavy particles produced by a field of standing waves are discussed from the standpoint of nonlinear dynamics.

The dynamics of coupled maps’ ensembles is investigated in the context of description of spatio­temporal processes in the myocardium. Particular, the dynamics of two coupled maps is explored as well as modeling the interaction of pacemaker (oscillatory) cell and myocyte (excitable cell), and the interation of two pacemakers.

Paper presents the lecture which was conducted for pupils on workshop «Nonlinear Days in Saratov for Youth – 2011». In the lecture brief introduction in physics of open systems is presented and several examples of process of selforganization and pattern formation in the systems of different nature are discussed.

The work presents the results of experimental investigation of roller domains parametrically excited by the capillary waves. Domains rollers were oriented parallel to the different borders of the rectangular cell and perpendicular to each other. Found that depending on the initial and boundary conditions on the edges of the cell can emerge two-dimensional domains of different forms. The dynamics of the domain is determined by the movement of their fronts. A model is proposed to explain the observed phenomena, numerical calculations by which agree well with experiment.

The paper presents experimental studies on the formation of spiral structures of heavy particles by the field of parametrically excited standing spiral waves. Particles move under the influence of the average currents field generated near the bottom in a viscous liquid by standing waves. The formation of structures has a threshold character and depends on the intensity of the field of standing waves. Formation of multi-armed structures revealed.