S.V. Kiyashko1, V.O. Afenchenko2

1,2 Institute of Applied Physics of RAS (Nizhny Novgorod, Russia)

In nonlinear systems with instability, multistability often arises. In the study of processes occurring in real environments, the problem arises of finding ways that lead to any state of equilibrium and the search for new stable states. In two-dimensional space-time systems, the resulting structures can consist of domains and differ by different orientations in space of the rolls forming them.

The aim of this work is to experimentally determine the features of the generation of multidomain structures in a two-dimensional system in the presence of complex boundaries of the liquid layer, which experiences periodic vertical oscillations.

The paper presents the results of an experimental study of the dynamics of roller domains of parametrically excited capillary waves in a square cell with a rounded corner and a rectangular protrusion at the boundary. In different domains, the rollers were oriented parallel and perpendicular to the cell boundaries and to the boundaries that appear near the rectangular ledge. It was found that the dynamics of domains is determined by the motion of their fronts, and, depending on the initial and boundary conditions, stable two-dimensional roller structures with rounded corners can appear at the edges of a cell with a rounded corner and a rectangular protrusion. In this case, roundings with a large radius exerted the strongest influence on the dynamics of domains.

The multistability of the equilibrium states of the roller structures is found, which is characterized by the fact that, with the system parameters unchanged, various scenarios of domain competition arise. As a result, this led to 5 different stable equilibrium states, which differed in the number of domains, their shape, and the lack of spatial symmetry. It has been experimentally shown that the most stable equilibrium states of domains arise when a rectangular protrusion is symmetrical relative to the lateral sides of the cell, and the coordinates of the protrusion corners should be on the diagonals of the cell corners.

A phenomenological model of the observed phenomenon is proposed, according to which numerical calculations are in good agreement with experiment.

The results obtained may be of interest in studying the processes of establishing stable regimes in active media under strong competition and in studying the formation of two-dimensional structures from conducting particles capable of scattering electromagnetic waves.

Кияшко С.В., Афенченко В.О. Динамика роликовых доменов при параметрическом возбуждении капиллярных волн в квадратной кювете с закругленным углом и прямоугольным выступом на границе // Нелинейный мир. 2022. Т. 20. №3. С. 17-27. DOI: https://doi.org/10.18127/j20700970-202203-02

Kiyashko S.V., Afenchenko V.O. Dynamics of roller domains under parametric excitation of capillary waves in a square cell with a rounded corner and a rectangular protrusion at the boundary. Nonlinear World. 2022. V. 20. № 3. 2022. P. 17-27. DOI: https://doi.org/10.18127/j20700970-202203-02 (In Russian)