Multistability of roller structures under parametric excitation of capillary waves in a square cell with a round protrusion in the center

Abstract

In nonlinear systems with instability, multistability often occurs. When studying processes occurring in real environments, the problem arises of finding paths leading to any state of equilibrium and searching for new stable states. In two-dimensional systems, they can consist of domains and differ in orientation in space. The goal of the 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 a liquid layer that 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 round insert in the center of the cell. In different domains, the rollers were oriented parallel and perpendicular to the boundaries of the cuvette and the boundaries of the circular insert. It was found that the dynamics of domains is determined by the movement of their fronts, and depending on the initial and boundary conditions, stable two-dimensional roller structures can appear at the edges of a square cell with a round protrusion in the center of the cell. In different domains, the rollers had different orientations. In this case, roundings with a large radius had the strongest effect on the dynamics of defects. Multistability of equilibrium states of roller structures was discovered, characterized by the fact that, with constant system parameters, various scenarios of domain competition arose, leading to 11 different stable equilibrium states, which differed in the number of domains, their shape and the presence of spatial symmetry. It turned out that during the occurrence of defects and the growth of domain walls, slow liquid flows arise near the boundaries of the cuvette and the circular insert. The rollers begin to move, and then a new stable equilibrium state is established in the form of a single domain containing one or two domain walls. It has been experimentally shown that the most stable equilibrium states of domains arise when the circular protrusion is symmetrically positioned relative to the sides of the cuvette. The results obtained may be of interest when studying the processes of establishing stable regimes in active media under strong competition and when studying the formation of two-dimensional structures from conducting particles capable of scattering electromagnetic waves.