Dissipative Solitons and Metastable States in a Chain of Active Particles

Abstract

The dynamics of a chain of interacting active particles of Rayleigh-type is studied. Particles are interconnected via Morse potential forces. The steady-state modes (attractors) of the chain with periodic boundary conditions look like cnoidal waves with a uniform distribution of the particles’ density maxima along the chain. However, if the system starts from random initial conditions, a metastable state with nonuniform distribution of density maxima is formed. Characteristics of metastable states, excitation probability of different modes and their lifetimes are studied by numerical simulation.

Collective vibrations of confined levitating droplets

“…Emergent wave propagation in fluid-based, many-body systems, both passive and active, is an area of burgeoning interest, having been observed in a wide range of settings including bacterial suspensions [1][2][3][4]; colloidal fluids composed of synthetic microrollers and spinners [5][6][7]; and crystals of driven microfluidic water droplets [8][9][10][11]. Elsewhere, theoretical models of one-dimensional driven-dissipative lattices exhibit instabilities in the form of solitary waves, as well as unidirectional motion and out-of-phase (optical) oscillations [12][13][14][15][16][17][18], prompting experimental realizations in the form of active electronic circuits [19][20][21][22][23]. We here introduce a robust, mechanical analog of an active nonlinear lattice, comprised of quasi-one-dimensional assemblies of self-propelled fluid droplets.…”

Collective vibrations of a hydrodynamic active lattice

“…Examples include the complex flows arising from active stresses exerted by bacteria suspended in fluid [3,4]; vortex generation and nonlinear wave propagation in colloidal fluids [5–8]; phonon-like excitations in passively driven crystals of particles and droplets confined to microfluidic channels [9–13]; and emergent magnetic order in hydrodynamic spin lattices of walking dropets [14,15]. In non-fluidic systems, theoretical models of active nonlinear lattices are shown to exhibit instabilities in the form of out-of-phase oscillations and solitary waves [16–20], prompting experimental analogues in the form of active electronic circuits [21–24].…”

“…particles and droplets confined to microfluidic channels [9][10][11][12][13]; and emergent magnetic order in hydrodynamic spin lattices of walking dropets [14,15]. In non-fluidic systems, theoretical models of active nonlinear lattices are shown to exhibit instabilities in the form of out-of-phase oscillations and solitary waves [16][17][18][19][20], prompting experimental analogues in the form of active electronic circuits [21][22][23][24].…”

Мобильные Диссипативные Бризеры В Цепочке Нелинейных Осцилляторов

“…Особый интерес представляет динамика упорядоченных систем взаимодействующих частиц, которые могут быть как консервативными [1,2], так и активными [3][4][5], и ансамблей связанных осцилляторов [6][7][8][9]. Варьированием параметров элементов и связей модели, описывающей упорядоченный ансамбль осцилляторов, можно получать в асимптотике известные модели цепочки консервативных частиц (Тоды, Морзе, Леннарда−Джонса, Ферми−Паста−Улама) и цепочки активных частиц (например, Рэлея-Морзе [10,11]), а также цепочки консервативных осцилляторов [7] и цепочки активных осцилляторов [6,8]. В настоящей работе исследуется поведение цепочек активных частиц и активных осцилляторов, которые переходят друг в друга при стремлении частоты осцилляторов к нулю.…”