相关论文: Collective phase description of oscillatory convec…

In this paper we study a model for phase segregation consisting in a sistem of a partial and an ordinary differential equation. By a careful definition of maximal solution to the latter equation, this system reduces to an Allen-Cahn…

Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…

We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents…

We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…

The nature of emergent collective behaviors of moving physical agents interacting with their neighborhood is a long-standing open issue in physical and biological systems alike. This calls for studies on the control of synchronization and…

For oblique anti-plane shear waves in periodic layered elastic composites, it is shown that negative energy refraction is accompanied by positive phase-velocity refraction and positive energy refraction is accompanied by negative…

We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the…

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase…

Recent analysis of the helioseismic observations indicate that the previously observed surface torsional oscillations extend significantly downwards into the solar convection zone. In an attempt to understand these oscillations, we study…

Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the…

A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…

The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly-averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure…

Stochastic oscillators play a prominent role in different fields of science. Their simplified description in terms of a phase has been advocated by different authors using distinct phase definitions in the stochastic case. One notion of…

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…

We present a framework for controlling the collective phase of a system of coupled oscillators described by the Kuramoto model under the influence of a periodic external input by combining the methods of dynamical reduction and optimal…

We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

The linear instability of Faraday waves in Hele-Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of…

In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This…

We apply the phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows are described in terms of the phase dynamics reducing the high-dimensional fluid flow to its single scalar…