Effect of noise on the collective dynamics of a heterogeneous population of active rotators.

We study the collective dynamics of a heterogeneous population of globally coupled active rotators subject to intrinsic noise. The theory is constructed on the basis of the circular cumulant approach, which yields a low-dimensional model reduction for the macroscopic collective dynamics in the thermodynamic limit of an infinitely large population. With numerical simulation, we confirm a decent accuracy of the model reduction for a moderate noise strength; in particular, it correctly predicts the location of the bistability domains in the parameter space.

Non-Fickian diffusion and the accumulation of methane bubbles in deep-water sediments.

In the absence of fractures, methane bubbles in deep-water sediments can be immovably trapped within a porous matrix by surface tension. The dominant mechanism of transfer of gas mass therefore becomes the diffusion of gas molecules through porewater. The accurate description of this process requires non-Fickian diffusion to be accounted for, including both thermal diffusion and gravitational action. We evaluate the diffusive flux of aqueous methane considering non-Fickian diffusion and predict the existence of extensive bubble mass accumulation zones within deep-water sediments. The limitation on the hydrate deposit capacity is revealed; too weak deposits cannot reach the base of the hydrate stability zone and form any bubbly horizon.

Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations.

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.