arXiv subjects

Anastasiya V. Dolmatova

Publications and source records attributed to Anastasiya V. Dolmatova.

7 recordsLinked to original sources

arXiv2023

Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise

We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussian white noise. Two-cumulant reduction equations for alpha-stable noises are derived. The implementation of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of direct numerical simulation of the ensemble of N=1500 oscillators and the "exact" numeric solution for the fractional Fokker-Planck equation in the Fourier space are found to be in good agreement with the analytical solutions for two feasible circular cumulant model reductions. We also illustrate that the two-cumulant model reduction is useful for studying the bifurcations of chimera states in hierarchical populations of coupled noisy phase oscillators.

nlin.AO↗

arXiv2021

Fertilization of liquid-saturated porous medium with multicomponent gases due to surface temperature oscillation

We study non-isothermal diffusive transport of a weakly-soluble two-component substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. Particular attention is given to the example case of infiltration of nitrogen and oxygen from the atmosphere under the annual temperature oscillation. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In such a system, the zones of saturated solution and nondissolved phase coexist with the zones of undersaturated solution; these zones migrate with time. Moreover, the solubility of a multicomponent substance depends on its composition, which results in a much more intricate mathematical model of solubility as compared to the single-component case. We describe the phenomenon of formation of a near-surface bubbly horizon due to the temperature oscillation. An analytical theory of the phenomenon is developed. For multicomponent solutions we report the formation of diffusion boundary layer, which is not possible for single-component solutions. We construct an analytical theory for this boundary layer; in particular, we derive effective boundary conditions for the problem of the diffusive transport beyond this layer.

physics.flu-dyn↗

arXiv2020

Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise

We demonstrate the application of the circular cumulant approach for thermodynamically large populations of phase elements, where the Ott-Antonsen properties are violated by a multiplicative intrinsic noise. The infinite cumulant equation chain is derived for the case of a sinusoidal sensitivity of the phase to noise. For inhomogeneous populations, a Lorentzian distribution of natural frequencies is adopted. Two-cumulant model reductions, which serve as a generalization of the Ott-Antonsen ansatz, are reported. The accuracy of these model reductions and the macroscopic collective dynamics of the system are explored for the case of a Kuramototype global coupling. The Ott-Antonsen ansatz and the Gaussian approximation are found to be not uniformly accurate for non-high frequencies.

cond-mat.stat-mech↗

arXiv2019

Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series

The cumulant representation is common in classical statistical physics for variables on the real line and the issue of closures of cumulant expansions is well elaborated. The case of phase variables significantly differs from the case of linear ones; the relevant order parameters are the Kuramoto-Daido ones but not the conventional moments. One can formally introduce `circular' cumulants for Kuramoto-Daido order parameters, similar to the conventional cumulants for moments. The circular cumulant expansions allow to advance beyond the Ott-Antonsen theory and consider populations of real oscillators. First, we show that truncation of circular cumulant expansions, except for the Ott-Antonsen case, is forbidden. Second, we compare this situation to the case of the Gaussian distribution of a linear variable, where the second cumulant is nonzero and all the higher cumulants are zero, and elucidate why keeping up to the second cumulant is admissible for a linear variable, but forbidden for circular cumulants. Third, we discuss the implication of this truncation issue to populations of quadratic integrate-and-fire neurons [E. Montbrió, D. Pazó, A. Roxin, Phys. Rev. X, vol. 5, 021028 (2015)], where within the framework of macroscopic description, the firing rate diverges for any finite truncation of the cumulant series, and discuss how one should handle these situations. Fourth, we consider the cumulant-based low-dimensional reductions for macroscopic population dynamics in the context of this truncation issue. These reductions are applicable, where the cumulant series exponentially decay with the cumulant order, i.e., they form a geometric progression hierarchy. Fifth, we demonstrate the formation of this hierarchy for generic distributions on the circle and experimental data for coupled biological and electrochemical oscillators.

cond-mat.stat-mech↗

arXiv2019

Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators

We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered. The derivation is performed within the framework of the phase reduction, which fully accounts for the amplitude degrees of freedom. Firstly, we consider the case of identical oscillators subject to intrinsic noise, obtain the synchronization condition, and find that the distribution of phase deviations always possesses lower-law heavy tails. Secondly, we consider the case of nonidentical oscillators. For the average oscillator frequency as a function of the natural frequency mismatch, limiting scaling laws are derived; these laws exhibit the nontrivial phenomenon of frequency repulsion accompanying synchronization under negative coupling. The analytical theory is illustrated with examples of Van der Pol and Van der Pol--Duffing oscillators and the neuron-like FitzHugh--Nagumo system; the results are also underpinned by the direct numerical simulation for ensembles of these oscillators.

nlin.AO↗

arXiv2018

Comparison of the effect of horizontal vibrations on interfacial waves in a two-layer system of inviscid liquids to effective gravity inversion

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

physics.flu-dyn↗

arXiv2017

Synchronization of coupled active rotators by common noise

We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate angle-action variables and averaging over fast rotations. For identical rotators, we describe a transition from full to partial synchrony at a critical value of repulsive coupling. For nonidentical rotators, the most nontrivial effect occurs at moderate repulsive coupling, where a juxtaposition of phase locking with frequency repulsion (anti-entrainment) is observed. We show that the frequency repulsion obeys a nontrivial power law.

cond-mat.stat-mech↗