arXiv subjects

Denis S. Goldobin

Publications and source records attributed to Denis S. Goldobin.

At least 19 recordsLinked to original sources

arXiv2026

Entrainment of magnetic fluid by a moving boundary of a plane gap

A fluid mechanics problem is solved which technological prototype is a fluid acoustic contact that is an inherent element of ultrasonic non-destructive testing procedures. It is well known that the acoustic contact established with an ordinary fluid suffers from essential disadvantage that is the loss of stability due to the gravity-induced fluid leakage in the course of dynamic scanning. The use of magnetic fluid (MF) is one of the ways to resolve the issue. A compact portion of MF held in place by a permanent magnet enables one to maintain a stable acoustic contact (fluid bridge) under arbitrary orientation of the ultrasonic sensor and, simultaneously, to radically minimize the drain of the contact fluid. The model system under consideration comprises a MF bridge that fills a flat gap, one of whose boundaries moves with constant velocity. Due to its wetting by the fluid, the receding plane carries away a fluid film thus depleting the contact. Theoretical expressions are obtained which define the profile of the film in the dynamic regime and the dependencies of the magnetic fluid drain on the boundary velocity, gap height and configuration of the imposed magnetic field. On that basis the optimal parameters are evaluated which ensure effective retention of the fluid contact under minimal drain of the fluid from it.

physics.flu-dyn↗

arXiv2025

Kinetic description of one-dimensional stochastic dynamics with small inertia

We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (phase oscillators, rotators, superconducting Josephson junctions) with an effective inertia in the case of a linear dissipation term and active Brownian particles in the case of a nonlinear dissipation. Elimination of a fast variable (velocity) reduces the characterization of the system state to a single variable and is formulated in four representations: moments, cumulants, the basis of Hermite functions, and the formal cumulant variant of the last. This elimination provides rigorous mathematical description for the overdamped limit in the case of linear dissipation and the overactive limit of active Brownian particles. For the former, we derive a low-dimensional equation system which generalizes the Ott-Antonsen Ansatz to systems with small effective inertia. In the latter case, we derive a Fokker-Planck-type equation with a forced drift term and an effective diffusion in one dimension, where the standard two-/three-dimensional mechanism is impossible. In the four considered representations, truncated equation chains are demonstrated to be utilitary for numerical simulation for a small finite inertia.

cond-mat.stat-mech↗

arXiv2025

Low dimensional dynamics of a sparse balanced synaptic network of quadratic integrate-and-fire neurons

Kinetics of a balanced network of neurons with a sparse grid of synaptic links is well representable by the stochastic dynamics of a generic neuron subject to an effective shot noise. The rate of delta-pulses of the noise is determined self-consistently from the probability density of the neuron states. Importantly, the most sophisticated (but robust) collective regimes of the network do not allow for the diffusion approximation, which is routinely adopted for a shot noise in mathematical neuroscience. These regimes can be expected to be biologically relevant. For the kinetics equations of the complete mean field theory of a homogeneous inhibitory network of quadratic integrate-and-fire neurons, we introduce circular cumulants of the genuine phase variable and derive a rigorous two cumulant reduction for both time-independent conditions and modulation of the excitatory current. The low dimensional model is examined with numerical simulations and found to be accurate for time-independent states and dynamic response to a periodic modulation deep into the parameter domain where the diffusion approximation is not applicable. The accuracy of a low dimensional model indicates and explains a low embedding dimensionality of the macroscopic collective dynamics of the network. The reduced model can be instrumental for theoretical studies of inhibitory-excitatory balanced neural networks.

q-bio.NC↗

arXiv2025

Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks

Neural dynamics is determined by the transmission of discrete synaptic pulses (synaptic shot-noise) among neurons. However, the neural responses are usually obtained within the diffusion approximation modeling synaptic inputs as continuous Gaussian noise. Here, we present a rigorous mean-field theory that encompasses synaptic shot-noise for sparse balanced inhibitory neural networks driven by an excitatory drive. Our theory predicts new dynamical regimes, in agreement with numerical simulations, which are not captured by the classical diffusion approximation. Notably, these regimes feature self-sustained global oscillations emerging at low connectivity (in-degree) via either continuous or hysteretic transitions and characterized by irregular neural activity, as expected for balanced dynamics. For sufficiently weak (strong) excitatory drive (inhibitory feedback) the transition line displays a peculiar re-entrant shape revealing the existence of global oscillations at low and high in-degrees, separated by an asynchronous regime at intermediate levels of connectivity. The mechanisms leading to the emergence of these global oscillations are distinct: drift-driven at high connectivity and cluster activation at low connectivity. The frequency of these two kinds of global oscillations can be varied from slow (around 1 Hz) to fast (around 100 Hz), without altering their microscopic and macroscopic features, by adjusting the excitatory drive and the synaptic inhibition strength in a prescribed way. Furthermore, the cluster-activated oscillations at low in-degrees could correspond to the gamma rhythms reported in mammalian cortex and hippocampus and attributed to ensembles of inhibitory neurons sharing few synaptic connections [G. Buzsaki and X.-J. Wang, Annual Review of Neuroscience 35, 203 (2012)].

cond-mat.dis-nn↗

arXiv2025

Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise

We report the effect of nonlinear bias of the frequency of collective oscillations of sin-coupled phase oscillators subject to individual asymmetric Cauchy noises. The noise asymmetry makes the Ott-Antonsen Ansatz inapplicable. We argue that, for all stable non-Gaussian noises, the tail asymmetry is not only possible (in addition to the trivial shift of the distribution median) but also generic in many physical and biophysical set-ups. For the theoretical description of the effect, we develop a mathematical formalism based on the circular cumulants. The derivation of rigorous asymptotic results can be performed on this basis but seems infeasible in traditional terms of the circular moments (the Kuramoto-Daido order parameters). The effect of the entrainment of individual oscillator frequencies by the global oscillations is also reported in detail. The accuracy of theoretical results based on the low dimensional circular cumulant reductions is validated with the high-accuracy "exact" solutions calculated with the continued fraction method.

cond-mat.stat-mech↗

arXiv2023

Deterministic dynamics of overactive Brownian particle in 2D and 3D potential wells

We study deterministic dynamics of overactive Brownian particles in 2D and 3D potentials. This dynamics is Hamiltonian. Integrals of motion for continuous rotational symmetries are reported. The cases of 2D, axisymmetric and non-axisymmetric 3D potentials are characterized and compared to each other. The strong impact of the rotational symmetry integrals of motion on the chaotic and quasiperiodic orbits is revealed. The scattering cross section is reported for spherically symmetric Gaussian-shape potential wells and obstacles as a function of self-propulsion speed.

cond-mat.stat-mech↗

arXiv2023

Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise

We study macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian noises; we argue that these noises must be alpha-stable whenever they are delta-correlated (white). For the case of additive-in-voltage noise, we derive the governing equation of the dynamics of the characteristic function of the membrane voltage distribution and construct a linear-in-noise perturbation theory. Specifically for the recurrent network with global synaptic coupling, we theoretically calculate the observables: population-mean membrane voltage and firing rate. The theoretical results are underpinned by the results of numerical simulation for homogeneous and heterogeneous populations. The possibility of the generalization of the pseudocumulant approach to the case of a fractional $α$ is examined for both irrational and fractional rational $α$. This examination seemingly suggests the pseudocumulant approach or its modifications to be employable only for the integer values of $α=1$ (Cauchy noise) and $2$ (Gaussian noise) within the physically meaningful range $(0;2]$. Remarkably, the analysis for fractional $α$ indirectly revealed that, for the Gaussian noise, the minimal asymptotically rigorous model reduction must involve three pseudocumulants and the two-pseudocumulant model reduction is an artificial approximation. This explains a surprising gain of accuracy for the three-pseudocumulant models as compared to the the two-pseudocumulant ones reported in the literature.

cond-mat.stat-mech↗

arXiv2023

Discrete synaptic events induce global oscillations in balanced neural networks

Neural dynamics is triggered by discrete synaptic inputs of finite amplitude. However, the neural response is usually obtained within the diffusion approximation (DA) representing the synaptic inputs as Gaussian noise. We derive a mean-field formalism encompassing synaptic shot-noise for sparse balanced networks of spiking neurons. For low (high) external drives (synaptic strengths) irregular global oscillations emerge via continuous and hysteretic transitions, correctly predicted by our approach, but not from the DA. These oscillations display frequencies in biologically relevant bands.

q-bio.NC↗

arXiv2023

Stochastic parametric excitation of convective heat transfer

We study the parametric excitation of the free thermal convection in a horizontal layer and a rectangular cell by random vertical vibrations. The mathematical formulation we use allows one to explore the cases of heating from below and above and the lowgravity conditions. The excitation threshold of the second moments of the current velocity and the temperature perturbations is derived. The heat flux through the system quantified by the Nusselt number is reported to be related to the second moment of temperature perturbations; therefore, the threshold of the stochastic excitation of second moments gives the threshold for the excitation of the convective heat transfer. Comparison of the stochastic parametric excitation to the effect of high-frequency periodic modulation reveals dramatic dissimilarity between the two.

physics.flu-dyn↗

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↗

arXiv2022

High-Order Schemes of Exponential Time Differencing for Stiff Systems with Nondiagonal Linear Part

Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models often possess fast oscillating or decaying modes -- in other words, are stiff systems. Practical implementation of these methods for the systems with nondiagonal linear part of equations is exacerbated by infeasibility of an analytical calculation of the exponential of a nondiagonal linear operator; in this case, the coefficients of the exponential time differencing scheme cannot be calculated analytically. We suggest an approach, where these coefficients are numerically calculated with auxiliary problems. We rewrite the high-order Runge--Kutta type schemes in terms of the solutions to these auxiliary problems and practically examine the accuracy and computational performance of these methods for a heterogeneous Cahn--Hilliard equation, a sixth-order spatial derivative equation governing pattern formation in the presence of an additional conservation law, and a Fokker--Planck equation governing macroscopic dynamics of a network of neurons.

math.NA↗

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↗

arXiv2021

Four approaches for description of stochastic systems with small and finite inertia

We analyse four approaches to elimination of a fast variable, which are applicable to systems like passive Brownian particles: (i) moment formalism, (ii) corresponding cumulant formalism, (iii) Hermite function basis, (iv) formal `cumulants' for the Hermit function basis. The accuracy and its strong order are assessed. The applicability and performance of two first approaches are also demonstrated for active Brownian particles.

cond-mat.stat-mech↗

arXiv2021

A reduction methodology for fluctuation driven population dynamics

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a `pseudo-cumulants' expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous noise sources, thus generalizing the mean-field formulation introduced in [E. Montbrió et al., Phys. Rev. X 5, 021028 (2015)].

cond-mat.stat-mech↗

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

Small and Finite Inertia in Stochastic Systems: Moment and Cumulant Formalisms

We analyze two approaches to elimination of a fast variable (velocity) in stochastic systems: moment and cumulant formalisms. With these approaches, we obtain the corresponding Smoluchovski-type equations, which contain only the coordinate/phase variable. The adiabatic elimination of velocity in terms of cumulants and moments requires the first three elements. However, for the case of small inertia, the corrected Smoluchowski equation in terms of moments requires five elements, while in terms of cumulants the same first three elements are sufficient. Compared to the method based on the expansion of the velocity distribution in Hermite functions, the considered approaches have comparable efficiency, but do not require individual mathematical preparation for the case of active Brownian particles, where one has to construct a new basis of eigenfunctions instead of the Hermite ones.

cond-mat.stat-mech↗

arXiv2019

Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in 2D XY arrays is addressed. The system is modeled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole-dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking $T_b$ temperature is lower than that ($T_\text{af}$) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean field approximation. With the technique of a generalized Ott-Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the antiferromagnetic order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented.

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↗