Denis Goldobin | Institute of Continuous Media Mechanics UrB RAS (original) (raw)

Papers by Denis Goldobin

ВЕСТНИК ПЕРМСКОГО УНИВЕРСИТЕТА. ФИЗИКА, 2016

In the dynamics of viscous fluid, the case of vanishing kinematic viscosity is actually equivalen... more In the dynamics of viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for description of flow of inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.

Mathematical Modelling of Natural Phenomena, 2021

We consider the implementation of a weak feedback with two delay times for controlling the cohere... more We consider the implementation of a weak feedback with two delay times for controlling the coherence of both deterministic chaotic and stochastic oscillators. This control strategy is revealed to allow one to decrease or enhance the coherence, which is quantified by the phase diffusion constant, by 2–3 orders of magnitude without destruction of the chaotic regime, which is by an order of magnitude more than one can achieve with a single delay time. Within the framework of the phase reduction, which is a rough approximation for the chaotic oscillators and rigorous for the stochastic ones, an analytical theory of the effect is constructed.

Journal of Applied Mechanics and Technical Physics, 2017

В работе рассматривается молекулярно-диффузионный транспорт в бесконечно разбавленных растворах п... more В работе рассматривается молекулярно-диффузионный транспорт в бесконечно разбавленных растворах при неизотермических условиях. Данное рассмотрение носит отчасти методический характер и мотивировано распространенностью искаженных интерпретаций уравнений термодинамического транспорта, записанных в терминах химического потенциала, при наличии градиента температуры. Уравнения транспорта содержат вклады, имеющие калибровочное происхождение, а именно, связанные с тем, что химический потенциал определен с точностью до слагаемого (AT+B) с произвольными константами A и B, где A-константа, с точностью до которой определена энтропия, а B-константа, с точностью до которой определена потенциальная энергия. Коэффициенты пропорциональности между термодинамическими силами и перекрестными термодинамическими потоками имеют вклады, связанные с необходимой инвариантностью по отношению к калибровочным преобразованиям-эти вклады не связаны с реальными физическими эффектами перекрестного транспорта. Представляемый анализ полагается на рассмотрение баланса энтропии и может подсказать многообещающие подходы для задачи об аналитическом вычислении константы термодиффузии из первых принципов. Кроме того, для разбавленных растворов обсуждается невозможность бародиффузии, понимаемой как диффузионный поток, создаваемый непосредственно градиентом давления. В литературе же «бародиффузией» часто называют дрейф под действием внешней потенциальной силы (например, в электростатическом или гравитационном поле), при котором в итоговых уравнениях сила, действующая на частицы, выражается через гидростатический градиент давления, который эта сила создает. Очевидно, интерпретация последнего как бародиффузии не вполне корректна и может спровоцировать ошибки при попытке учесть истинно бародиффузионные потоки.

28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES, 2020

We analyze two approaches to elimination of a fast variable (velocity) in stochastic systems: mom... more 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.

Journal of Physics: Conference Series, 2017

View the article online for updates and enhancements. Content from this work may be used under th... more View the article online for updates and enhancements. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Radiophysics and Quantum Electronics, 2019

UDC 537.862+517.925.42 We consider the dynamics of the Kuramoto ensemble oscillators not included... more UDC 537.862+517.925.42 We consider the dynamics of the Kuramoto ensemble oscillators not included in a common synchronized cluster, where the mean field is subject to fluctuations. The fluctuations can be either related to the finite size of the ensemble or superimposed on the mean field in the form of common noise due to the constructive features of the system. It is shown that the states of such oscillators with close natural frequencies appear correlated with each other, since the meanfield fluctuations act as common noise. We quantify the effect with the synchronization index of two oscillators, which is calculated numerically and analytically as a function of the frequency difference and noise intensity. The results are rigorous for large ensembles with additional noise superimposed on the mean field and are qualitatively true for the systems where the mean-field fluctuations are due to the finite size of the ensemble. In the latter case, the effect is found to be independent of the number of oscillators in the ensemble.

Fluctuation and Noise Letters, 2019

The Watanabe–Strogatz (WS) and Ott–Antonsen (OA) theories provided a seminal framework for rigoro... more The Watanabe–Strogatz (WS) and Ott–Antonsen (OA) theories provided a seminal framework for rigorous and comprehensive studies of collective phenomena in a broad class of paradigmatic models for ensembles of coupled oscillators. Recently, a “circular cumulant” approach was suggested for constructing the perturbation theory for the OA approach. In this paper, we derive the relations between the distribution of WS phases and the circular cumulants of the original phases. These relations are important for the interpretation of the circular cumulant approach in the context of the WS and OA theories. Special attention is paid to the case of hierarchy of circular cumulants, which is generally relevant for constructing perturbation theories for the WS and OA approaches.

The European Physical Journal E, 2017

In the dynamics of a viscous fluid, the case of vanishing kinematic viscosity is actually equival... more In the dynamics of a viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for the description of the flow of an inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of an inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of the flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.

Physica Scripta, 2018

The effect of spatial localization of states in distributed parameter systems under frozen parame... more The effect of spatial localization of states in distributed parameter systems under frozen parametric disorder is well known as the Anderson localization and thoroughly studied for the Schrödinger equation and linear dissipation-free wave equations. Some similar (or mimicking) phenomena can occur in dissipative systems such as the thermal convection ones. Specifically, many of these dissipative systems are governed by a modified Kuramoto-Sivashinsky equation, where the frozen spatial disorder of parameters has been reported to lead to excitation of localized patterns. Imposed advection in the modified Kuramoto-Sivashinsky equation can affect the localized patterns in a nontrivial way; it changes the localization properties and suppresses the pattern. The latter effect is considered in this paper by means of both numerical simulation and model reduction, which turns out to be useful for a comprehensive understanding of the bifurcation scenarios in the system. Two possible bifurcation scenarios of advective suppression ("washing-out") of localized patterns are revealed and characterised.

IOP Conference Series: Materials Science and Engineering, 2017

Our research is related to the employment of photoplethysmography (PPG) and laser Doppler flowmet... more Our research is related to the employment of photoplethysmography (PPG) and laser Doppler flowmetry (LDF) techniques (measuring the blood volume and flux, respectively) for the peripheral vascular system. We derive the governing equations of the wave dynamics for the case of extremely inhomogeneous parameters. We argue for the conjecture that the blood-vascular system as a wave-conducting medium should be nearly reflection-free. With the reflectionlessness condition, one can find the general solution to the governing equation and, on the basis of this solution, analyse the relationships between PPG-and LDF-signals.

Computational Continuum Mechanics, 2016

Physical Review E, 2015

We study non-isothermal diffusion transport of a weakly-soluble substance in a liquid-saturated p... more We study non-isothermal diffusion transport of a weakly-soluble substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. 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 non-dissolved phase coexist with the zones of undersaturated solution. The effect is firstly considered for the case of annual oscillation of the surface temperature of water-saturated ground being in contact with atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to the temperature oscillation. An analytical theory of the phenomenon is developed. Further, the treatment is extended to the case of higher frequency oscillations and case of weakly-soluble solids and liquids.

Journal of Physics: Conference Series, 2016

We construct a thermodynamic model for theoretical calculation of the boiling process of multicom... more We construct a thermodynamic model for theoretical calculation of the boiling process of multicomponent mixtures of hydrocarbons (e.g., crude oil). The model governs kinetics of the mixture composition in the course of the distillation process along with the boiling temperature increase. The model heavily relies on the theory of dilute solutions of gases in liquids. Importantly, our results are applicable for modelling the process under elevated pressure (while the empiric models for oil cracking are not scalable to the case of extreme pressure), such as in an oil field heated by lava intrusions.

Proceedings of 1st International Electronic Conference on Entropy and Its Applications, 2014

We discuss the molecular diffusion transport in dilute liquid solutions under non-isothermal cond... more We discuss the molecular diffusion transport in dilute liquid solutions under non-isothermal conditions. This discussion is actualized by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential. Our treatment is based on the consideration of the entropy production.

Physica A: Statistical Mechanics and its Applications, 2005

We study the stability of self-sustained oscillations under the influence of external noise. For ... more We study the stability of self-sustained oscillations under the influence of external noise. For small-noise amplitude a phase approximation for the Langevin dynamics is valid. A stationary distribution of the phase is used for an analytic calculation of the maximal Lyapunov exponent. We demonstrate that for small noise the exponent is negative, which corresponds to synchronization of oscillators.

EPL (Europhysics Letters), 2011

PACS 47.56.+r-Fluid flow through porous media PACS 92.40.Kf-Groundwater: aquifers PACS 91.50.Hc-M... more PACS 47.56.+r-Fluid flow through porous media PACS 92.40.Kf-Groundwater: aquifers PACS 91.50.Hc-Marine geology: gas and hydrate systems Abstract.-Porous sediments in geological systems are exposed to stress by the above-laying mass and consequent compaction, which may be significantly nonuniform across the massif. We derive scaling laws for the compaction of sediments of similar geological origin. With these laws, we evaluate the dependence of the transport properties of a fluid-saturated porous medium (permeability, effective molecular diffusivity, hydrodynamic dispersion, electrical and thermal conductivities) on its porosity. In particular, we demonstrate that the assumption of a uniform geothermal gradient is not adequate for systems with nonuniform compaction and show the importance of the derived scaling laws for mathematical modelling of methane hydrate deposits; these deposits are believed to have potential for impact on global climate change and Glacial-Interglacial cycles.

Journal of Physics: Conference Series, 2021

We analyse for approaches to elimination of a fast variable, which are applicable for systems lik... more We analyse for approaches to elimination of a fast variable, which are applicable for 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.

We present a detailed analysis of the dynamical regimes observed in a balanced network of identic... more We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence...

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact resu... more 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 fluctuations, thus obtaining an unified mean-field formulation encompassing quenched and dynamical disorder sources.