arXiv subjects

Andrey Pototsky

Publications and source records attributed to Andrey Pototsky.

At least 19 recordsLinked to original sources

arXiv2025

The effect of self-induced Marangoni flow on polar-nematic waves in active-matter systems

We study the formation of propagating large-scale density waves of mixed polar-nematic symmetry in a colony of self-propelled agents that are bound to move along the planar surface of a thin viscous film. The agents act as an insoluble surfactant, i.e. the surface tension of the liquid depends on their density. Therefore, density gradients generate a Marangoni flow. We demonstrate that for active matter in the form of self-propelled surfactants with local (nematic) aligning interactions such a Marangoni flow nontrivially influences the propagation of the density waves. Upon gradually increasing the Marangoni parameter, which characterises the relative strength of the Marangoni flow as compared to the self-propulsion speed, the density waves broaden while their speed may either increase or decrease depending on wavelength and overall mean density. A further increase of the Marangoni parameter eventually results in the disappearance of the density waves. This may occur either discontinuously at finite wave amplitude via a saddle-node bifurcation or continuously with vanishing wave amplitude at a wave bifurcation, i.e. a finite-wavelength Hopf bifurcation.

physics.flu-dyn↗

arXiv2023

Electromagnetically driven flow in unsupported electrolyte layers: lubrication theory and linear stability of annular flow

We consider a thin horizontal layer of a non-magnetic electrolyte containing a bulk solution of salt and carrying an electric current. The layer is bounded by two deformable free surfaces loaded with an insoluble surfactant and is placed in a vertical magnetic field. The arising Lorentz force drives the electrolyte in the plane of the layer. We employ the long-wave approximation to derive general two-dimensional hydrodynamic equations describing symmetric pinching-type deformations of the free surfaces. These equations are used to study the azimuthal flow in an annular film spanning the gap between two coaxial cylindrical electrodes. In weakly deformed films, the base azimuthal flow and its linear stability with respect to azimuthally invariant perturbations are studied analytically. For relatively thick layers and weak magnetic fields, the leading mode with the smallest decay rate is found to correspond to a monotonic azimuthal velocity perturbation. The Marangoni effect leads to further stabilisation of the flow while perturbations of the solute concentration in the bulk of the fluid have no influence on the flow stability. In strongly deformed films in the diffusion-dominated regime, the azimuthal flow becomes linearly unstable with respect to an oscillatory mixed mode characterised by the combination of radial and azimuthal velocity perturbations when the voltage applied between electrodes exceeds the critical value.

physics.flu-dyn↗

arXiv2023

Reservoir computing based on solitary-like waves dynamics of film flows: a proof of concept

Several theoretical works have shown that solitons -- waves that self-maintain constant shape and velocity as they propagate -- can be used as a physical computational reservoir, a concept where machine learning algorithms designed for digital computers are replaced by analog physical systems that exhibit nonlinear dynamical behaviour. Here we propose and experimentally validate a novel reservoir computing (RC) system that for the first time employs solitary-like (SL) waves propagating on the surface of a liquid film flowing over an inclined surface. We demonstrate the ability of the SL wave RC system (SLRC) to forecast chaotic time series and to successfully pass essential benchmark tests, including a memory capacity test and a Mackey-Glass model test.

physics.flu-dyn↗

arXiv2023

Nonlinear periodic and solitary rolling waves in falling two-layer viscous liquid films

We investigate nonlinear periodic and solitary two-dimensional rolling waves in a falling two-layer liquid film in the regime of non-zero Reynolds numbers. At any flow rate, a falling two-layer liquid film is known to be linearly unstable with respect to long-wave deformations of the liquid-air surface and liquid-liquid interface. Two different types of zero-amplitude neutrally stable waves propagate downstream without growing or shrinking: a zig-zag surface mode and a thinning varicose interface mode. Using a boundary-layer reduction of the Navier-Stokes equation, we investigate the onset, possible bifurcations and interactions of nonlinear periodic travelling waves. Periodic waves are obtained by continuation as stationary periodic solutions in the co-moving reference frame starting from small-amplitude neutrally stable waves. We find a variety of solitary waves that appear when a periodic solution approaches a homoclinic loop. Wave interactions are studied using direct numerical simulations of the boundary-layer model. We reveal that in the early stages of temporal evolution coarsening is dominated by an inelastic collision and merging of waves that travel at different speeds. Eventually, coarsening becomes arrested when the waves have reached the largest admissible amplitude. Bifurcation analysis confirms the existence of an upper bound of possible solitary wave amplitudes, thus explaining the arrest of coarsening. In the mixed regime, when both mode types are unstable, the temporal dynamics becomes highly irregular due to the competition between a faster-travelling zig-zag mode and a slower-travelling varicose mode. A quintessentially two-layer dynamical regime is found, which corresponds to a ruptured second layer. In this r

physics.flu-dyn↗

arXiv2023

Experimental and Theoretical Study of Solitary-like Wave Dynamics of Liquid Film Flows over a Vibrated Inclined Plane

Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in the physical system of other nature. Here we investigate, experimentally and theoretically, the dynamics of solitary-like surface waves in a liquid layer on an inclined plane that is subjected to a harmonic low-frequency vibration in the range from 30 to 50 Hz. We demonstrate that the vibration results in a decrease in the average and peak amplitude of the long solitary-like surface waves. However, the speed of these waves remains largely unaffected by the vibration, implying that they may propagate over large distances almost without changing their amplitude, thus rendering them suitable for a number of practical applications, where the immunity of pulses that carry information to external vibrations is required.

physics.flu-dyn↗

arXiv2022

Planar Rotational Equilibria of Two Non-identical Microswimmers

We study a planar motion of two hydrodynamically coupled non-identical micro-swimmers, each modelled as a force dipole with intrinsic self-propulsion. Using the method of images, we demonstrate that our results remain equally applicable at a stress-free liquid-gas interface as in the bulk of a fluid. A closed analytical form of circular periodic orbits for a pair of two pullers and a pair of two pushers is presented and their linear stability is determined with respect to two- and three-dimensional perturbations. A universal stability diagram of the orbits with respect to two-dimensional perturbations is constructed and it is shown that two non-identical pushers or two non-identical pullers moving at a stress-free interface may form a stable rotational equilibrium. For two non-identical pullers, we find stable quasi-periodic localized states, associated with the motion on a two-dimensional torus in the phase space. Stable tori are born from circular periodic orbits as the result of a torus bifurcation. All stable equilibria in two dimensions are shown to be monotonically unstable with respect to three-dimensional perturbations.

nlin.CD↗

arXiv2022

Acoustic, phononic, Brillouin light scattering and Faraday wave based frequency combs: physical foundations and applications

Frequency combs (FCs) -- spectra containing equidistant coherent peaks -- have enabled researchers and engineers to measure the frequencies of complex signals with high precision thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs) including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions, where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.

physics.optics↗

arXiv2022

Neural Echo State Network using oscillations of gas bubbles in water

In the framework of physical reservoir computing (RC), machine learning algorithms designed for digital computers are executed using analog computer-like nonlinear physical systems that can provide energy-efficient computational power for predicting time-dependent quantities that can be found using nonlinear differential equations. We suggest a bubble-based RC (BRC) system that combines the nonlinearity of an acoustic response of a cluster of oscillating gas bubbles in water with a standard Echo State Network (ESN) algorithm that is well-suited to forecast chaotic time series. We confirm the plausibility of the BRC system by numerically demonstrating its ability to forecast certain chaotic time series similarly to or even more accurately than ESN.

physics.flu-dyn↗

arXiv2021

Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid

A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show theoretically and experimentally that such a floating liquid drop with a sufficiently small volume has two distinct stable equilibrium shapes: one with a larger and one with a smaller radius of the triple-phase contact line. Next, we experimentally study the floatability of a less viscous water drop on the surface of a more viscous and less dense oil, subjected to a low frequency (Hz-order) vertical vibration. We find that in a certain range of amplitudes, vibration helps heavy liquid drops to stay afloat. The physical mechanism of the increased floatability is explained by the horizontal elongation of the drop driven by subharmonic Faraday waves. The average length of the triple-phase contact line increases as the drop elongates that leads to a larger average lifting force produced by the surface tension.

physics.flu-dyn↗

arXiv2020

Intermittent dynamic bursting in vertically vibrated liquid drops

A previously unreported regime of type III intermittency is observed in a vertically vibrated milliliter-sized liquid drop submerged in a more viscous and less dense immiscible fluid layer supported by a hydrophobic solid plate. As the vibration amplitude is gradually increased, subharmonic Faraday waves are excited at the upper surface of the drop. We find a narrow window of vibration amplitudes slightly above the Faraday threshold, where the drop exhibits an irregular sequence of large amplitude bursting events alternating with intervals of low amplitude activity. The triggering physical mechanism is linked to the competition between surface Faraday waves and the shape deformation mode of the drop.

physics.flu-dyn↗

arXiv2019

Excitation of Faraday-like body waves in vibrated living earthworms

Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally of a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm's body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.

cond-mat.soft↗

arXiv2019

Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70 Hz are in qualitative agreement with the predictions of our modelling.

physics.flu-dyn↗

arXiv2017

Shaping liquid drops by vibration

We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration amplitude, spontaneously elongating in horizontal direction. Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger drops evolve by transforming into a snake-like structure with gradually increasing length. The worm state is long-lasting with a potential to fragmentat into smaller drops.

nlin.PS↗

arXiv2016

Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer

We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. Although the particles predominantly swim normal to the free film surface, their motion also has a component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by three physical effects: the upward pushing force of the swimmers onto the liquid-gas interface that always destabilizes the flat film, the solutal Marangoni force due to gradients in the swimmer concentration that always acts stabilising, and finally the rotational diffusion of the swimmers together with the in-plance active motion that acts either stabilising or destabilising. After reviewing and extending the analysis of the linear stability of the flat film with uniform swimmer density, we analyse the full nonlinear dynamic equations and show that point-like swimmers, which only interact via long-wave deformations of the liquid film, self-organise in highly regular (standing, travelling and modulated waves) and various irregular patterns for swimmer density and film height.

cond-mat.soft↗

arXiv2014

Stability of liquid films covered by a carpet of self-propelled surfactant particles

We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles excert an excess pressure on the interface and also move along the interface while the swimming direction performs rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity several characteristic instability modes can occur. In particular, rotational diffusion can either stabilize the film or induce instabilities of different character.

cond-mat.soft↗

arXiv2014

Coarsening modes of clusters of aggregating particles

There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process in which particles diffuse from one cluster to the other whilst the cluster centres remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move towards each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use Dynamical Density Functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal size clusters. As long as the particle hard-core diameter is non-zero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a cross-over in the dominance of the two different coarsening modes, that depends on the strength of the attraction between particles, the cluster sizes and the separation distance between clusters.

cond-mat.soft↗

arXiv2013

Rectification of self-propelled particles by symmetric barriers

The motion of self-propelled particles can be rectified by asymmetric or ratchet-like periodic patterns in space. Here we show that a non-zero average drift can already be induced in a periodic potential with symmetric barriers when the self-propulsion velocity is also symmetric and periodically modulated but phase-shifted against the potential. In the adiabatic limit of slow rotational diffusion we determine the mean drift analytically and discuss the influence of temperature. In the presence of asymmetric barriers modulating the self-propulsion can largely enhance the mean drift or even reverse it.

cond-mat.stat-mech↗

arXiv2012

Feedback-induced oscillations in one-dimensional colloidal transport

We investigate a driven, one-dimensional system of colloidal particles in a periodically currogated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on Dynamical Density Functional Theory (DDFT).

cond-mat.soft↗