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 computerlike 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.

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.

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 on 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.

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 70Hz are in qualitative agreement with the predictions of our modeling.

Dynamics of a fully wetted Marangoni surfer at the fluid-fluid interface.

Marangoni flow created by the gradient of surface tension can be used to transport small objects along fluid interfaces. We study lateral motion of a fully wetted self-propelled body (swimmer) at a fluid-fluid interface. The swimmer releases a surfactant at a constant rate inducing a surface tension gradient. The dynamics of the insoluble surfactant is incorporated by taking into account advection by the Marangoni flow, surface diffusion and homogeneous decomposition reaction. We show that the translational speed of a Marangoni swimmer is increased as compared with the self-propulsion speed of a chemically inactive surface-bound swimmer. Flow induced in-plane rotation of the swimmer with an elongated body is generally weak so that its trajectory in the steady state is a straight line. A non-motile thin rod that releases surfactant at one of its ends is capable of surfing on the self-generated surfactant cloud. Steady surfing occurs along the body length with the source of the surfactant at the back end acting as a propulsion engine.

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. The particles predominantly swim normal to the free film surface with only a small 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 i) the upward pushing force of the swimmers onto the liquid-gas interface, ii) the solutal Marangoni force due to gradients in the swimmer concentration, and iii) the rotational diffusion of the swimmers together with the in-plane active motion. After reviewing and extending the analysis of the linear stability of the uniform state, we analyse the fully 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.

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 exert an excess pressure on the interface and also move along the interface while the swimming direction changes due to 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.

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 while the cluster centers remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move toward 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-sized clusters. As long as the particle hard-core diameter is nonzero, 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 crossover in the dominance of the two different coarsening modes, which depends on the strength of the attraction between particles, the cluster sizes, and the separation distance between clusters.

Ratcheting of driven attracting colloidal particles: temporal density oscillations and current multiplicity.

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a dc or an ac external potential. In addition, the walls of the channel interact with the particles via a ratchetlike periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of dc drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time-dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

Ratcheting of neutral elastic dimers on a charged filament.

We consider an elastic neutral dimer formed by two bound equal masses carrying opposite charges and moving along an electrically active filament in one dimension. An ac electrical field drives the two dimer heads, when set free or bound together to form a rigid rod, to opposite directions, thus yielding a zero net dimer current for zero and infinite elastic constants. Under the same driving conditions, an elastically deformable dimer can get rectified and the ensuing net current maximized for an optimal value of dimer elastic constant. The dependence of the dimer current on the periodic charge distribution along the filament is analyzed in terms of global symmetries of the dimer dynamics.

Delay-induced spatial correlations in one-dimensional stochastic networks with nearest-neighbor coupling.

We consider a network of deterministic and stochastic locally coupled oscillators with positive or negative dissipation and local time-delayed feedback. (i) For a deterministic system, we study propagation of waves through the network. We show that time delay leads to a coexistence of several neutral modes with different wave numbers and group velocities, which we compute analytically. (ii) For noisy system, we study the response of the network to external random forcing correlated in space and uncorrelated in time. Below the threshold of spatial instability, noise induces spatiotemporal fluctuations, which can be characterized by the structure function. We give an analytical expression for the structure function and demonstrate the effect of the time delay and of the correlation length of noise on the wave number of the most excited mode.

Excitable systems with noise and delay, with applications to control: renewal theory approach.

We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a control term taken after Pyragas [K. Pyragas, Phys. Lett. A 170, 421 (1992)] as a difference between the current system state and its state tau time units before. This approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term.

Correlation theory of delayed feedback in stochastic systems below Andronov-Hopf bifurcation.

Here we address the effect of large delay on the statistical characteristics of noise-induced oscillations in a nonlinear system below Andronov-Hopf bifurcation. In particular, we introduce a theory of these oscillations that does not involve the eigenmode expansion, and can therefore be used for arbitrary delay time. In particular, we show that the correlation matrix (CM) oscillates on two different time scales: on the scale of the main period of noise-induced oscillations, and on the scale close to the delay time. At large values of the delay time, the CM is shown to decay exponentially only for large values of its argument, while for the arguments comparable with the value of the delay, the CM remains finite disregarding the delay time. The definition of the correlation time of the system with delay is discussed.

Morphology changes in the evolution of liquid two-layer films.

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.

Alternative pathways of dewetting for a thin liquid two-layer film.

We consider two stacked ultrathin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Depending on the long-range van der Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate. We predict that the faster layer drives the evolution and may accelerate the rupture of the slower layer by orders of magnitude, thereby promoting the rupture of rather thick films.