Sand dunes, which arise spontaneously due to the dynamical interplay between a sedimentary interface and a fluid flow, are one of the most famous examples of emergence in a geological system. The large scale organization of a dune field is believed to be controlled by pairwise (either remote or direct) dune-dune interactions. Recent studies have shown that remote long-range feedback is closely related to the turbulent wake structure forming downstream of a dune. Here, we study the stability of an idealized two-dune system arising as a consequence of such remote, wake-induced interactions. The system is realized in a subaqueous quasi-2D laboratory experiment and the results are compared with a qualitative dynamical systems model. Despite its simplicity, the system exhibits rich dynamical behavior. In particular, we show that, depending on the parameter regime, the dune-dune feedback can either stabilize or destabilize the symmetric dune configuration, and we demonstrate the existence of an asymmetric attracting state coupling dunes of different sizes.

Microscale Janus emulsions represent a versatile material platform for dynamic refractive, reflective, and light-emitting optical components. Here, we present a mechanism for droplet actuation that exploits thermocapillarity. Using optically induced thermal gradients, an interfacial tension differential is generated across the surfactant-free internal capillary interface of Janus droplets. The interfacial tension differential causes droplet-internal Marangoni flows and a net torque, resulting in a predictable and controllable reorientation of the droplets. The effect can be quantitatively described with a simple model that balances gravitational and thermal torques. Occurring in small thermal gradients, these optothermally induced Marangoni dynamics represent a promising mechanism for controlling droplet-based micro-optical components.

We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatiotemporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous, and sloshing modes. Standing azimuthal waves are also studied leading to polygonlike patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.

We demonstrate the self-propulsion of a volatile drop on the surface of a bath of an immiscible liquid. Evaporative heat pumping is converted into directed motion through thermocapillary stresses, which arise from the coupling between surface-tension-driven flows and temperature advection. A propulsive force arises from convection-sustained temperature gradients along the drop interface, resulting in a warmer pool of liquid being advected by the hydrodynamic flow in the underlying bath toward the back of the drop. The dependence of the drop speed on the activity source, i.e., the evaporation flux, is derived with scaling arguments and captures the experimental data.

We observe chaotic optical wave dynamics characterized by erratic energy transfer and soliton annihilation and creation in the aftermath of a three-soliton collision in a photorefractive crystal. Irregular dynamics are found to be mediated by the nonlinear Raman effect, a coherent interaction that leads to nonreciprocal soliton energy exchange. Results extend the analogy between solitons and particles to the emergence of chaos in three-body physics and provide new insight into the origin of the irregular dynamics that accompany extreme and rogue waves.

Given a dynamical system with $m$ independent conserved quantities, we construct a multiparameter family of new systems in which these quantities evolve monotonically and proportionally, and are replaced by $m-1$ conserved linear combinations of themselves, with any of the original quantities as limiting cases. The modification of the dynamics employs an exterior product of gradients of the original quantities, and often evolves the system toward asymptotic linear dependence of these gradients in a nontrivial state. The process both generalizes and provides additional structure to existing techniques for selective dissipation in the literature on fluids and plasmas, nonequilibrium thermodynamics, and nonlinear controls. It may be iterated or adapted to obtain any reduction in the degree of integrability. It may enable discovery of extremal states, limit cycles, or solitons, and the construction of new integrable systems from superintegrable systems. We briefly illustrate the approach by its application to the cyclic three-body Toda lattice, driven from an aperiodic orbit toward a limit cycle.

Viscoelastic plane Poiseuille flow is shown to become linearly unstable in the absence of inertia, in the limit of high elasticities, for ultradilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues up to a Reynolds number (Re) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultradilute polymer solutions, a single linearly unstable modal branch may underlie transition to elastic turbulence at zero Re and to elasto-inertial turbulence at moderate Re, implying the existence of continuous pathways connecting the turbulent states to each other and to the laminar base state.

Optical frequency combs (OFCs) are essential in precision metrology, spectroscopy, distance measurement, and optical communications. Significant advances have been made recently in achieving micro-OFC devices based on parametric frequency conversion or electro-optic phase modulation. Here, we demonstrate a new kind of microcomb using a cavity optomechanical system with giant oscillation amplitude. We observe both optical and microwave frequency combs in a microtoroid resonator, which feature a flat OFC with 938 comb lines and a repetition rate as low as 50.22 MHz, as well as a flat microwave frequency comb with 867 comb lines. To generate such giant oscillation amplitude, we excite an overcoupled optical mode with a large blue detuning that is assisted with the thermo-optic nonlinearity. A new type of nonlinear oscillation, induced by competition between the optomechanical oscillation and thermo-optic nonlinearity, is also observed.

Transition between stream and droplet regimes in a coflow is typically achieved by adjusting the capillary numbers (Ca) of the phases. Remarkably, we experimentally evidence a reversible transition between the two regimes by controlling exposure of the system to acoustic standing waves, with Ca fixed. By satisfying the ratio of acoustic radiation force to the interfacial tension force, ${\mathrm{Ca}}_{\mathrm{ac}}>1$, experiments reveal a reversible stream drop transition for $\mathrm{Ca}<1$, and stream relocation for $\mathrm{Ca}\ge 1$. We explain the phenomenon in terms of the pinching, advection, and relocation timescales and a transition between convective and absolute instability from a linear stability analysis [P. Guillot et al., Phys. Rev. Lett. 99, 104502 (2007)].

Electromagnetic void space is a medium, while geometrically occupying a finite volume of space, optically equivalent to an infinitesimal point, in which electromagnetic waves do not experience any phase accumulation. Here, we report the first realization of three-dimensional (3D) electromagnetic void space by an all-dielectric photonic crystal possessing vanishing permittivity and permeability simultaneously. The 3D electromagnetic void space offers distinctive functionalities inaccessible to its 2D or acoustic counterparts because of the fundamental changes in topology, which comes from the ascension of dimensionality as well as the transverse nature of electromagnetic waves. In particular, we demonstrate, both theoretically and experimentally, that the transmission through such a 3D void space is unaffected by its inner boundaries, but highly sensitive to the outer boundaries. This enables many applications such as the impurity “antidoping” effect, outer-boundary-controlled switching, and 3D perfect wave steering. Our work paves a road toward 3D exotic optics of an optically infinitesimal point.

When employing nonlinear methods to characterize complex systems, it is important to determine to what extent they are capturing genuine nonlinear phenomena that could not be assessed by simpler spectral methods. Specifically, we are concerned with the problem of quantifying spectral and phasic effects on an observed difference in a nonlinear feature between two systems (or two states of the same system). Here we derive, from a sequence of null models, a decomposition of the difference in an observable into spectral, phasic, and spectrum-phase interaction components. Our approach makes no assumptions about the structure of the data and adds nuance to a wide range of time series analyses.

Volatile drops deposited on a hot solid can levitate on a cushion of their own vapor, without contacting the surface. We propose to understand the onset of this so-called Leidenfrost effect through an analogy to nonequilibrium systems exhibiting a directed percolation phase transition. When performing impacts on superheated solids, we observe a regime of spatiotemporal intermittency in which localized wet patches coexist with dry regions on the substrate. We report a critical surface temperature, which marks the upper bound of a large range of temperatures in which levitation and contact coexist. In this range, with decreasing temperature, the equilibrium wet fraction increases continuously from zero to one. Also, the statistical properties of the spatiotemporally intermittent regime are in agreement with that of the directed percolation universality class. This analogy allows us to redefine the Leidenfrost temperature and shed light on the physical mechanisms governing the transition to the Leidenfrost state.

We investigate thin film drainage between a viscous oil drop and a mica surface, clearly illustrating the competing effects of Laplace pressure and viscous normal stress (${\tau }_v$) in the drop. ${\tau }_v$ dominates the initial stage of drainage, leading to dimple formation ($h_d$) at a smaller critical thickness with an increase in the drop viscosity (the dimple is the inversion of curvature of the drop in the film region). Surface forces and interfacial tension control the last stage of film drainage. A scaling analysis shows that $h_d$ is a function of the drop size $R$ and the capillary numbers of the film (${\mathrm{Ca}}_f$) and drop (${\mathrm{Ca}}_d$), which we estimate by $h_d=0.5R\sqrt{{\mathrm{Ca}}_f/(1+2{\mathrm{Ca}}_d)}$. This equation clearly indicates that the drop viscosity needs to be considered when ${\mathrm{Ca}}_d>0.1$. These results have implications for industrial systems where very viscous liquids are involved, for example, in 3D printing and heavy oil extraction process.

Modulation instability (MI) in the presence of noise typically leads to an irreversible and complete disintegration of a plane wave background. Here we report on experiments performed in a coherently driven nonlinear optical resonator that demonstrate nonlinear localization of dissipative MI: formation of persisting domains of MI-driven spatiotemporal chaos surrounded by a stable quasi-plane-wave background. The persisting localization ensues from a combination of bistability and complex spatiotemporal nonlinear dynamics that together permit a locally induced domain of MI to be pinned by a shallow modulation on the plane wave background. We further show that the localized domains of spatiotemporal chaos can be individually addressed—turned on and off at will—and we explore their transport behavior as the strength of the pinning is controlled. Our results reveal new fundamental dynamics at the interface of front dynamics and MI, and offer a route for tailored patterns of noiselike bursts of light.

Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we show that in thermalized flows $\lambda \propto \sqrt{T}$, in agreement with results from frustrated spin systems. This suggests an underlying universality and provides evidence for recent conjectures on the thermal scaling of $\lambda$. We also reconcile seemingly disparate effects—equilibration on one hand and pushing systems out of equilibrium on the other—of many-body chaos by relating $\lambda$ to $T$ through the dynamical structures of the flow.

Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time ($1+1$) nonlinear Schrödinger equation is often used to model rogue waves; it is an envelope description of plane waves and admits the so-called Pergerine and Kuznetov-Ma soliton solutions. However, in deep water waves and certain electromagnetic systems where there are two significant transverse dimensions, the $2+1$ hyperbolic nonlinear Schrödinger equation is the appropriate wave envelope description. Here we show that these rogue wave solutions suffer from strong transverse instability at long and short frequencies. Moreover, the stability of the Peregrine soliton is found to coincide with that of the background plane wave. These results indicate that, when applicable, transverse dimensions must be taken into account when investigating rogue wave pheneomena.

Optical nonlinearities are known to coherently couple amplitude and phase of light, which can result in the formation of periodic waveforms. Such waveforms are referred to as optical frequency combs. Here we show that Bloch gain—a nonclassical phenomenon that was first predicted in the 1930s—can play an essential role in comb formation. We develop a self-consistent theoretical model that considers all aspects of comb dynamics: band structure, electron transport, and cavity dynamics. In quantum cascade lasers, Bloch gain gives rise to a giant Kerr nonlinearity, which enables frequency modulated combs and serves as the physical origin of the linewidth enhancement factor. Bloch gain also triggers the formation of solitonlike structures in ring resonators, paving the way toward electrically driven Kerr combs.