The present work considers systems whose dynamics are governed by the nonlinear interactions among groups of 6 nonlinear waves, such as those described by the unforced quintic nonlinear Schrödinger equation. Specific parameter regimes in which ensemble-averaged dynamics of such systems with finite size are accurately described by a wave kinetic equation, as used in wave turbulence theory, are theoretically predicted. In addition, the underlying reasons that the wave kinetic equation may be a poor predictor of wave dynamics outside these regimes are also discussed. These theoretical predictions are directly verified by comparing ensemble averages of solutions to the dynamical equation with corresponding solutions of the wave kinetic equation.

Coupled oscillators are one of the basic models in nonlinear dynamics. Here, we study numerically and analytically the spectra of two harmonic oscillators with stochastically fluctuating coupling and driving forces reproducing a thermostat. We show that, even at small coupling, vanishing on average, the oscillation spectra exhibit mixing, even though no cross-correlations exists between the oscillators. Our results reveal a new mechanism of mode mixing for stochastically uncorrelated systems that is crucial for analysis of spectra in various systems, from simple liquids to living systems.

The transition to turbulence in wall-bounded shear flows is typically subcritical, with a poorly understood interplay between spatial fluctuations, pattern formation, and stochasticity near the critical Reynolds number. Here, we present a spatially extended stochastic minimal model for the energy budget in transitional pipe flow, which successfully recapitulates the way localized patches of turbulence (puffs) decay, split, and grow, respectively, as the Reynolds number increases through the laminar-turbulent transition. Our approach takes into account the flow geometry, as we demonstrate by extending the model to quasi-one-dimensional Taylor-Couette flow, reproducing the observed directed percolation pattern of turbulent patches in space and time.

Heat transport in turbulent thermal convection increases with thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport became independent of the molecular diffusivities—the heat transport scaling exponent is smaller than the mixing-length (or “ultimate”) value of $1/2$. This is due to thermal boundary layers that throttle heat transport in configurations driven either by thermal boundary conditions or by internal heating, giving a scaling exponent close to the boundary-limited (or “classical”) value of $1/3$. With net-zero internal heating and cooling in different regions, the larger mixing-length exponent can be attained because heat need not cross a boundary. We report numerical simulations in which heating and cooling are unequal. As heating and cooling rates are made closer, the scaling exponent of heat transport varies from its boundary-limited value to its mixing-length value.

Single-mode operation is a desirable but elusive property for lasers operating at high pump powers. Typically, single-mode lasing is attainable close to threshold, but increasing the pump power gives rise to multiple lasing peaks due to inter-modal gain competition. We propose a laser with the opposite behavior: multimode lasing occurs at low output powers, but pumping beyond a certain value produces a single lasing mode, with all other candidate modes experiencing negative effective gain. This phenomenon arises in a lattice of coupled optical resonators with non-fine-tuned asymmetric couplings, and is caused by an interaction between nonlinear gain saturation and the non-Hermitian skin effect. The single-mode lasing is observed in both frequency domain and time domain simulations. It is robust against on-site disorder, and scales up to large lattice sizes. This finding might be useful for implementing high-power laser arrays.

We proposed a photonic approach to a lasing mode supported by low-loss oscillation of polarized bound electrons in an active nano-slit-waveguide cavity, which circumvents the confinement-loss trade-off of nanoplasmonics, and offers an optical confinement down to sub-1-nm level with a peak-to-background ratio of $\sim 30\mathrm{dB}$. Experimentally, the extremely confined lasing field is realized as the dominant peak of a ${\mathrm{TE}}_0$-like lasing mode around 720-nm wavelength, in 1-nm-level width slit-waveguide cavities in coupled CdSe nanowire pairs. The measured lasing characteristics agree well with the theoretical calculations. Our results may pave a way towards new regions for nanolasers and light-matter interaction.

Exceptional points (EPs)—spectral singularities of non-Hermitian linear systems—have recently attracted interest for sensing. While initial proposals and experiments focused on enhanced sensitivities neglecting noise, subsequent studies revealed issues with EP sensors in noisy environments. Here we propose a single-mode Kerr-nonlinear resonator for exceptional sensing in noisy environments. Based on the resonator’s dynamic hysteresis, we define a signal that displays a square-root singularity reminiscent of an EP. However, our sensor has crucial fundamental and practical advantages over EP sensors: the signal-to-noise ratio increases with the measurement speed, the square-root singularity is easily detected through intensity measurements, and both sensing precision and information content of the signal are enhanced around the singularity. Our sensor also overcomes the fundamental trade-off between precision and averaging time characterizing all linear sensors. All these unconventional features open up new opportunities for fast and precise sensing using hysteretic resonators.

The effect of freezing on contact line motion is a scientific challenge in the understanding of the solidification of capillary flows. In this Letter, we experimentally investigate the spreading and freezing of a water droplet on a cold substrate. We demonstrate that solidification stops the spreading because the ice crystals catch up with the advancing contact line. Indeed, we observe the formation and growth of ice crystals along the substrate during the drop spreading, and show that their velocity equals the contact line velocity when the drop stops. Modeling the growth of the crystals, we predict the shape of the crystal front and show that the substrate thermal properties play a major role on the frozen drop radius.

The novel physics of twisted bilayer graphene has motivated extensive studies of magic-angle flat bands hosted by moiré structures in electronic, photonic, and acoustic systems. On the other hand, bound states in the continuum (BICs) have also attracted great attention in recent years because of their potential applications in the field of designing superior optical devices. Here, we combine these two independent concepts to construct a new optical state in a twisted bilayer photonic crystal slab, which is called as moiré quasi-BIC, and numerically demonstrate that such an exotic optical state possesses dual characteristics of moiré flat bands and quasi-BICs. To illustrate the mechanism for the formation of moiré flat bands, we develop an effective model at the center of the Brillouin zone and show that moiré flat bands could be fulfilled by balancing the interlayer coupling strength and the twist angle around the band edge above the light line. Moreover, by decreasing the twist angle of moiré photonic crystal slabs with flat bands, it is shown that the moiré flat-band mode at the Brillouin center gradually approaches a perfect BIC, where the total radiation loss from all diffraction channels is significantly suppressed. To clarify the advantage of moiré quasi-BICs, enhanced second-harmonic generation (SHG) is numerically proven with a wide-angle optical source. The efficiency of SHG assisted by designed moiré quasi-BICs can be greatly improved compared with that based on dispersive quasi-BICs with similar quality factors.

We report on the thermalization of light carrying orbital angular momentum in multimode optical fibers, induced by nonlinear intermodal interactions. A generalized Rayleigh-Jeans distribution of asymptotic mode composition is obtained, based on the conservation of the angular momentum. We confirm our predictions by numerical simulations and experiments based on holographic mode decomposition of multimode beams. Our work establishes new constraints for the achievement of spatial beam self-cleaning, giving previously unforeseen insights into the underlying physical mechanisms.

Wave frequency is a critical parameter for applications ranging from structural health monitoring, noise control, and medical imaging to quantum of energy in matter. Frequency conversion is an inevitable wave phenomenon in nonlinear or time-modulated media. However, frequency conversion in linear media holds the promise of breaking limits imposed by the physics laws of wave diffraction such as Snell’s law and Rayleigh criterion. In this Letter, we physically introduce a linear active metalayer in a structural beam that can convert the wave frequency of an flexural incidence into arbitrary frequencies of transmitted waves, which is underpinned by time modulation of sensing signals and insensitive to incident amplitude. The active element, involving piezoelectric components and time-modulated transfer function, breaks energy conservation such that the generated harmonics can be fully decoupled, making the frequency conversion linear and independent. By leveraging the time-modulated unit, phase-gradient and frequency-gradient metalayers are proposed for frequency-converted wave steering and dynamic beam steering, respectively. The linear active metalayer proposed herein suggests a promising solution to fully control time-domain signals of flexural waves, in stark contrast with existing elastic metasurfaces, regardless of being passive or active.

The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range. The acceleration variance at higher Reynolds numbers departs from previous predictions based on multifractal models, which characterize Lagrangian intermittency as an extension of Eulerian intermittency. The disagreement is even more prominent for higher-order moments of the acceleration. Instead, starting from a known exact relation, we relate the scaling of acceleration variance to that of Eulerian fourth-order velocity gradient and velocity increment statistics. This prediction is in excellent agreement with the variance data. Our Letter highlights the need for models that consider Lagrangian intermittency independent of the Eulerian counterpart.

We study the dynamics of flow networks in porous media using two and three dimensional pore-network models. We consider a class of erosion dynamics for a single phase flow with no deposition, chemical reactions, or topology changes assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.

We report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for the turbulent energy spectrum, $E(k)=C_1\sqrt{ϵa{c}_s}/k$, of acoustic waves in 2D with almost linear dispersion law, ${\omega }_k=c_{s}k[1+(ak{)}^2]$, $ak\ll 1$. Here, $ϵ$ is the energy flux over scales, and $C_1$ is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates. The corresponding 3D counterpart of turbulent acoustic spectrum was found over half a century ago, however, due to the singularity in 2D, no solution has been obtained until now. We show the spectrum $E(k)$ is realizable in direct numerical simulations of forced-dissipated Gross-Pitaevskii equation in the presence of strong condensate.

Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the $\mathcal{P}\mathcal{T}$ phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the $\mathcal{P}\mathcal{T}$ symmetries belonging to different edges. Moreover, we discover the $\mathcal{P}\mathcal{T}$ phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and $\mathcal{P}\mathcal{T}$ phase transition in higher-dimensional systems.

Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without bulk closure and exhibits as an obstruction of higher-dimensional boundary states. Here, we report the first experimental realization of three-dimensional surface-obstructed topological insulators with using acoustic crystals. Our acoustic measurements demonstrate unambiguously the emergence of one-dimensional topological hinge states in the middle of the bulk and surface band gaps, as a direct manifestation of the higher-order band topology. Together with comparative measurements for the trivial and phase-transition-point insulators, our experimental data conclusively evidence the unique bulk-boundary physics for the surface-obstructed band topology. That is, the topological phase transition is determined by the closure of the surface gap, rather than by closing the bulk gap. Our study might spur on new activities to deepen the understanding of such elusive topological phases.