When a liquid film drains on a vertical plate, the film becomes nonuniform near the vertical edge. Here we experimentally report the three-dimensional (3D) self-similar shape of this film. Based on the well-known 2D self-similar solution of a draining film far from the edge, we identify a new 3D self-similar scaling, which converts the partial differential equation for the film thickness with three independent variables into an ordinary differential equation. Interferometry is performed to measure the film thickness as a function of position and time, and the results are in excellent agreement with the theoretical predictions.

In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating that turbulent flows in both experiment and numerics transiently display time-periodic dynamics when they shadow unstable periodic orbits (UPOs). We show that UPOs we computed are also statistically significant, with turbulent flows spending a sizable fraction of the total time near these solutions. As a result, the average rates of energy input and dissipation for the turbulent flow and frequently visited UPOs differ only by a few percent.

We reveal the universal effect of gauge fields on the existence, evolution, and stability of solitons in the spinor multidimensional nonlinear Schrödinger equation. Focusing on the two-dimensional case, we show that when gauge field can be split in a pure gauge and a nonpure gauge generating effective potential, the roles of these components in soliton dynamics are different: the localization characteristics of emerging states are determined by the curvature, while pure gauge affects the stability of the modes. Respectively the solutions can be exactly represented as the envelopes which may depend on the pure gauge implicitly through the effective potential, and modulating stationary carrier-mode states, which are independent of the curvature. Our central finding is that nonzero curvature can lead to the existence of unusual modes, in particular, enabling stable localized self-trapped fundamental and vortex-carrying states in media with constant repulsive interactions without additional external confining potentials and even in the expulsive external traps.

We demonstrate by breaking the $C_6$ symmetry for higher-order at-$\mathrm{\Gamma }$ bound states in the continuum (BICs) with topological charge $-2$ in photonic crystals (i) deterministic generation of off-$\mathrm{\Gamma }$ BICs from the at-$\mathrm{\Gamma }$ BIC and (ii) a variety of pair-creation and annihilation processes of circularly polarized states with opposite topological charges and the same handedness. To explain these phenomena, we introduce the handedness-wise topological charge quantized to a half-integer. The handedness-wise charge gives a unified picture of various phenomena involving BICs and circularly polarized states.

The large-scale circulation (LSC) of fluid is one of the main concepts in turbulent thermal convection as it is known to be important in global heat and mass transport in the system. In turbulent Rayleigh-Bénard convection (RBC) in slender containers, the LSC is formed of several dynamically changing convective rolls that are stacked on top of each other. The present study reveals the following two important facts: (i) the mechanism which causes the twisting and breaking of a single-roll LSC into multiple rolls is the elliptical instability and (ii) the heat and momentum transport in RBC, represented by the Nusselt (Nu) and Reynolds (Re) numbers, is always stronger (weaker) for smaller (larger) number $n$ of the rolls in the LSC structure. Direct numerical simulations support the findings for $n=1,\dots ,4$ and the diameter-to-height aspect ratio of the cylindrical container $\mathrm{\Gamma }=1/5$, the Prandtl number $\mathrm{Pr}=0.1$ and Rayleigh number $\mathrm{Ra}=5\times {10}^5$. Thus, Nu and Re are, respectively, 2.5 and 1.5 times larger for a single-roll LSC ($n=1$) than for a LSC with $n=4$ rolls.

Non-Euclidean geometry, discovered by negating Euclid’s parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general theory of relativity. Notably, an infinite number of regular tessellations in hyperbolic geometry—hyperbolic lattices—are expected to extend Euclidean Bravais lattices and the consequent wave phenomena to non-Euclidean geometry. However, topological states of matter in hyperbolic lattices have yet to be reported. Here we investigate topological phenomena in hyperbolic geometry, exploring how the quantized curvature and edge dominance of the geometry affect topological phases. We report a recipe for the construction of a Euclidean photonic platform that inherits the topological band properties of a hyperbolic lattice under a uniform, pseudospin-dependent magnetic field, realizing a non-Euclidean analog of the quantum spin Hall effect. For hyperbolic lattices with different quantized curvatures, we examine the topological protection of helical edge states and generalize Hofstadter’s butterfly, by employing two empirical parameters that measure the edge confinement and defect immunity. We demonstrate that the proposed platforms exhibit the unique spectral-magnetic sensitivity of topological immunity in highly curved hyperbolic planes. Our approach is applicable to general non-Euclidean geometry and enables the exploitation of infinite lattice degrees of freedom for band theory.

We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the timescale over which the instability develops is given by the volume fraction dependent settling timescale of the grains in the cell. We then show that the mobility inversion and the nonequilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.

Depending on the geometry of their Fermi surfaces, Weyl semimetals and their analogs in classical systems have been classified into two types. In type-I Weyl semimetals (WSMs), the conelike spectrum at the Weyl point is not tilted, leading to a pointlike closed Fermi surface. In type-II WSMs, on the contrary, the energy spectrum around the Weyl point is strongly tilted such that the Fermi surface transforms from a point into an open surface. Here, we demonstrate, both theoretically and experimentally, a new type of (classical) Weyl semimetal whose Fermi surface is neither a point nor a surface, but a flat line. The distinctive Fermi surfaces of such semimetals, dubbed as type-III or zero-index WSMs, gives rise to unique physical properties: one of the edge modes of the semimetal exhibits a zero index of refraction along a specific direction, in stark contrast to type-I and type-II WSMs for which the index of refraction is always nonzero. We show that the zero-index response of such topological phases enables exciting applications such as extraordinary wave transmission.

Inspired by the jamming in leaky systems that arises in many physiological and industrial settings, we study the propagation of clogs in a leaky microfluidic channel. By driving a colloidal suspension through such a channel with a fluid-permeable wall adjoining a gutter, we follow the formation and propagation of jams and show that they move at a steady speed, in contrast with jams in channels that have impermeable walls. Furthermore, by varying the ratio of the resistance from the leaky wall and that of the gutter, we show that it is possible to control the shape of the propagating jam, which is typically wedge shaped. We complement our experiments with numerical simulations, where we implement an Euler-Lagrangian framework for the simultaneous evolution of both immersed colloidal particles and the carrier fluid. Finally, we show that the particle ordering in the clog can be tuned by adjusting the geometry of the leaky wall. Altogether, the leaky channel serves both as a filter and a shunt with the potential for a range of uses.

It is a long-standing belief that, in the diffusion regime, the intensity statistics is always stationary and its probability distribution follows a negative exponential decay. Here, we demonstrate that, in fact, in reflection from strong disordered media, the intensity statistics changes through different stages of the diffusion. We present a statistical model that describes this nonstationary property and takes into account the evolving balance between recurrent scattering and near field coupling. The predictions are further verified by systematic experiments in the optical regime. This statistical nonstationary is akin to the nonequilibrium but steady-state diffusion of particulate systems.

Strong mode coupling and Fano resonances arisen from exceptional interaction between resonant modes in single nanostructures have raised much attention for their advantages in nonlinear optics, sensing, etc. Individual electromagnetic multipole modes such as quadrupoles, octupoles, and their counterparts from mode coupling (toroidal dipole and nonradiating anapole mode) have been well investigated in isolated or coupled nanostructures with access to high $Q$ factors in bound states in the continuum. Albeit the extensive study on ordinary dielectric particles, intriguing aspects of light-matter interactions in single chiral nanostructures is lacking. Here, we unveil that extraordinary multipoles can be simultaneously superpositioned in a chiral nanocylinder, such as two toroidal dipoles with opposite moments, and electric and magnetic sextupoles. The induced optical lateral forces and their scattering cross sections can thus be either significantly enhanced in the presence of those multipoles with high-$Q$ factors, or suppressed by the bound states in the continuum. This work for the first time reveals the complex correlation between multipolar effects, chiral coupling, and optical lateral force, providing a distinct way for advanced optical manipulation.

Kerr resonators support novel nonlinear wave phenomena including technologically important optical solitons. Fiber Kerr resonator solitons enable wavelength and repetition-rate versatile femtosecond-pulse and frequency-comb generation. However, key performance parameters, such as pulse duration, lag behind those from traditional mode-locked laser-based sources. Here we present new pulse generation in dispersion-managed Kerr resonators based on stretched-pulse solitons, which support the shortest pulses to date from a fiber Kerr resonator. In contrast to established Kerr resonator solitons, stretched-pulse solitons feature Gaussian temporal profiles that stretch and compress each round trip. Experimental results are in excellent agreement with numerical simulations. The dependence on dispersion and drive power are detailed theoretically and experimentally and design guidelines are presented for optimizing performance. Kerr resonator stretched-pulse solitons represent a new stable nonlinear waveform and a promising technique for femtosecond pulse generation.

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian band topology was proposed in nodal link systems, where the nodal lines formed by consecutive pairs of bands exhibit interesting braiding structures and the underlying topological charges are described by quaternions. Here, we experimentally demonstrate non-Abelian nodal links in a biaxial hyperbolic metamaterial. The linked nodal lines threading through each other are formed by the crossings between three adjacent bands. Based on the non-Abelian charges, we further analyze various admissible nodal link configurations for the three-band system. On the interface between the metamaterial and air, surface bound states in the continuum are observed, which serves as the symmetry-enforced derivative of drumhead surface states from the linked nodal lines. Our work serves as a direct observation of the global topological structures of nodal links, and provides a platform for studying non-Abelian topological charge in the momentum space.

We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: (i) phase noise acting on the oscillator state variable and (ii) stochastic fluctuations of the coupling delay. For both types of stochastic perturbations the system hops between the deterministic regimes, but it shows dramatically different scaling properties for different types of noise. The robustness to conventional phase noise increases with coupling strength. However for stochastic variations in the coupling delay, the lifetimes decrease exponentially with the coupling strength. We provide an analytic explanation for these scaling properties in a linearized model. Our findings thus indicate that the robustness of a system to stochastic perturbations strongly depends on the nature of these perturbations.

We examine the dynamics of small anisotropic particles (spheroids) sedimenting through homogeneous isotropic turbulence using direct numerical simulations and theory. The gravity-induced inertial torque acting on sub-Kolmogorov spheroids leads to pronouncedly non-Gaussian orientation distributions localized about the broadside-on (to gravity) orientation. Orientation distributions and average settling velocities are obtained over a wide range of spheroid aspect ratios, Stokes, and Froude numbers. Orientational moments from the simulations compare well with analytical predictions in the inertialess rapid-settling limit, with both exhibiting a nonmonotonic dependence on spheroid aspect ratio. Deviations arise at Stokes numbers of order unity due to a spatially inhomogeneous particle concentration field resulting from a preferential sweeping effect; as a consequence, the time-averaged particle settling velocities exceed the orientationally averaged estimates.

Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the $\beta$-Fermi-Pasta-Ulam-Tsingou chain, considered a prototypical model for one-dimensional anharmonic crystals, in contact with thermostats at different temperatures. We give evidence that, in steady state conditions, the local wave energy spectrum can be naturally split into modes that are essentially ballistic (noninteracting or scarcely interacting) and kinetic modes (interacting enough to relax to local thermodynamic equilibrium). We show numerically that the well-known divergence of the energy conductivity is related to how the transition region between these two sets of modes shifts in $k$ space with the system size $L$, due to properties of the collision integral of the system. Moreover, we show that the kinetic modes are responsible for a macroscopic behavior compatible with Fourier’s law. Our work sheds light on the long-standing problem of the applicability of standard thermodynamics in one-dimensional nonlinear chains, testbed for understanding the thermal properties of nanotubes and nanowires.

When material parameters are fixed, optical responses of nanoresonators are dictated by their shapes and dimensions. Therefore, both designing nanoresonators and understanding their underlying physics would benefit from a theory that predicts the evolutions of resonance modes of open systems—the so-called quasinormal modes (QNMs)—as the nanoresonator shape changes. QNM perturbation theories (PTs) are one ideal choice. However, existing theories developed for tiny material changes are unable to provide accurate perturbation corrections for shape deformations. By introducing a novel extrapolation technique, we develop a rigorous QNM PT that faithfully represents the electromagnetic fields in perturbed domain. Numerical tests performed on the eigenfrequencies, eigenmodes, and optical responses of deformed nanoresonators evidence the predictive force of the present PT, even for large deformations. This opens new avenues for inverse design, as we exemplify by designing super-cavity modes and exceptional points with remarkable ease and physical insight.

In a two-dimensional non-Hermitian topological photonic system, the physics of topological states is complicated, which brings great challenges for clarifying the topological phase transitions and achieving precise active control. Here, we prove the topological phase transition exists in a two-dimensional parity-time-symmetric coupled-resonator optical waveguide system. We reveal the inherent condition of the appearance of topological phase transition, which is described by the analytical algebraic relation of coupling strength and the quantity of gain-loss. In this framework, the system can be switched between the topological and trivial states by pumping the site rings. This work provides a new degree of freedom to control topological states and offers a scheme for studying non-Hermitian topological photonics.