We consider oscillator ensembles consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz, we reduce the dynamics of the ensemble to a relatively small number of dynamical variables plus constants of motion. This reduction is independent of the sizes of subpopulations and remains valid in the thermodynamic limits. The theory is applied to the standard Kuramoto model and to the description of two interacting subpopulations, where we report a novel, quasiperiodic chimera state.

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities ($0.2–0.8c_s$), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be nonunique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the $r^{-1/2}$ divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.

The common approach to crack dynamics, linear elastic fracture mechanics, assumes infinitesimal strains and predicts a $r^{-1/2}$ strain divergence at a crack tip. We extend this framework by deriving a weakly nonlinear fracture mechanics theory incorporating the leading nonlinear elastic corrections that must occur at high strains. This yields strain contributions “more divergent” than $r^{-1/2}$ at a finite distance from the tip and logarithmic corrections to the parabolic crack tip opening displacement. In addition, a dynamic length scale, associated with the nonlinear elastic zone, emerges naturally. The theory provides excellent agreement with recent near-tip measurements that cannot be described in the linear elastic fracture mechanics framework.

The extremal transmission of the acoustic wave near the Dirac point in two-dimensional (2D) sonic crystals, being inversely proportional to the thickness of sample, has been demonstrated experimentally for the first time. Some unusual beating effects have been observed experimentally, when the acoustic pulse transports through the 2D sonic crystal slabs. Such phenomena are completely different from the oscillations of the wave in a slab or cavity originating from the interface reflection or the Fabry-Perot effect. They can be regarded as an acoustic analogue effect to Zitterbewegung of the relativistic electron. The physical origination for the phenomenon has been analyzed.

We show that oscillating flow of a simple fluid in both the Newtonian and the non-Newtonian regime can be described by a universal function of a single dimensionless scaling parameter $\omega \tau$, where $\omega$ is the oscillation (angular) frequency and $\tau$ is the fluid relaxation time; geometry and linear dimension bear no effect on the flow. Energy dissipation of mechanical resonators in a rarefied gas follows this universality closely in a broad linear dimension (${10}^{-6}\mathrm{m}<L<{10}^{-2}\mathrm{m}$) and frequency (${10}^5\mathrm{Hz}<\omega /2\pi <{10}^8\mathrm{Hz}$) range. Our results suggest a deep connection between flows of simple and complex fluids.

We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear $\sigma$ model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon $-u_{\mathrm{tt}}+[{\Phi }^{\prime }(u_x){]}_x=P^{\prime }(u)$ equation, where ${\Phi }^{\prime }(\sigma )=\sigma +\beta {\sigma }^3$ and endowed with a subquadratic site potential $P(u)\sim |1-u^2{|}^{\alpha +1}$, $0\le \alpha <1$, and the Schrödinger $i{Z}_t+{\nabla }^{2}Z=G(|Z|)Z$ equation in a plane with $G(A)=\gamma A^{-\delta }-\sigma A^2$, $0<\delta \le 1$.

We demonstrate a classical analog of electromagnetically induced transparency in a planar metamaterial. We show that pulses propagating through such metamaterials experience considerable delay. The thickness of the structure along the direction of wave propagation is much smaller than the wavelength, which allows successive stacking of multiple metamaterial slabs leading to increased transmission and bandwidth.

While topological defects are essential to our understanding of self-organizing periodic systems, little is known about how these systems respond when their defects are subjected to geometrical constraints. In an experiment on spatially modulated thermal convection patterns, we observe that applied geometrical constraints bind topological defects into robust self-localized structures that evolve through aggregation, annihilation, and self-replication. We demonstrate that this unexpected cooperative response to the modulation is a natural consequence of three generic elements: phase locking, symmetry breaking, and spatial resonance. Our work provides new insights into the interplay between order, chaos, and control in self-organizing systems.

The full structure of a shock front around a blunt body in a quasi-two-dimensional granular flow is studied. Two features, a large density gradient and a very small thickness of the front, characterize this shock and make it different from shocks in molecular gases. Both of these features can be understood using a modified version of the granular kinetic theory. Our model separates the particles into two subpopulations: fast particles having experienced no collisions and randomly moving particles. This separation is motivated by direct measurements of the particle velocities which show a bimodal distribution. Our results not only shed new light on the use of the granular kinetic theory under extreme conditions (shock formation) but bring new insight into the physics of shocks in general.

We report on experimental observations of homoclinic snaking in a vertical-cavity semiconductor optical amplifier. Our observations in a quasi-one-dimensional and two-dimensional configurations agree qualitatively well with what is expected from recent theoretical and numerical studies. In particular, we show the bifurcation sequence leading to a snaking bifurcation diagram linking single localized states to “localized patterns” or clusters of localized states and demonstrate a parameter region where cluster states are inhibited.

We give experimental evidence of hyperbolic patterns in a nonlinear optical resonator. Such transverse patterns are a new kind of 2D dissipative structures, characterized by a distribution of the active modes along hyperbolas in the transverse wave-vector domain, in contrast with the usual (elliptic) patterns where the active modes distribute along rings. The hyperbolic character is realized by manipulating diffraction inside the optical resonator with cylindrical lenses. We also investigate theoretically hyperbolic patterns in corresponding Swift-Hohenberg models.

The ion flux dynamics across a straight nanoslot is imaged to understand the nonequilibrium phenomenon of overlimiting current density across a nanoporous membrane. With a slow ac field, an ion-depletion front is generated intermittently from one end of the nanochannel, and a vortex instability first predicted by Rubinstein, Staude, and Kedem [Desalination 69, 101 (1988).] is found to arrest the self-similar diffusive front growth. This electrokinetic instability evolves into a stationary interfacial vortex array that specifies the overlimiting current, independent of external stirring or convective flow.

We exploit the recent developments of microfluidic technologies to investigate the collective shear-induced diffusion in suspensions of micron-sized particles. Whereas spherical particles do not diffuse on the time scale of our experiments, the results with platelike clay particles show a strong cross-stream shear-induced diffusivity at low volume fraction (${\varphi }_0\le 0.01$). Moreover, we find a linear dependence of the collective diffusion coefficient with the average shear rate (in the range ${10}^2–{10}^4{\mathrm{s}}^{-1}$) and the particle concentration. These data are in good agreement with previous experimental and theoretical results for spheres when rescaled with the particle number density.

We demonstrate the generation of a coherent water window x ray by extending the plateau region of high-order harmonics under a neutral-medium condition. The maximum harmonic photon energies attained are 300 and 450 eV in Ne and He, respectively. Our proposed generation scheme, combining a $1.6\mu \mathrm{m}$ laser driver and a neutral Ne gas medium, is efficient and scalable in output yields of the water window x ray. Thus, the precept of the design parameter for a single-shot live-cell imaging by contact microscopy is presented.

We propose a new perspective on communication using chaos. A binary message is encoded into the temporally causal relations on a coupled maps ring of $N$ chaotic nodes. From the analysis of temporal transfer entropy, the masked information can be recovered from transmitted signals at the receiver. The communication scheme has been demonstrated to be robust against external noise and some traditional attacks.

The trajectory of a stream of bubbles is measured in a microfluidic pressure-driven flow. For Newtonian fluids with or without surfactants, or viscoelastic fluids without surfactants, the bubbles maintain stable positions equally spaced along the channel center line. However, for viscoelastic fluids with surfactant, a transverse instability is observed, which has the characteristics of a linear instability, whose growth rate increases with the speed of the flow. The results are shown to be consistent with the action of shear-induced normal stresses in the fluid, where the magnitude increases with shear rate and so is augmented by surfactants that make the interface rigid.

Existing continuum models of multiphase flow in porous media are unable to explain why preferential flow (fingering) occurs during infiltration into homogeneous, dry soil. Following a phase-field methodology, we propose a continuum model that accounts for an apparent surface tension at the wetting front and does not introduce new independent parameters. The model reproduces the observed features of fingered flows, in particular, the higher saturation of water at the tip of the fingers, which is believed to be essential for the formation of fingers. From a linear stability analysis, we predict that finger velocity and finger width both increase with infiltration rate, and the predictions are in quantitative agreement with experiments.

We report the observation of wave turbulence on the surface of a ferrofluid mechanically forced and submitted to a static normal magnetic field. We show that magnetic surface waves arise only above a critical field. The power spectrum of their amplitudes displays a frequency-power law leading to the observation of a magnetic wave turbulence regime which is experimentally shown to involve a 4-wave interaction process. The existence of the regimes of gravity, magnetic and capillary wave turbulence is reported in the phase space parameters as well as a triple point of coexistence of these three regimes. Most of these features are understood using dimensional analysis or the dispersion relation of the ferrohydrodynamic surface waves.

We consider the problem of initiation of a propagating wave in a one-dimensional bistable or excitable fiber. In the Zeldovich-Frank-Kamenetskii equation, also known as the Nagumo equation and Schlögl model, the key role is played by the “critical nucleus” solution whose stable manifold is the threshold surface separating initial conditions leading to the initiation of propagation and decay. An approximation of this manifold by its tangent linear space yields an analytical criterion of initiation which is in good agreement with direct numerical simulations.