Experiments of pure tensile fracture in thin brittle gels reveal a new dynamic oscillatory instability whose onset occurs at a critical velocity, $V_C=0.87C_S$, where $C_S$ is the shear wave speed. Until $V_C$, crack dynamics are well described by linear elastic fracture mechanics (LEFM). These extreme speeds are obtained by suppression of the microbranching instability, which occurs when sample thicknesses are made comparable to the minimum microbranch width. The wavelength of these sinusoidal oscillations is independent of the sample dimensions, thereby suggesting that these macroscopic effects are due to an intrinsic microscopic scale that is unrelated to LEFM.

The stability of a rapid dynamic crack in a two-dimensional infinite strip is studied in the framework of linear elastic fracture mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack becomes unstable by a finite wavelength oscillatory mode at a velocity $v_c$, $0.8c_R<v_c<0.85c_R$, where $c_R$ is the Rayleigh wave speed. The relevance of this theoretical calculation to the oscillatory instability reported in the companion experimental Letter is discussed.

We analyze experimentally and theoretically $>1\mathrm{GHz}$ optoexcited mechanical vibration in an on-chip micron-scaled sphere. Different eigen-mechanical modes are excited upon demand by the centrifugal radiation pressure of the optical whispering-gallery-mode, enabling an optomechanical modal spectroscopy investigation of many vibrational modes. Spectral analysis of the light emitted from the device enables deduction of its natural vibrational modes in analogy with spectroscopy of a molecule’s vibrational levels, and its eccentricity perturbation is shown to induce spectral splitting.

We report controlled enhancement of optical third harmonic generation (THG) from hydrodynamically expanding clusters of $\sim 6\times {10}^5$ noble-gas atoms several hundred femtoseconds following ionization and heating by ultrashort pump pulses. This resonant enhancement is more pronounced for orthogonal than for parallel pump-probe polarizations, a consequence of faster cluster expansion along the pump polarization. Simulations show that the nonlinear susceptibility ${\chi }^{(3)}$ of the individual clusters and the coherence length of the clustered plasma medium are optimized nearly simultaneously as the clusters expand, and both contribute to the observed THG enhancement. This dual enhancement mechanism may be scalable to relativistic probe intensity and to generation of high-order harmonics in the soft-x-ray regime.

Nanobubbles on a hydrophilic surface immersed in water and ethanol are inferred from the response of the surface to two consecutive heat pulses with a variable separation time. Bubble nucleation occurs at specific positions on the surface during the first heat pulse but at lower nucleation temperatures and random locations on the second. Nanobubbles are hypothesized to form on collapse of the bubble from the first pulse.

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle.

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea is characterized using scaling arguments revealing critical exponents connected by an analytic relationship. The formalism is widely applicable to systems with mixed phase space, and especially in studies of the transition from integrability to nonintegrability, including that in classical billiard problems.

We show experimentally that clogging is basically a matter of the probability of the presence of particles. We describe this process as a function of the main variables of the process, namely, the ratio of particle to mesh hole size, the solid fraction, and the number of grains arriving at each mesh hole during one test, with the help of a simple model, the predictions of which are in very good agreement with our experimental data.

We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schrödinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.

We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a single real unstable Floquet multiplier, can in fact be stabilized. We derive explicit analytical conditions for the control matrix in terms of the amplitude and the phase of the feedback control gain, and present a numerical example. Our results are of relevance for a wide range of systems in physics, chemistry, technology, and life sciences, where subcritical Hopf bifurcations occur.

In selective withdrawal, fluid is withdrawn through a nozzle suspended above the flat interface separating two immiscible, density-separated fluids of viscosities ${\nu }_{\mathrm{upper}}$ and ${\nu }_{\mathrm{lower}}=\lambda {\nu }_{\mathrm{upper}}$. At low withdrawal rates, the interface gently deforms into a hump. At a transition withdrawal rate, a spout of the lower fluid becomes entrained with the flow of the upper one into the nozzle. When $\lambda =0.005$, the spouts at the transition are very thin with features that are over an order of magnitude smaller than any observed in the humps. When $\lambda =20$, there is an intricate pattern of hysteresis and a spout appears which is qualitatively different from those seen at lower $\lambda$. No corresponding qualitative difference is seen in the hump shapes.

Experiments and computer simulations on the generation of high order harmonics from steep plasma gradients using intense femtosecond laser pulses are presented. Qualitative changes in the harmonic emission take place when the intensities are increased above ${10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ and/or the plasma scale length is varied. Good agreement between experimental and calculated spectra makes it possible to clearly distinguish between nonrelativistic and relativistic mechanisms of harmonic generation.

We present a new and complete analysis of the $n$-bounce resonance and chaotic scattering in solitary-wave collisions. In these phenomena, the speed at which a wave exits a collision depends in a complicated fractal way on its input speed. We present a new asymptotic analysis of collective-coordinate ordinary differential equations (ODEs), reduced models that reproduce the dynamics of these systems. We reduce the ODEs to discrete-time iterated separatrix maps and obtain new quantitative results unraveling the fractal structure of the scattering behavior. These phenomena have been observed repeatedly in many solitary-wave systems over 25 years.

Hamiltonian systems that locally violate the twist condition arise in many applications. Numerical simulations reveal that, when systems of this type are perturbed, the degenerate or nontwist tori are remarkably stable. This phenomenon, which we refer to as strong Kolmogorov-Arnold-Moser (KAM) stability, is shown to be linked to very small resonance widths near degenerate tori. Quantitative estimates of degenerate resonance widths are derived and bifurcations of degenerate resonances are described. Strong KAM stability leads to robust transport barriers, which are important in all of the many applications in which Hamilitonians with the nontwist property arise.

We consider far from equilibrium heat transport in chaotic billiard chains with noninteracting charged particles in the presence of nonuniform transverse magnetic field. If half of the chain is placed in a strong magnetic field, or if the strength of the magnetic field has a large gradient along the chain, heat current is shown to be asymmetric with respect to exchange of the temperatures of the heat baths. Thermal rectification factor can be arbitrarily large for sufficiently small temperature of one of the baths.

This Letter reports on work performed to locate and interrogate a nonlinear scatterer in a linearly elastic medium through the use of a time reversal mirror in combination with nonlinear dynamics. Time reversal provides the means to spatially and temporally localize elastic energy on a scattering feature while the nonlinear dynamics spectrum allows one to determine whether the scatterer is nonlinear (e.g., mechanical damage). Here elastic waves are measured in a solid and processed to extract the nonlinear elastic response. The processed elastic signals are then time reversed, rebroadcast, and found to focus on the nonlinear scatterer, thus defining a time-reversed nonlinear elastic wave spectroscopy process. Additionally, the focusing process illuminates the complexity of the nonlinear scatterer in both space and time, providing a means to image and investigate the origins and physical mechanisms of the nonlinear elastic response.

We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on $k$ space singularities in photonic lattices. In addition, we demonstrate “honeycomb gap solitons” residing in the gap between the second and the third bands, reflecting the special properties of these lattices.

We present numerical simulations of a turbulent magnetic dynamo mimicking closely the Riga-dynamo experiment at $\mathrm{Re}\approx 3.5\times {10}^6$ and $15\le {\mathrm{Re}}_m\le 20$. The Reynolds-averaged Navier-Stokes equations for the fluid flow and turbulence field are solved simultaneously with the direct numerical solution of the magnetic field equations. The fully integrated two-way-coupled simulations reproduced all features of the magnetic self-excitation detected by the Riga experiment, with frequencies and amplitudes of the self-generated magnetic field in good agreement with the experimental records, and provided full insight into the unsteady magnetic and velocity fields and the mechanisms of the dynamo action.

We investigate the spatiotemporal dynamics of a large array of laser oscillators. The oscillators are locally coupled and their natural frequencies are randomly detuned. We show that synchronization of the array elements results in localized excitations wandering along well-defined trajectories.

We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.