To explore the validity of theories forwarded to explain the dynamics of hydrodynamic perturbations on high Mach number blast waves, we have studied the decay rate of perturbations on blast waves traveling through nitrogen gas. In our experiments, 1 kJ pulses from the Z-Beamlet laser at Sandia National Laboratories illuminated solid targets immersed in gas and created blast waves. The polytropic index implied by comparing experiment to theoretical predictions is compared to simulation results.

We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Korteveg–de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.

We propose a new method to reconstruct the electric field of attosecond pulse trains. The phase of the high-order harmonic emission electric field is Taylor expanded around the maximum of the laser pulse envelope in the time domain and around the central harmonic in the frequency domain. Experimental measurements allow us to determine the coefficients of this expansion and to characterize the radiation with attosecond accuracy over a femtosecond time scale. The method gives access to pulse-to-pulse variations along the train, including the timing, the chirp, and the attosecond carrier envelope phase.

Simulations of convection in ${}^3\mathrm{He}\mathrm{\text{−}}{}^4\mathrm{He}$ mixtures with a negative separation ratio in two-dimensional containers with realistic boundary conditions and moderately large aspect ratio reveal, at supercritical Rayleigh numbers, the existence of “convectons,” i.e., localized states of stationary convection, separated by regions of no convection. The origin and properties of these states are described.

Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell’s equations. It is shown that these metamaterials cannot be described in general by local, frequency-dependent permittivities and permeabilities for small periods compared to the wavelength, except in certain limiting cases that are discussed in detail. New related metamaterials are shown to exhibit exciting optical properties that are elucidated in the light of our simple analytical approach.

Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown that deviation from strict periodicity in the driving rapidly destroys dynamical localization. We report experimental results showing that this destruction is partially reversible when the deterministic perturbation that destroyed it is slowly reversed. We also provide an explanation for the partial character of the reversibility.

We investigate numerically the limits of the resonant magnetic response with a negative effective permeability ${\mu }_{\mathrm{eff}}$ for single-ring multicut split-ring resonator (SRR) designs up to optical frequencies. We find the breakdown of linear scaling due to the free electron kinetic energy for frequencies above $\sim 100\mathrm{THz}$. Above the linear scaling regime, the resonance frequency saturates, while the amplitude of the resonant permeability decreases, ultimately ceasing to reach negative value. The highest resonance frequency at which ${\mu }_{\mathrm{eff}}<0$ increases with the number of cuts in the SRR. A $LC$ circuit model provides explanation of the numerical data.

We demonstrate a new scheme for extreme ultraviolet (xuv) Fourier-transform spectroscopy based on the generation of two phase-locked high-harmonic beams. It allows us to measure for the first time interferograms at wavelengths as short as 90 nm, and open the perspective of performing high-resolution Fourier-transform absorption spectroscopy in the xuv. Our measurements also demonstrate that a precise control of the relative phase of harmonic pulses can be obtained with an accuracy on an attosecond time scale, of importance for future xuv pump-xuv probe attosecond spectroscopy.

We present measurements of the near-field heat transfer between the tip of a thermal profiler and planar material surfaces under ultrahigh vacuum conditions. For tip-sample distances below ${10}^{-8}\mathrm{m}$, our results differ markedly from the prediction of fluctuating electrodynamics. We argue that these differences are due to the existence of a material-dependent small length scale below which the macroscopic description of the dielectric properties fails, and discuss a heuristic model which yields fair agreement with the available data. These results are of importance for the quantitative interpretation of signals obtained by scanning thermal microscopes capable of detecting local temperature variations on surfaces.

We study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well-developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.

Self-similar space-filling bearings have been proposed some time ago as models for the motion of tectonic plates and appearance of seismic gaps. These models have two features which, however, seem unrealistic, namely, high symmetry in the arrangement of the particles, and lack of a lower cutoff in the size of the particles. In this work, an algorithm for generating random bearings in both two and three dimensions is presented. Introducing a lower cutoff for the sizes of the particles, the instabilities of the bearing under an external force such as gravity, are studied.

It is shown by comparison with numerical solutions of the Schrödinger equation that the three step model (TSM) of high harmonic generation (HHG) can be improved to give a quantitatively reliable description of the process. Excellent agreement is demonstrated for the H atom and the ${\mathrm{H}}_2^{+}$ molecular ion. It is shown that the standard TSM heavily distorts the HHG spectra, especially of ${\mathrm{H}}_2^{+}$, and an explanation is presented for this behavior. Key to the improvement is the use of the Ehrenfest theorem in the TSM.

We show for the first time that a weak perturbation in a Hamiltonian system may lead to an arbitrarily wide chaotic layer and fast chaotic transport. This generic effect occurs in any spatially periodic Hamiltonian system subject to a sufficiently slow ac force. We explain it and develop an explicit theory for the layer width, verified in simulations. Chaotic spatial transport as well as applications to the diffusion of particles on surfaces, threshold devices, and others are discussed.

Phase separation between two fluids in two dimensions is investigated by means of direct numerical simulations of coupled Navier-Stokes and Cahn-Hilliard equations. We study the phase ordering process in the presence of an external stirring acting on the velocity field. For both active and passive mixtures we find that, for a sufficiently strong stirring, coarsening is arrested in a stationary dynamical state characterized by a continuous rupture and formation of finite domains. Coarsening arrest is shown to be independent of the chaotic or regular nature of the flow.

We introduce a mesoscopic three-dimensional lattice Boltzmann model which attempts to mimic the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard lattice Boltzmann dynamics with self-consistent constraints based on the nonlocal density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic heterogeneous fluids, such as non-Gaussian density distributions and long-time relaxation. Because of its intrinsically parallel dynamics, and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo, and lattice glass models.

We present an experimental study on wave propagation in highly nonlocal optically nonlinear media, for which far-away boundary conditions significantly affect the evolution of localized beams. As an example, we set the boundary conditions to be anisotropic and demonstrate the first experimental observation of coherent elliptic solitons. Furthermore, exploiting the natural ability of such nonlinearities to eliminate azimuthal instabilities, we perform the first observation of stable vortex-ring solitons. These features of highly nonlocal nonlinearities affected by far-away boundary conditions open new directions in nonlinear science by facilitating remote control over soliton propagation.

A theory of time-dependent nonlinear dispersive equations of the Schrödinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, “selection of the ground state,” and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides.

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.

Scattering of a dispersive wave by optical solitons is studied experimentally in photonic crystal fibers in cases when the soliton and the dispersive wave have either identical or orthogonal polarization states. Observations of new resonant frequencies are reported. The experimental results are compared to numerical simulations and predictions from the recently derived wave vector matching conditions.

Pure rotational stimulated Raman scattering spectra containing nine strong spectral components were generated from a $\sim 11\mathrm{m}$ long hollow-core photonic crystal fiber filled with hydrogen and pumped with nanosecond pulses having energies around 100–300 nJ. Observation of both transient and steady-state scattering threshold behavior is reported. Passage from the transient to the steady state is observed with a pulse as long as 14 ns. Convenient analytical expressions for energy and power threshold are deduced for the present configuration.