Fingering instabilities similar to those commonly observed in viscous systems have been observed in purely elastic layers that are strained in tension. The instability is driven by the release of lateral constraints within a confined elastic layer and is observed when the lateral confinement significantly exceeds the thickness of the elastic layer. Our results show convincingly that yielding or flow of a material is not required in order for fingering to be initiated in a confined material.

Fragmentation of a two-dimensional brittle solid by impact and “explosion,” and a fluid by “explosion” are all shown to become critical. The critical points appear at a nonzero impact velocity, and at infinite explosion duration, respectively. Within the critical regimes, the fragment-size distributions satisfy a scaling form qualitatively similar to that of the cluster-size distribution of percolation, but they belong to another universality class. Energy balance arguments give a correlation length exponent that is exactly one-half of its percolation value. A single crack dominates fragmentation in the slow-fracture limit, as expected.

The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable.

We study the existence, the stability properties, and the bifurcation structure of static localized solutions in one dimension, near the robust existence of stable fronts between homogeneous solutions and periodic patterns.

Experimental evidence of the collapse of dilute lamellar phases due to shear flow is presented. Two systems are used: one composed of brine and an ionic surfactant, and another composed of water, a nonionic surfactant, and cosurfactant. We observe this transition for a range of lamellar spacings and brine salinity. The results are in reasonable agreement with recent theory in which the suppression of fluctuations by shear plays an important role.

We prove ergodicity of unitary random-matrix theories by showing that the autocorrelation function with respect to energy or magnetic field strength of any observable vanishes asymptotically. We do so using Efetov's supersymmetry method, a polar decomposition of the saddle-point manifold, and an asymptotic evaluation of the boundary terms generated in this fashion.

The dynamics of the kicked rotor, which is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular, is studied statistically. The evolution operator of phase space densities in the chaotic component is calculated in the presence of noise, and the limit of vanishing noise is taken in the end. The relaxation rates to the equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. A global picture is presented of relaxation to the equilibrium density in the chaotic component when the system is bounded and to diffusive behavior when it is unbounded.

We consider a classically chaotic system that is described by a Hamiltonian $H(Q,P;x)$, where $x$ is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where $x$ controls a deformation of the boundary or the position of a “piston.” The quantum eigenstates of the system are $|n\left(x\right)〉$. We describe how the parametric kernel $P\left(n\mid m\right)=|〈n\left(x\right)\mid m\left(x_0\right)〉{|}^2$ evolves as a function of $\delta {x=x-x}_0$. We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.

Brewster's scattering angle in electromagnetic wave scattering from slightly random metal surfaces is investigated by means of the stochastic functional approach. While there are dips due to Brewster's scattering angle in scattering profiles from dielectric surfaces, Brewster's scattering angle does not exist in scattering from metal surfaces. However, the dips can exist in scattering from rough metal surfaces with the optically denser medium to convert evanescent wave into radiative wave.

We introduce a technique for ultrasensitive absorption spectroscopy using the GHz-rate pulse train from a phase-locked free-electron laser (FEL), in which the fractional power absorbed from one or more laser lines reappears as a signal on the dark background between the pulses emerging from the sample. Preliminary absorption experiments in 15 Torr cm of methane at $3.25\mu \mathrm{m}$, using phase-locked pulses from the Mark III FEL, clearly reveal an interpulse beat signal due to absorption by adjacent molecular rotational lines which is generated only in the presence of interpulse phase coherence.

We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold. The frequency and the size of the gaps depend on the local order rather than on the symmetry or the global long range order. Good agreement between theory and experiment is obtained in the microwave regime. Calculations show that the approach can be scaled up to optical frequencies even in the presence of absorption.

Under quite general conditions, we prove that for classical many-body lattice Hamiltonians in one dimension (1D) total momentum conservation implies anomalous conductivity in the sense of the divergence of the Kubo expression for the coefficient of thermal conductivity, $\kappa$. Our results provide rigorous confirmation and explanation of many of the existing “surprising” numerical studies of anomalous conductivity in 1D classical lattices, including the celebrated Fermi-Pasta-Ulam problem.

By defining a direction phase as the direction of two sequential iterations of the logistic map, a transition of a net direction phase $M$ from zero to a finite value as the parameter $\mu$ increases is found. Near the transition point ${\mu }_0$ a scaling $M\sim (\mu -{\mu }_0{)}^{\alpha }$ with $\alpha =0.5\mathrm{}$ is obtained. The order state of the direction phases in a coupled map lattice is also studied. A phase synchronization of the direction phases is found although the lattices still remain chaotic.

Transverse instabilities correspond to a class of perturbations traveling in a direction transverse to the direction of the basic solitary wave. Solitary waves traveling in one space direction generally come in one-parameter families. We embed them in a two-parameter family and deduce a new geometric condition for transverse instability of solitary waves. This condition is universal in the sense that it does not require explicit properties of the solitary wave—or the governing equation. In this paper the basic idea is presented and applied to the Zakharov-Kuznetsov equation for illustration. An indication of how the theory applies to a large class of equations in physics and oceanography is also discussed.

We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing intermittency. The latter is found to be constrained by dynamical anomalies expressing finite dissipation in the inviscid limit. The link between dynamical anomalies and intermittency is argued to be important in a wider context of turbulence.

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential $U\left(X\right)=U(X+2\mathrm{}\pi )$ under the influence of a time-periodic space-homogeneous external field $E\left(t\right)=E(t+T)$. If $E\left(t\right)$ is neither a symmetric function of $t$ nor antisymmetric under time shifts $E(t\pm T/2)\ne -E\left(t\right)$, an ensemble of trajectories with zero current at $t=0\mathrm{}$ yields a nonzero finite current as $t\to \infty$. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.

We show that the continuous phase space of a hard particle system can be mapped onto a discrete but infinite phase space. For three pointlike particles confined to a ring, the evolution of the system maps onto a chaotic walk on a hexagonal lattice. This facilitates direct measurement of the departure of the system from its original configuration. In special cases of mass ratios the phase space becomes closed and finite (nonergodic). There are qualitative differences between this chaotic walk and a random walk, in particular a more rapid sampling of phase space.

We investigate how far it is possible to identify and separate dynamical noise from measurement noise in observed nonlinear time series. Using Bayesian methods, we derive estimates for the two noise levels, and find that, given a good model of the dynamics, these can give accurate results even if the dynamical noise level is orders of magnitude smaller than the measurement noise level, whereas a simple calculation of root mean square error badly understates the dynamical noise. We argue that this allows better estimates of the underlying dynamical time series, and so better predictions of its future and of its fundamental dynamical properties.

The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.

We present the first observation of incoherent antidark spatial solitons in noninstantaneous nonlinear media. This new class of soliton states involves bright solitons on a partially incoherent background of infinite extent. In the case where the nonlinearity is of the Kerr type, their existence is demonstrated analytically by means of an exact solution. Computer simulations and experiments indicate that these incoherent antidark solitons can propagate in a stable fashion provided that the spatial coherence of their background is reduced below the incoherent modulation instability threshold.