We have measured the photon statistics of random lasers with resonant feedback. With an increase of the pump intensity, the photon number distribution in a single mode changes continuously from Bose-Einstein distribution at the threshold to Poisson distribution well above the threshold. The second-order correlation coefficient drops gradually from 2 to 1. By comparing the photon statistics of a random laser with resonant feedback and that of a random laser with nonresonant feedback, we illustrate very different lasing mechanisms for the two types of random lasers.

We have investigated the amplification of a spatially periodic perturbation applied to a wide fundamental beam launched near phase matching for second-harmonic generation in a lithium niobate film waveguide. We measured the gain coefficient for the modulational instability of quadratic eigenmodes as a function of periodicity, intensity, and wave-vector mismatch. Excellent agreement with theory was obtained.

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accordance with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.

The instability, dynamics, and morphological transitions of patterns in thin liquid films on chemically heterogeneous striped surfaces are investigated based on 3D nonlinear simulations. The film breakup is suppressed on some potentially destabilizing nonwettable sites when their spacing is below a characteristic length scale of the instability, ${\lambda }_h$. The thin film pattern replicates the substrate surface energy pattern closely only when (i) the periodicity of substrate pattern lies between ${\lambda }_h$ and $2{\lambda }_h$, and (ii) the stripe width is within a range bounded by a lower critical length, below which no heterogeneous rupture occurs, and an upper transition length above which complex morphological features unlike the substrate pattern are formed.

A Comment on the Letter by Mete Atatüre, et al., Phys. Rev. Lett. 84, 618 (2000).

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.

We present a novel twinned-square periodic structure for ultrasonic wave bending and splitting that does not require the existence of a complete band gap and plays the role of an ultrasonic wedge. The device allows 45° bending of waves and by adequately switching the twinned structure to an ultrasonic crystal 90° bending is achieved. An extreme refraction law at the grain boundaries is experimentally observed.

When sand falling in the spacing between two plates goes past an obstacle, a dynamic dune with a parabolic shape and an inner triangular region of nonflowing or slowly creeping sand forms. The angle of the triangular zone increases with the height of the dune and saturates at a value determined by the geometry of the cell. The width of the dune, related to the radius of curvature at the tip, shows universal features versus its height rescaled by geometrical parameters. The velocity profile in the flowing part is determined and found to be nonlinear. The parabolic shape can be accounted for using a simple driven convection-diffusion equation for the interface.

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose that this is due to air being drawn into the narrow channel of a cusp singularity that generically forms on free surfaces. Since the width of the cusp is exponentially small in the driving strength, even the minute viscosity of air is enough to destroy the stationary solution, and a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory is confirmed by quantitative comparison with numerical simulations of the flow equations, and is found to be in qualitative agreement with experimental observation.

A generalized hydrodynamic theory of shock wave structures is presented for rigid diatomic gases. The theory yields shock solutions for all Mach numbers. The accuracy of the theory is examined for nitrogen gas as an example. Excellent agreement with experiment is obtained for the inverse shock widths for the entire range of Mach number studied by experiment. The comparison made shows that we are now in possession of a successful continuum theory of shock waves in molecular gases for all Mach numbers.

Fluid flow fields in a pair of quasi-two-dimensional channel models, each of which vacillates chaotically between distinct flow regimes, synchronize if only the small-scale eddy components of the two flows are coupled. The synchronization behavior also governs the relationship between different sectors of the same continuous channel. Where there is no natural boundary to define the sectors, but the sectors are separately forced, the channel can be represented as two coextensive, coupled channel models with different forcing terms. Generalized synchronization of these two systems implies a relationship between the Atlantic and Pacific sectors of the Earth's climate system.

Thermal convection was studied as a function of the porosity in random-site percolation model objects in a Rayleigh-Bénard configuration. NMR velocity mapping experiments and numerical simulations using the finite-volume method are compared. Velocity histograms were evaluated and can be described by power laws in a wide range. The maximum velocity as a function of the porosity indicates a combined percolation/Rayleigh-Bénard transition.

We present the first experimental observation of superpersistent chaotic transients. In particular, we investigate the effect of noise on phase synchronization in coupled chaotic electronic circuits and obtain the scaling relation that is characteristic of those extremely long chaotic transients.

The first observation of parametric light scattering patterns (rings, lines, and dots) in bulk periodically poled nonlinear media is reported. Development of the scattering patterns proves efficient photorefractive grating recording and considerable parametric gain for seed radiation in this new nonlinear material. Several novel phase-matched parametric processes, caused by the periodicity of the domain structure, are revealed.

A kind of chaotic oscillations featuring random switching between sustained relaxation oscillations (RO) and spiking oscillations (SO) has been demonstrated in lasers with frequency-shifted feedback. The presence of stochastic frequency locking between two periodicities of RO and SO motions and selective quantum-noise-induced ordering of chaotic spiking oscillations is demonstrated theoretically and experimentally.

We examine the interplay of surface and volume effects in systems undergoing heat flow. In particular, we compute the thermal conductivity in the Fermi-Pasta-Ulam $\beta$ model as a function of temperature and lattice size, and scaling arguments are used to provide analytic guidance. From this we show that boundary temperature jumps can be quantitatively understood, and that they play an important role in determining the dynamics of the system, relating soliton dynamics, kinetic theory, and Fourier transport.

An eddy-viscous term is added to Navier-Stokes dynamics at wave numbers $k$ greater than the inflection point $k_c$ of the energy flux $F\left(\log \right(k\left)\right)$. The eddy viscosity is fixed so that the energy spectrum satisfies $E\left(k\right)=E\left(k_c\right)(k/k_c{)}^{-3\mathrm{}}$ for $k>\mathrm{}{k}_c$. This resulting forcing induces a rapid depletion of the energy cascade at $k>\mathrm{}{k}_c$. It is observed numerically that the model reproduces turbulence energetics at $k\le k_c$ and statistics of two-point velocity correlations at scales $r>\mathrm{}\lambda$ (Taylor microscale). Compared to a direct numerical simulation of $R_{\lambda }=130\mathrm{}$ an equivalent run with the present model results in a gain of a factor 20 in CPU time.

A general phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed, based on the fact that for most media these regions in the $p-V$ plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discussed.

We report the existence of self-organization in wet granular media or slurries, mixtures of particles of different sizes dispersed in a lower density liquid. As in the case of dry granular mixtures, axial banding (alternating bands rich in small and large particles in a long rotating cylinder) and radial segregation (in quasi-2D containers) are observed in slurries. However, when compared with the dry counterpart axial segregation is significantly faster and the spectrum of outcomes is richer. Moreover, experiments with suitable fluids reveal, for the first time, the internal structure of axially segregated systems, something that up to now has been accessible only via magnetic resonance imaging experimentation.

The pressure spectrum in homogeneous steady turbulence is studied using direct numerical simulation with resolution up to ${1024}^3$ and the Reynolds number $R_{\lambda }$ between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant $K=1.65\mathrm{}\pm 0.05$ followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately $P\left(k\right){=B}_p{\overline{\epsilon }}^{4/3}{k}^{-7/3\mathrm{}}$ with $B_p=8.0\mathrm{}\pm 0.5$, and followed by a bump of nearly $k^{-5/3\mathrm{}}$ at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.