We study heat conduction in one-dimensional mass-disordered harmonic and anharmonic lattices. It is found that the thermal conductivity $\kappa$ of the disordered anharmonic lattice is finite at low temperature, whereas it diverges as $\kappa \sim N^{0.43}$ at high temperature. Moreover, we demonstrate that a unique nonequilibrium stationary state in the disordered harmonic lattice does not exist at all.

The time and size distributions of the waves of topplings in the Abelian sandpile model are expressed as the first arrival at the origin distribution for a scale invariant, time-inhomogeneous Fokker-Plank equation. Assuming a linear conjecture for the time inhomogeneity exponent as a function of a loop-erased random walk (LERW) critical exponent, suggested by numerical results, this approach allows one to estimate the lower critical dimension of the model and the exact value of the critical exponent for LERW in three dimensions. The avalanche size distribution in two dimensions is found to be the difference between two closed power laws.

We study experimentally the jamming phenomenon of granular flow of monodisperse disks of $D=5\mathrm{}\mathrm{mm}$ diameter in a two-dimensional hopper with opening $R$. The jamming probability $J\left(d\right)$ is measured where $d\equiv R/D$. We found that $J\left(d\right)$ decreases from 1 to zero when $d$ increases from 2 to 5. From observing the disk configurations of the arch in the jamming events, the jamming probability can be explained quantitatively by treating the arch as the trajectory of a restricted random walker.

Using hydrothermal waves in a long narrow channel as an ideal supercritical nonlinear wave system, we study the critical behavior at onset for a finite cell with poorly reflecting boundaries. We observe a spatially nonuniform global eigenmode localized near the end of the cell and associated with a wave front invading the cell. The onset of this mode—corresponding to the absolute instability transition—is shifted above the value corresponding to convective instability, measured in an annular channel with periodic boundary conditions. Experimental critical exponents are discussed in the framework of existing theoretical descriptions and quantitative comparison with the complex Ginzburg-Landau model is attempted.

The energy transport velocity $v_E$ and the diffusion constant $D$ of electromagnetic waves in the presence of randomly distributed ferromagnetic scatterers are studied. $v_E$ presents a strong dependence on the relative magnetic permeability $\mu$ and, unlike the nonmagnetic case, exhibits sharp drops in the small-particle limit and never coincides with the phase velocity $v_p$. Both $v_E$ and $D$ exhibit an oscillatory dependence on $\mu$ and vanish for certain values of $\mu$. Since $\mu$ of ferromagnetic scatterers strongly depends on the temperature and applied magnetic field, we suggest that these facts can be explored in technological applications.

We report experimental evidence of phase synchronization of high dimensional chaotic oscillators in a laboratory experiment. The experiment consists of a thermocapillary driven convective cell in a time dependent chaotic regime. The synchronized states emerge as a consequence of a localized temperature perturbation to the heater. The transition to phase synchronization is studied as a function of the external perturbations. The existence and stability conditions for this phenomenon are discussed.

The propagation of intense electromagnetic waves in cold magnetized plasma is tackled through a relativistic hydrodynamic approach. The analysis of coupled transverse-longitudinal plasma oscillations is performed for traveling plane waves. When these waves propagate perpendicularly to a static magnetic field, the model is describable in terms of a nonlinear dynamical system with 2 degrees of freedom. A constant of motion is obtained and the powerful classical mechanics methods can be used. A new class of solutions, i.e., the chaotic solutions, is discovered by the Poincaré surface of sections. As a result, coupled transverse-longitudinal plasma oscillations become aperiodically modulated.

A novel mechanism is proposed for the generation of self-similar structure over a limited range of length scales. Our mechanism, which we call the monitor-outside-a-monitor effect, comprises repeated magnification and addition of small-scale structure. We invoke this mechanism to explain recent observations of fractal structure in the eigenmodes of unstable optical resonators [G. P. Karman et al., Nature (London) 402, 138 (1999)].

Turbulent flows disperse Lagrangian particles resulting in the growth of pairwise separations and, for sets of three or more particles, in a nontrivial dynamics of their configuration. The shape of such clusters is controlled by the competition between coherent straining of the cluster and the independent random motion of the particles due to small scale velocity fluctuations. We introduce a statistical description of the geometry of the Lagrangian clusters and predict a self-similar distribution of shapes, which should be observable in the inertial range of scales in high Reynolds numbers flows.

A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are found to play a dominant role. For untwisted scroll waves, modulations in the third dimension have stabilizing or destabilizing effects on the different modes depending on the parameter regimes, in partial agreement with previous predictions. The influence of twist on the different branches is investigated. In particular, the sproing instability is seen to arise from the twist-induced deformation of the translation branches above a threshold twist.

While previous studies of continuous emission of drops from a faucet have shown the richness of the system's nonlinear response, a theory of dripping has heretofore been lacking. Long-time behavior of dripping is simulated computationally by tracking the formation of up to several hundred drops in a sequence, rather than the usual single drop, at a given flow rate $Q$ and verified by experiments. As $Q$ increases, the system evolves from a period-1 system through a number of period doubling (halving) bifurcations as dripping ultimately gives way to jetting. That hysteresis can occur is also demonstrated.

We report the effect of interstitial fluid on the extent of segregation by imaging the pile that results after bidisperse color-coded particles are poured into a silo. Segregation is sharply reduced and preferential clumping of small particles is observed when a small volume fraction of fluid $V_f$ is added. We find that viscous forces in addition to capillary forces have an important effect on the extent of segregation $s$ and the angle of repose $\theta$. We show that the sharp initial change and the subsequent saturation in $s$ and $\theta$ occurs over similar $V_f$. We also find that a transition back to segregation can occur when the particles are completely immersed in a fluid at low viscosities.

Water bells appear when a cylindrical liquid jet impacts normally onto a disk of similar diameter. First observed and described experimentally by F. Savart, their stationary shape was analytically obtained by J. Boussinesq. Here we consider the stability of these bells and derive a general stability criterion showing their sensitivity both to the pressure difference across the liquid sheet and to the ejection angle from the impacting disk. In this later case, we find a critical angle of ejection above which the bell is periodically destroyed and created.

A Comment on the Letter by U. Leonhardt and P. Piwnicki, Phys. Rev. Lett. 84, 822 (2000). The authors of the Letter offer a Reply.

A Reply to the Comment by Matt Visser.

The propagation of material interfaces is investigated under the action of a localized moving source which deposits or removes material. Among others the latter process applies to beam cutting techniques. We develop a Kuramoto-Sivashinsky–type model and find a new type of ripple forming mechanism. This theory offers a new explanation for the occurrence of striation patterns which often degrade the quality of cutting edges.

We show analytically, numerically, and experimentally that a transversely stable one-dimensional $\left[\right(1+1\left)D\right]$ bright Kerr soliton can exist in a 3D bulk medium. The transverse instability of the soliton is completely eliminated if it is made sufficiently incoherent along the transverse dimension. We derive a criterion for the threshold of transverse instability that links the nonlinearity to the largest transverse correlation distance for which the 1D soliton is stable.

The methodology developed provides for a systematic way to find an infinite number of the novel stable bright and dark “soliton islands” in a “sea of solitary waves” of the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain or absorption. It is shown that solitons exist only under certain conditions and the parameter functions describing dispersion, nonlinearity, and gain or absorption inhomogeneities cannot be chosen independently. Fundamental soliton management regimes are discovered.

We describe a nonlinear optical system that supports spiral pattern solutions in the field intensity. This new spatial structure is found to bifurcate above a secondary instability in the internally pumped optical parametric oscillator. The analytical predictions of threshold and spatial scale for the instability are supplemented by detailed numerical investigations of the formation of spiral patterns.

We study an area preserving parabolic map which emerges from the Poincaré map of a billiard particle inside an elongated triangle. We provide numerical evidence that the motion is ergodic and mixing. Moreover, when considered on the cylinder, the motion appears to follow a Gaussian diffusive process.