We present an analytical approach to random lasing in a one-dimensional medium, consistent with transfer matrix numerical simulations. It is demonstrated that the lasing threshold is defined by transmission through the passive medium and thus depends exponentially on the size of the system. Lasing in the most efficient regime of strong three-dimensional localization of light is discussed. We argue that the lasing threshold should have anomalously strong fluctuations from probe to probe, in agreement with recent measurements.

We address the problem of heat conduction in 1D nonlinear chains; we show that, acting on the parameter which controls the strength of the on-site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.

Spontaneous decay behaviors from an assembly of atoms (or molecules) in 3D photonic crystals (PC's) with pseudogaps are investigated. Theoretically, a lifetime distribution function for these atoms or molecules is defined to reveal decay kinetics. Our calculations show that quite wide or narrow lifetime distributions can occur for different spread configurations of the atoms (or molecules). The pure PC effect may lead to coexistence of both accelerated and inhibited decay processes. These results provide theoretical clarification for substantial discrepancies in the recent reported experiments.

A micrometer-sized lipid tubule exhibits oscillatory swinging motion under stationary irradiation by a ${\mathrm{Nd}}^{3+}:\mathrm{Y}\mathrm{A}\mathrm{G}$ laser ( $\lambda =1064\mathrm{}\mathrm{nm}$). By choosing an appropriate optical path through an objective lens, the laser can be split into dual beams focused on the same position. Using this splitting, a lipid tubule can be shown to exhibit bistability with regard to the orientation of trapping. Driven by a temperature gradient induced by local photon heating, the trapped lipid tubule shows oscillatory motion between two possible orientations. This oscillatory phenomenon of the lipid tubule is thought to represent the breaking of time-translational symmetry under thermodynamically open conditions.

A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory number statistics for the model of a nonlinear dissipative oscillator. It is shown that the probability distributions and variances of oscillatory number states are strongly transformed in the order-to-chaos transition. A nonclassical, sub-Poissonian statistics of oscillatory excitation numbers is established for chaotic dissipative dynamics in the framework of the Fano factor and Wigner functions. It is proposed to use these results in experimental studies of the quantum dissipative chaos.

Relative dispersion in fully developed turbulence is investigated by means of direct numerical simulations. Lagrangian statistics is found to be compatible with Richardson description although small systematic deviations are found. The value of the Richardson constant is estimated as $C_2\simeq 0.55$, in a close agreement with recent experimental findings [S. Ott and J. Mann, J. Fluid Mech. 422, 207 (2000)]. By means of exit-time statistics it is shown that the deviations from Richardson’s law are a consequence of Eulerian intermittency. The measured Lagrangian scaling exponents require a set of Eulerian structure function exponents ${\zeta }_p$ which are remarkably close to standard ones known for fully developed turbulence.

We experimentally prove that light propagation in a discrete system, i.e., an array of coupled waveguides, exhibits striking anomalies. We show that refraction is restricted to a cone, irrespective of the initial tilt of the beam. Diffraction can be controlled in size and sign by the input conditions. Diffractive beam spreading can even be arrested and diverging light can be focused. The results can be thoroughly theoretically explained.

Recently, the thermal conductivity in disordered chains has attracted a lot of attention, including the discussion of the disorder anharmonic and harmonic chains. A natural problem concerns the higher-dimensional disordered lattice system. This paper gives a 2D harmonic lattice model with missing bond defects. When the defect density is large enough, a temperature gradient builds up and a finite heat conduction is found in this model.

We show theoretically that the waves generated through the generic parametric three- or four-wave-mixing processes exhibit, as a general rule, a hidden coherence characterized by skewed coherence lines along specific space-time trajectories. Our study generalizes the concept of coherence in the sense that these previously unrecognized coherent states cannot be described through the standard definitions of spatial and temporal coherence.

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.

We show, experimentally and numerically, that Ti:sapphire mode-locked lasers can operate in a regime in which they intermittently produce exploding solitons. This happens when the laser operates near a critical point. Explosions happen spontaneously, but external perturbations can trigger them. In stable operation, all explosions have similar features, but are not identical. The characteristics of the explosions depend on the intracavity dispersion.

Single-bubble sonoluminescence is characterized by a great concentration of energy during the collapse of a gas bubble, which leads to the generation of photons from low-frequency ultrasound. The narrow stability domain of sonoluminescence has limited previous attempts to reinforce this inertial confinement in order to generate photons of higher energy or to ignite a nuclear fusion reaction. We present a new experimental approach where an ultrasonic pulse of high frequency is adaptively focused on the bubble during the collapse. Using an array of eight transmitters, a pressure pulse of 0.7 MPa doubles the flash intensity; this technique can easily be extended to higher pressure.

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance $S$ above an unperturbed two-fluid interface. At low withdrawal rates, $Q$, the interface forms a steady state hump and only the upper fluid is withdrawn. When $Q$ is increased (or $S$ decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this discontinuous transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling is used to show that steady-state profiles for humps at different flow rates and tube heights can all be scaled onto a single similarity profile.

The superluminal group velocity of an ultrashort optical Bessel beam pulse is measured over its entire depth of field, corresponding to $\sim 2\times {10}^4$ optical wavelengths. The method used is to measure the traveling ionization front induced by the pulse.

In single-bubble sonoluminescence, repeated brief flashes of light are produced in a gas bubble strongly driven by a periodic acoustic field. A startling hypothesis has been made by Lohse and co-workers [Phys. Rev. Lett. 78, 1359 (1997)] that the non-noble gases in an air bubble undergo chemical reaction into soluble products, leaving only argon. In the present work, this dissociation hypothesis is supported by simulations, although the associated temperatures of about 7000 K seem too low for bremsstrahlung, which has been proposed as the dominant light emission mechanism. This suggests that emission from water vapor and its reaction products, heretofore not included, may play an important role.

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, macroscopic approach offers complete and easy control and allows unprecedented study of optical wave chaos.

A nonlinear equation describing curved stationary flames with arbitrary gas expansion $\theta ={\rho }_{\mathrm{fuel}}/{\rho }_{\mathrm{burnt}}$ is obtained in a closed form without an assumption of weak nonlinearity. The equation respects all conservation laws and takes into account vorticity production in the flame. In the scope of the asymptotic expansion for $\theta \to 1$, the new equation solves the problem of stationary flame propagation with accuracy of the sixth order in $\theta -1\mathrm{}$. Its analytical solutions give the flame velocity in tubes of arbitrary width, which agrees with available results of direct numerical modeling.

An optically injected semiconductor laser can produce excitable multipulses. Homoclinic bifurcation curves confine experimentally accessible regions in parameter space where the laser emits a certain number of pulses after being triggered from its steady state by a single perturbation. This phenomenon is organized by a generic codimension-two homoclinic bifurcation and should also be observable in other systems.

An investigation into the granular temperature distributions of a binary vibrofluidized granular bed has been conducted using positron emission particle tracking. By repeating each experiment with the tracer selected in turn from the two size components, the granular temperature and packing fraction distributions for each phase were determined. It was found that, for a range of size fractions, the granular temperature of the larger particles was higher than that of the smaller diameter grains, a result which was supported by a simple theoretical analysis based on the steady state energy equation.

We report Nusselt number measurements from high Prandtl number turbulent thermal convection experiments. The experiments are conducted in four fluids with the Prandtl number Pr varying from 4 to 1350 and the Rayleigh number Ra from $2\times {10}^7$ to $3\times {10}^{10}$, all in a single convection cell of unity aspect ratio. We find that the measured Nusselt number decreased about $\sim 20\%$ over the range of Pr spanned in the experiment. The measure data are also found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.