Theoretical results show that the drag on a bubble can be modified by the presence of isotropic, homogeneous, broadband acoustic noise, when the band overlaps the bubble's resonance width. While these results constitute an acoustic analog to the Einstein-Hopf drag on an oscillating dipole in the presence of electromagnetic fluctuations, an important difference is that band-limited acoustic noise can reduce the drag when the lower frequency of the spectrum coincides with the resonant frequency of the bubble. Applications to bubble migration, heat transfer, and acoustophoresis are suggested.

The process of heat conduction in a chain with a periodic potential of nearest-neighbor interaction is investigated by means of molecular dynamics simulation. It is demonstrated that the periodic potential of nearest-neighbor interaction allows one to obtain normal heat conductivity in an isolated one-dimensional chain with conserved momentum. The system exhibits a transition from infinite to normal heat conductivity with the growth of its temperature. The physical reason for normal heat conductivity is the excitation of high-frequency stationary localized rotational modes. These modes absorb the momentum and facilitate locking of the heat flux.

The statistical properties of a scalar field advected by the nonintermittent Navier-Stokes flow arising from a two-dimensional inverse energy cascade are investigated. The universality properties of the scalar field are probed by comparing the results obtained with two types of injection mechanisms. Scaling properties are shown to be universal, even though anisotropies injected at large scales persist down to the smallest scales and local isotropy is not fully restored. Scalar statistics is strongly intermittent and scaling exponents saturate to a constant for sufficiently high orders. This is observed also for the advection by a velocity field rapidly changing in time, pointing to the genericity of the phenomenon.

In this Letter, we discuss the effect of slow real modes in reaction-diffusion systems close to a supercritical Hopf bifurcation. The spatiotemporal effects of the slow mode cannot be captured by traditional descriptions in terms of a single complex Ginzburg-Landau equation (CGLE). We show that the slow mode coupling to the CGLE introduces a novel set of finite wavelength instabilities not present in the CGLE. For spiral waves, these instabilities highly affect the location of regions for convective and absolute instability. These new instability boundaries are consistent with transitions to spatiotemporal chaos found by simulation of the corresponding coupled amplitude equations.

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique that is a combination of time delay and spatial embedding. This embedding allows us to identify the local character of the equations of motion. Based on this method we present an approximate estimate of the entropy density by the correlation integral.

Spontaneous emission in photonic crystals with anisotropic three-dimensional dispersion relation is studied. If the upper level is below a characteristic frequency ${\omega }_1$, or above ${\omega }_2$, or between ${\omega }_1$ and ${\omega }_2$, the radiation is a localized field with a frequency in the band gap, or a propagating field with a frquency in the band, or a diffusion field, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is small compared to that in an ordinary vacuum or in one- or two-dimensional photonic crystals due to lower density of states.

We have experimentally observed the eigenmode splitting due to coupling of the evanescent defect modes in three-dimensional photonic crystals. The splitting was well explained with a theory based on the classical wave analog of the tight-binding (TB) formalism in solid state physics. The experimental results were used to extract the TB parameters. A new type of waveguiding in a photonic crystal was demonstrated experimentally. A complete transmission was achieved throughout the entire waveguiding band. We have also obtained the dispersion relation for the waveguiding band of the coupled periodic defects from the transmission-phase measurements and from the TB calculations.

We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1D nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase jumps. Our conclusions are confirmed by the analysis of two variants of this model.

A lattice-Boltzmann method has been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a continuous parameter, specified at each node and representing the fluid volume fraction associated with that node, we obtain second-order accuracy for boundaries at arbitrary positions and orientations with respect to the grid. The method does not require surface normals, and can therefore be applied to irregular geometries such as porous media. The new rules conserve mass and momentum, and reduce to the link bounce-back rule at aligned interfaces.

Adiabatic variation of the parameters of a chaotic system results in a fluctuating reaction force. The quantum analog of a classical dissipative force, proportional to the time integral of the force-force correlation function, vanishes. We study this quantum-classical crossover for random matrix models. For the Gaussian unitary ensemble the crossover is found to take place on the Heisenberg time scale and the finite time integral practically vanishes for longer times. For the Gaussian orthogonal case, there is no such time scale and the integral falls off inversely proportional to time.

Spatiotemporal time series are analyzed and predicted using reconstructed local states. As numerical examples the evolution of a Kuramoto-Sivashinsky equation and a coupled map lattice are predicted from previously sampled data.

We propose and illustrate in the context of the semiconductor laser that, in nonequilibrium fermionic systems with sources and sinks, the family of finite flux stationary solutions of the quantum Boltzmann equation is central and more important then the zero flux Fermi-Dirac spectrum. We present the quantum analog of the finite flux Kolmogorov spectra which are central to understanding nonequilibrium classical systems such as high Reynolds number hydrodynamics and the wave turbulence encountered in water waves, plasmas, and optics. In particular, we show how semiconductor laser efficiency can be improved by maximizing the flux of carriers (electrons and holes) towards the lasing frequencies.

Intrinsic bistability and hysteresis have been observed in the photoluminescence of bulk glass doped with ${\mathrm{Yb}}^{3+}$ and ${\mathrm{Tm}}^{3+}$ impurities at room temperature. Multiple instabilities also occur in channel waveguide lasers in this material. Consequently, local field effects exhibit more degrees of freedom than expected and have important implications for compact optical amplifiers and oscillators.

We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

“Light bullets” are multidimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multidimensional generalization of the one-dimensional sine-Gordon soliton.

Pattern selection, occurring when a nonuniform state of a nonlinear dissipative system propagates into an initially unstable, homogeneous basic state is reconsidered by application of the causality principle. In particular, the nonlinear marginal stability criterion that determines the selection of a nonlinear front solution is replaced by an exact general necessary condition that has never been considered before. The demonstration is based on the causal signaling problem derived in the context of plasma physics.

We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical transition point in its development (the decoherence transition). For asymmetric systems we also describe a migration of unstable periodic orbits that is of central importance in understanding these systems. Our framework provides an experimentally measurable transition, even in situations where previously described bifurcation structures are inapplicable.

We report the first experimental evidence of coherent backscattering enhancement for transient elastic waves propagating in a two-dimensional chaotic cavity. The time-integrated squared amplitude at the point source is twice as large as at the other points around the source. Contrary to analogous optical experiments, this effect is already clearly observable on a single realization. Especially, the spatial shape of the coherent backscattering enhancement is well predicted by a generalization of the existing theory.

Probability density functions of the enstrophy flux in two dimensional grid turbulence are found to be strongly non-Gaussian and can be mimicked by stretched exponential functions. Evidence of this behavior is found in experiments using turbulent soap films and numerical simulations. The enstrophy flux itself is found to be constant for a range of scales corresponding to the enstrophy cascade.

The evolution of axisymmetric equilibrium shapes of a rigidly rotating liquid drop can be extended beyond the 2-lobed shape bifurcation point if the rotating drop is driven in the $n=2\mathrm{}$ axisymmetric shape oscillation (perturbation), where $n$ is the mode of oscillation. A reason for the extended stability of the perturbed rotating drop is that the inertia of the driven axisymmetric shape oscillation suppresses growth of a natural nonaxisymmetric shape fluctuation which leads to the 2-lobed shape bifurcation. The axisymmetric shape of the drop eventually bifurcates into either a 2- or a 3-lobed shape at a higher bifurcation point which is asserted to be the 3-lobed shape bifurcation point.