New results are presented for the energy spectra of decaying 2D turbulence in a square container with no-slip walls for integral-scale Reynolds numbers up to 20 000. The one-dimensional energy spectra measured close to the walls reveal a $k^{-5\mathrm{}/3}$ inertial range, instead of a $k^{-3\mathrm{}}$ direct enstrophy cascade, due to the production of small-scale vorticity near no-slip boundaries. During the intermediate decay stage a $k^{-3\mathrm{}}$ spectrum starts to emerge and the change in location of the injection scale of small-scale vorticity is explained in terms of an average boundary-layer thickness.

We study the motion of a phase transition (PT) front at a constant temperature between stable and metastable states in fluids with the van der Waals equation of state. We focus on a case of relatively large metastability and low viscosity, when no steadily moving PT front exists. Simulating the one-dimensional hydrodynamic equations, we find that the PT front generates acoustic shocks in forward and backward directions. Through this mechanism, the nonsteady PT front drops its velocity and eventually stops. The shock wave may shuttle between the PT front and the system's edge, rarefaction waves appearing in the shuttle process. If the viscosity is below a certain threshold, a turbulent state sets in.

We study the Saffman-Taylor or viscous fingering instability in yield stress fluids. The theory for yield stress fluids shows that the dispersion equation of the instability is similar to that for Newtonian fluids; however, the capillary number governing the instability now contains the yield stress. Experiments using gels and foams reveal very branched fingers in the gel. The results are in excellent agreement with theory for the gel, with, in addition, a crossover from yield stress dominated to viscous behavior. The results for foams are very different due to the existence of wall slip.

We show that the transition between fixed points in a separable dynamical system is fully described by an invariant integral. We discuss in detail the case of a system with two temporal variables with bilinear coupling, where the new stable state is attained asymptotically through spiraling into the fixed point. Through the invariance, it is possible to establish conditions for the control parameter that permit a (targeted) transition in finite time and without relaxation oscillations.

We demonstrate time-resolved measurement of optical phase-space distributions as a new probe for investigating the propagation of light in disordered media. Phase-space techniques measure the joint transverse position and momentum distribution of the scattered light, and are sensitive to the spatially varying phase and amplitude of the field. Using this method we investigate light backscattered from a random medium. The measurements indicate that the weakly localized component is a phase conjugate of the incident light field. A new model of backscatter, based on Wigner phase-space distributions, elucidates the spatial and angular behavior of the localized and unlocalized components.

A model to simulate the phenomenon of random lasing is presented. It couples Maxwell's equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate $P_r^c$ exists for the appearance of the lasing peaks. The number of lasing modes increases with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length $\xi$ and average mode length $L_m$.

We present the observation of critical coupling in a high- $Q$ fused-silica microsphere whispering-gallery mode resonator coupled to a fiber taper. Extremely efficient and controlled power transfer to high- $Q$ $\left(\sim {10}^7\right)$ resonators has been demonstrated. Off-resonance scattering loss was measured to be less than $0.3\%$. On-resonance extinction in transmitted optical power through the fiber coupler was measured as high as 26 dB at the critical coupling point. This result opens up a range of new applications in fields as diverse as near-field sensing and quantum optics.

We report a direct experimental observation and provide a theory of the distribution of trajectories along which a fluctuating system moves over a potential barrier in escape from a metastable state. The experimental results are obtained for a semiconductor laser with optical feedback. The distribution of paths displays a distinct peak, which shows how the escaping system is most likely to move. We argue that the specific features of this distribution may give an insight into the nature of dropout events in lasers.

We find a new type of optical vector soliton that originates from trapping of a dipole mode by the soliton-induced waveguides. These solitons, which appear as a consequence of the vector nature of the two-component system, are more stable than the previously found optical vortex solitons and represent a new type of extremely robust nonlinear vector structure.

The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We describe periodic coherent structures of the CGLE, called modulated amplitude waves (MAWs). MAWs of various periods $P$ occur in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures evolve towards defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.

Self-adjusting, or adaptive, systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.

A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number ( $k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for all $k$ BCs is exactly equivalent to that of the renormalized QAM (with Planck's constant ${ħ}^{\prime }=ħ/k$) at some fixed BCs that can be of four types. The quantum cat maps are, up to time reversal, fixed points of the renormalization transformation. Several results at fixed BCs, in particular the existence of a complete basis of “crystalline” eigenstates in a classical limit, can then be derived and understood in a simple and transparent way in the general-BCs framework.

We investigate the diffusion generated deterministically by periodic iterated maps that are defined by $x_{t+1\mathrm{}}{=x}_t{+ax}_t^z\exp [-({b/x}_t{)}^{z-1\mathrm{}}]$, $z>\mathrm{}1\mathrm{}$. It is shown that the obtained mean squared displacement grows asymptotically as ${\sigma }^2\left(t\right)\sim {ln}^{1/(z-1\mathrm{})}\left(t\right)$ and that the corresponding propagator decays exponentially with the scaling variable $|x|/\sqrt{{\sigma }^2\left(t\right)}$. This strong diffusional anomaly stems from the anomalously broad distribution of waiting times in the corresponding random walk process and leads to a behavior obtained for diffusion in the presence of random local fields. A scaling approach is introduced which connects the explicit form of the maps to the mean squared displacement.

An efficient approach to the calculation of the $\epsilon$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations are larger than a certain threshold $\epsilon$, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of our method with respect to the usual one are shown by the examples of a deterministic map and a self-affine stochastic process.

We have observed optical patterns in GaAs/GaAlAs vertical-cavity microresonators. Rolls, rhombs, or hexagons were obtained depending on the wavelength detuning. We show that cavity thickness fluctuations contribute to pattern selection.

Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.

We study a two-dimensional granular gas of inelastic spheres subject to multiplicative driving proportional to a power $|v\left(\mathit{x}\right){|}^{\delta }$ of the local particle velocity $v\left(\mathit{x}\right)$. The steady state properties of the model are examined for different values of $\delta$, and compared with the homogeneous case $\delta =0\mathrm{}$. A driving linearly proportional to $v\left(\mathit{x}\right)$ seems to reproduce some experimental observations which could not be reproduced by a homogeneous driving. Furthermore, we obtain that the system can be homogenized even for strong dissipation, if a driving inversely proportional to the velocity is used.

We study the time until a filter becomes clogged due to the trapping of suspended particles as they pass through a porous medium. This trapping progressively impedes and eventually stops the flow of the carrier fluid. We develop a simple description for the pore geometry and the motion of the suspended particles which, together with extreme-value statistics, predicts that the distribution of times until a filter clogs has a power-law long-time tail, with an infinite mean clogging time. These results and its consequences are in accord with simulations on a square lattice porous network.

The phase velocity transform (PVT) is an integral transform that divides a function of space and time into components that propagate at uniform phase velocities without distortion. This paper examines the PVT as a method to analyze spatiotemporal fluctuation data. The transform is extended to systems with discretely sampled data on a periodic domain, and applied to data from eight azimuthally distributed probes on the Sustained Spheromak Physics Experiment (SSPX). This reveals features not shown by Fourier analysis, particularly regarding nonsinusoidal mode structure.

A nonadiabatic mechanism for pattern formation in parametrically forced systems subjected to a slow periodic modulation of the excitation frequency is proposed and discussed in detail for the case of an optical parametric oscillator. It is demonstrated that nonautonomous dynamics may induce nonadiabatic off-axis emission of down-converted photons even when the signal field is blueshifted from the nearby cavity resonance.