We investigate the influence of dispersion on parametric solitary waves. We show that dispersion is responsible for a transition towards a new type of dynamical solitary wave characterized by the presence of traveling phase defect arrays within their envelopes. The transition is described analytically through an original extension of the Kolmogorov-Petrovskii-Piskunov approach to front propagation into unstable states.

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.

We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power-law distribution of resonance widths and a power-law dependence of conductance increments apparently reflecting the classical dwell time exponent, in striking difference to the case of a fully chaotic phase space. Surprisingly, these power laws appear on energy scales below the mean level spacing, in contrast to semiclassical expectations.

We report the temporal characteristics of laser radiation transmitted through impulsively excited ${\mathrm{SF}}_6$ and exhibiting sideband Raman lines. Even without special dispersion control we observed a sequence of compressed fs pulses following with the period of the excited $A_{1g}$ vibrational mode of ${\mathrm{SF}}_6$. The use of both negative and positive group velocity dispersion compensation for the temporal compression was found to be as appropriately efficient. The results prove our new concept of the ultrafast molecular phase modulator.

We develop a quasilinear theory of the 2D Euler equation and derive an integrodifferential equation for the evolution of the coarse-grained vorticity $\overline{\omega }(\mathbf{r},t)$. This equation respects all of the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive an $H$ theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.

The amplitude death phenomenon has been experimentally observed with a pair of thermo-optical oscillators linearly coupled by heat transfer. A parametric analysis has been done and compared with numerical simulations of a time delayed model. The role of the coupling strength is also discussed from experimental and numerical results.

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the nonmonotonic dispersion relation of a ferrofluid.

We report experiments on thermally driven convection in an inclined layer of large aspect ratio in a fluid of Prandtl number $\sigma \approx 1$. We observed a number of new nonlinear, mostly spatiotemporally chaotic, states. At small angles of inclination we found longitudinal rolls, subharmonic oscillations, Busse oscillations, undulation chaos, and crawling rolls. At larger angles, in the vicinity of the transition from buoyancy- to shear-driven instability, we observed drifting transverse rolls, localized bursts, and drifting bimodals. For angles past vertical, when heated from above, we found drifting transverse rolls and switching diamond panes.

We establish the equivalence of 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.

A general method is presented for the analysis of the asynchronous state in networks of identical, all-to-all coupled, limit-cycle oscillators of arbitrary dimension and with arbitrarily strong coupling. It is shown that, with strong coupling, this state can be destabilized in directions orthogonal to the limit cycle, which may change the units' behavior qualitatively. An example, involving integrate and fire neurons with spike adaptation, exhibits a bifurcation to a synchronized bursting state for strong feedback coupling. The analysis can account for transitions that cannot be studied in the commonly used phase-coupled approximation.

A new phenomenon associated with a nonlinear interaction of optically excited space charge waves has been discovered in photorefractive crystals of the sillenite family. This interaction provides a spatial rectification of the electric field of the space charge waves and leads to a temporally oscillating, but spatially homogeneous electric field of the order of $50–60\mathrm{V}/\mathrm{cm}$ which is detected by a probe beam via the electro-optic effect. Taking into account that the displacement current plays an important role, we demonstrate a very good agreement between the experimental data and the suggested theoretical model.

We demonstrate the noise-induced amplification of a weak periodic signal inscribed in the coherence of a two-level atom, interacting with a single mode of the quantized radiation field coupled to a dissipative environment.

We investigate the dynamic evolution of jamming in granular media through fluctuations in the granular drag force. The successive collapse and formation of jammed states give a stick-slip nature to the fluctuations which is independent of the contact surface between the grains and the dragged object, thus implying that the stress-induced collapse is nucleated in the bulk of the granular sample. We also find that while the fluctuations are periodic at small depths, they become “stepped” at large depths, a transition which we interpret as a consequence of the long-range nature of the force chains.

We observe ripples forming on the surface of a granular powder in a container submitted from below to a series of brief and distinct shocks. After a few taps, the pattern turns out to be stable against any further shock of the same amplitude. We find that the wavelength of the pattern is proportional to the amplitude of the shocks. Starting from considerations involving air flow through the porous granulate and avalanche properties, we build up a semiquantitative model which satisfactorily fits the set of experimental observations of either tapped or blown powder.

The effects of viscous heating on the stability of Taylor-Couette flow were investigated through flow visualization experiments for Newtonian and viscoelastic fluids. For highly viscous Newtonian fluids, viscous heating drives a transition to a new, oscillatory mode of instability at a critical Reynolds number significantly below that at which the inertial transition is observed in isothermal flows. The effects of viscous heating may explain the discrepancies between the observed and predicted critical conditions and the symmetry of the disturbance flow for viscoelastic instabilities.

We investigate the effect of drag force on the enstrophy cascade of two-dimensional Navier-Stokes turbulence. We find a power law decrease of the energy wave number $\left(k\right)$ spectrum that is faster than the classical (no-drag) prediction of $k^{-3\mathrm{}}$. It is shown that the enstrophy cascade with drag can be analyzed by making use of a previous theory for finite lifetime passive scalars advected by a Lagrangian chaotic fluid flow. Using this we relate the power law exponent of the energy wave number spectrum to the distribution of finite time Lyapunov exponents and the drag coefficient.

The possibility of observing superluminal behavior in the propagation of localized microwaves over distances of tens of wavelengths is experimentally demonstrated. These types of waves, better than the evanescent modes of tunneling, can contribute to answering the question on the luminal limit of the signal velocity.

We have demonstrated small signal gain saturation on several transient-gain Ni-like ion x-ray lasers by using a high-power, chirped-pulse amplification, tabletop laser. These results have been achieved at wavelengths from 139–203 Å using a total of 5–7 J energy in a traveling-wave excitation scheme. Strong amplification is also observed for Ni-like Sn at 119 Å. Gain of $62{\mathrm{cm}}^{-1\mathrm{}}$ and gL product of 18 are determined on the $4d\to 4p$ transition for Ni-like Pd at 147 Å with an output energy of $12\mu \mathrm{J}$. A systematic evaluation of the laser driver parameters yields optimum beam divergence and small deflection angles of 2–5 mrads, in good agreement with simulations.

Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation to oscillating hexagons the dynamics are well described by a single complex Ginzburg-Landau equation (CGLE) coupled to the phases of the hexagonal pattern. At the band center these equations reduce to the usual CGLE and the system exhibits defect chaos. Away from the band center a transition to a frozen vortex state is found.