We discuss a general mechanism explaining the taming effect of phase disorder in external forces on chaotic solitons in damped, driven, Frenkel-Kontorova chains. We deduce analytically an effective random equation of motion governing the dynamics of the soliton center of mass for which we obtain numerically the regions in the control parameter space where chaotic solitons are suppressed. We find that such predictions are in excellent agreement with results of computer simulations of the original Frenkel-Kontorova chains. We show theoretically how such a fundamental mechanism explains recent numerical results concerning extended chaos in arrays of coupled pendula [S. F. Brandt et al., Phys. Rev. Lett. 96, 034104 (2006)].

Coherent nondispersive structures are known to play a crucial role in explaining transport in nonautonomous dynamical systems such as ocean flows. These structures are difficult to extract from model output as they are Lagrangian by nature and not revealed by the underlying Eulerian velocity fields. In the last few years heuristic concepts such as finite-time Lyapunov exponents have been used in an attempt to detect barriers to oceanic transport and thus identify regions that trap material such as nutrients and phytoplankton. In this Letter we pursue a novel, more direct approach to uncover coherent regions in the surface ocean using high-resolution model velocity data. Our method is based upon numerically constructing a transfer operator that controls the surface transport of particles over a short period. We apply our technique to the polar latitudes of the Southern Ocean.

We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.

We present data on the pinch-off and coalescence of thin liquid alkane lenses floating on water. Pinch-off in quasi-2D lenses is distinctly different from pinch-off in axisymmetric 3D drops and involves a cascade of satellite droplets which extends to micron length scales. In contrast, coalescence of lenses is qualitatively similar to coalescence of 3D drops. Coalescence is predicted to involve entrainment of the exterior fluid as the droplets merge. This reentrant folding is obscured in 3D droplets but is clearly visible in coalescence of thin lenses.

We report on saturated absorption in a hollow-core photonic band-gap fiber filled with ${}^{12}\mathrm{C}_2{\mathrm{H}}_2$ molecules. We find that slow molecules provide a major contribution to the signal in the limit of low optical power and low pressure where the signal deviates significantly from the usual Lorentzian line shape. In particular, we observe a linewidth reduction of about 3 times as compared to the transit-time limited linewidth.

We report the first theoretical prediction and experimental demonstration of gap soliton trains in a self-defocusing photonic lattice. Without a priori spectral or phase engineering, a stripe beam whose spatial power spectrum lies only in one transverse direction evolves into a gap soliton train with power spectrum growing also in the orthogonal direction due to nonlinear transport and spectrum reshaping. Our results suggest that, in nonlinear $k$-space evolution, energy can transfer not only between regions of normal and anomalous diffraction, but also from initially excited regions to initially unexcited regions.

We performed optical pulse propagation experiments in a system in which two ultrahigh-$Q$ silica microspheres of different diameters were coupled in tandem to a fiber taper to yield coupled-resonator-induced transparency. Nearly Gaussian-shaped optical pulses propagated with a large positive delay of 8.5 ns through a transparent frequency window, without significant attenuation, amplification, or pulse deformation, demonstrating classical analogy of the extremely slow light obtained with electromagnetically induced transparency.

Both bright and dark traveling, locked, intrinsic localized modes (ILMs) have been generated with a spatially uniform driver at a frequency in the acoustic spectrum of a nonlinear micromechanical cantilever array. Complementary numerical simulations show that a minimum density of modes, hence array size, is required for the formation of such locked smoothly running excitations. Additional simulations on a small 1D antiferromagnetic spin system are used to illustrate that such uniformly driven running ILMs should be a generic feature of a nanoscale atomic lattice.

We demonstrate by electronic circuit experiments the feasibility of an unstable control loop to stabilize torsion-free orbits by time-delayed feedback control. Corresponding analytical normal form calculations and numerical simulations reveal a severe dependence of the basin of attraction on the particular coupling scheme of the control force. Such theoretical predictions are confirmed by the experiments and emphasize the importance of the coupling scheme for the global control performance.

The opening motion of a bileaflet valve driven by a pulsed stream is studied in the limiting condition of rigid massless leaflets closing a two-dimensional channel. This simple arrangement allows us to write simple dynamical equations for the solid that are solved numerically with the Navier-Stokes equation for the fluid. The analysis is focused on the influence of asymmetry on the coupled fluid-valve dynamics when parameters are taken with references to cardiac valves. Results show that the wake generation from the leaflet’s trailing edge can be partly inhibited; the primary vortex downstream does not occur in an intermediate range of asymmetry. The potential emergence of such a phenomenon in realistic cases would present implications in development of diagnostic schemes.

The structure of discrete resonances in water wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds of millions) even in a comparatively small spectral domain when both scale and angle energy transport is taken into account. It is also shown that angle transport can contribute inexplicitly to scale transport. Restrictions for quasiresonance to start are written out. The general approach can be applied directly to mesoscopic systems encountered in condensed matter (quantum dots), medical physics, etc.

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the interface between a dielectric medium (air) and a nonlinear material with a very long-range nonlocal response. These surface solitons are always attracted toward the surface, and unlike their Kerr-like counterparts, they do not exhibit a power threshold.

We sketch a rigorous derivation of Fourier’s law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile.

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples “restricted Euler” (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.

In this Letter we report observations of optically induced self-organization of colloidal arrays in the presence of unpatterned counterpropagating evanescent waves. The colloidal arrays formed along the laser propagation axis are shown to be linked to the breakup of the incident field into optical spatial solitons, the lateral spacing of the arrays being related to modulation instability of the soft condensed matter system.

We investigate the dynamics of a system of coupled electron billiards by using a magnetic field to dramatically modify the underlying mixed phase space. At specific values of the magnetic field the sea of chaos is drained. At these fields there exist reflected or transmitted orbits associated with maxima and minima in the experimentally observed magnetoresistance. These effects are studied by comparing the classical and quantum-mechanical phase-space dynamics leading to a basic understanding of the role of chaos in the transport in an array of billiards.

We theoretically investigate the high-order harmonic generation in a helium atom with a two-color optical field synthesized by an intense 6 fs pulse at 800 nm and a relatively weak 21.3 fs pulse at 400 nm. When the frequency-doubled pulse is properly time shifted with respect to the fundamental pulse, an ultrabroad extreme ultraviolet supercontinuum spectrum with a 148 eV spectral width can be generated which directly creates an isolated 65 as pulse even without phase compensation. We explain this extraordinary phenomenon by analyzing maximum electron kinetic energies at different return times.

Shock wave induced cavitation experiments and atomic force microscopy measurements of flat polyamide and hydrophobized silicon surfaces immersed in water are performed. It is shown that surface nanobubbles, present on these surfaces, do not act as nucleation sites for cavitation bubbles, in contrast to the expectation. This implies that surface nanobubbles are not just stable under ambient conditions but also under enormous reduction of the liquid pressure down to $-6\mathrm{MPa}$. We denote this feature as superstability.

Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of $O(1)$ streaks, $O(R^{-1})$ streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number $R$. Higher harmonics become negligible. These unstable lower branch states appear to have a single unstable eigenvalue at all Reynolds numbers. These results suggest that lower branch coherent states control transition to turbulence and that they may be promising targets for new turbulence prevention strategies.

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome of numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. Finally, the effects on the flow behavior of the channel symmetry and aspect ratio are also investigated.