We propose a new algorithm to control frictional dynamics of a small array of particles towards preassigned values of the average sliding velocity. The control is based on the concepts of non-Lipschitzian dynamics and terminal attractor. Extensive numerical simulations illustrate the robustness, efficiency, and convenience of the algorithm.

We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.

We demonstrate the phenomenon of directed diffusion in a symmetric periodic potential. This has been realized with cold atoms in a one-dimensional dissipative optical lattice. The stochastic process of optical pumping leads to a diffusive dynamics of the atoms through the periodic structure, while a zero-mean force which breaks the temporal symmetry of the system is applied by phase modulating one of the lattice beams. The atoms are set into directed motion as a result of the breaking of the temporal symmetry of the system.

We measure structure functions and structures in uniformly sheared strong turbulence using an array of hot-wire velocity sensors. We find that the large-scale shear persists down to the smallest scales. There is a marked asymmetry between velocity increments measured in the shear direction, and those measured in the plane perpendicular to it. In the shear direction the scaling exponents tend to a constant, signifying the presence of small-scale cliffs. Direct evidence for those is presented by the spatial structure of the strongest velocity gradients.

A theoretical study of linear wave scattering by time-periodic spatially localized excitations (discrete breathers) is presented. A peculiar effect of total reflection occurs due to a Fano resonance when a localized state originating from closed channels resonates with the open channel. For the discrete nonlinear Schrödinger chain, we give an analytical result for the frequency dependence of the transmission coefficient, including the possibility of resonant reflection. We extend the analysis to chains of weakly coupled anharmonic oscillators and discuss the relevance of the effect for electronic transport spectroscopy of mesoscopic systems.

This Letter describes dynamic self-assembly in a system of stainless steel spheres ($\sim 1\mathrm{m}\mathrm{m}$ in diameter) rolling on a flat dielectric surface under the influence of an external magnetic field that rotates parallel to the plane of the surface. As the spheres move, they charge triboelectrically. Self-assembly is mediated by two types of electrostatic interactions among these charges: (i) attraction between negatively charged regions of the surface and positively charged spheres and (ii) repulsion between the like-charged spheres. The spheres organize into highly ordered rings as a result of these electrostatic interactions.

Layered heterostructures combining ordinary and negative refractive index materials are shown to display a new type of photonic band gap corresponding to zero (volume) averaged refractive index. Distinct from band gaps induced by Bragg scattering, the zero-$\overline{n}$ gap is invariant upon a change of scale length and is insensitive to disorder that is symmetric in the random variable. A metallic structure that exhibits such a band gap is explicitly designed, and its properties are calculated with accurate finite difference time domain simulations.

We have observed enhanced fluorescence and laser emission due to a photonic defect mode in a dye doped cholesteric polymer network. The defect is caused by a phase jump of the cholesteric helix at the interface of two stacked layers of a cholesteric polymer film. Fluorescence spectra show an additional resonant mode inside the photonic stop band. Pulsed excitation gives rise to laser emission of the defect mode, with an exceptionally low lasing threshold. The defect mode emission has a circular polarization whose sense of rotation is opposite to that of the cholesteric helix.

We present a generalized Fokker-Planck equation for the joint position-velocity probability distribution of a single fluid particle in a turbulent flow. Based on a simple estimate, the diffusion term is related to the two-point two-time Eulerian acceleration-acceleration correlation. Dimensional analysis yields a velocity increment probability distribution with normal scaling $v\approx t^{1/2}$. However, the statistics need not be Gaussian.

We show that the complete characterization of arbitrarily short isolated attosecond x-ray pulses can be achieved by applying spectral shearing interferometry to photoelectron wave packets. These wave packets are coherently produced through the photoionization of atoms by two time-delayed replicas of the x-ray pulse, and are shifted in energy with respect to each other by simultaneously applying a strong laser field. The x-ray pulse is reconstructed with the algorithm developed for optical pulses, which requires no knowledge of ionization physics. Using a 800-nm shearing field, x-ray pulses shorter than $\sim 400\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{c}$ can be fully characterized.

Large amplitude multiphase solutions of the periodic Korteweg–de Vries equation are excited and controlled by a small forcing. The approach uses passage through an ensemble of resonances and subsequent multiphase self-locking of the system with eikonal-type perturbations. The synchronization of each phase in the Korteweg–de Vries wave is robust, provided the corresponding driving amplitude exceeds a threshold.

We report free-surface waves in granular flows near boundaries in an inclined chute. The chevron-shaped traveling waves spontaneously develop at inclinations close to the angle of repose for both steady and accelerating flows. Two distinct regimes are characterized by internal angle and frequency variations. Experimental measurements indicate that subsurface circulation driven by velocity gradients near frictional walls plays a central role in the pattern formation mechanism, suggesting that wave generation is controlled by the granular analog of a fluid boundary layer.

Local convective heat flux in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one convection cell filled with water. It is found that fluctuations of the vertical heat flux are highly intermittent and are determined primarily by the thermal plumes in the system. The experiment reveals a unique mechanism for the heat transport in turbulent convection.

The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the instability, using elementary geometry and the physics of bending and stretching. Our main result is a set of simple scaling laws; the wavelength of the wrinkles $\lambda \sim K^{-1/4}$, where $K$ is the stiffness due to an “elastic substrate” effect with a multitude of origins, and the amplitude of the wrinkle $A\sim \lambda$. These could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.

A critical interplay of two correlated noises in a nonlinear symmetrical two-well potential system is experimentally demonstrated. One state can become completely noise free, leading to an infinite Kramers time. If an independent lever breaks the potential symmetry, stochastic resonance is recovered. In this new regime, we obtain a plateau, i.e., a high signal-to-noise ratio even for vanishing forcing signals.

Laser action on a single spatially chaotic wave function is obtained as a final stable state in a nonlinear dynamical model of a stadium shaped resonant cavity with an active medium. The stable single-mode lasing state corresponds to a particular metastable resonance of the cavity which wins a competition among multiple modes with positive net linear gain and has a distinct lasing threshold.

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized “phase” one encounters two different scenarios: For moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously.

A shadow is an exact solution to a chaotic system of equations that remains close to a numerically computed solution for a long time. Using a variable-order, variable–time-step integrator, we numerically compute solutions to a gravitational $N$-body problem in which many particles move and interact in a fixed potential. We then search for shadows of these solutions with the longest possible duration. We find that in “softened” potentials, shadow durations are sufficiently long for significant evolution to occur. However, in unsoftened potentials, shadow durations are typically very short.

Femtosecond light pulses interacting with solids are studied. With a power close to the self-focusing threshold, an optical pulse evolves like a solitary wave with a temporal duration shrunk to a few femtoseconds through the defocusing action of multiphoton ionization. Self-steepening and space-time focusing are shown to form shock profiles, which do not prevent the pulse from keeping a shorter duration over one Rayleigh length. Theoretical estimates justify the key mechanisms leading to pulse compression, whose influence on the power spectra is finally discussed.

Band-gap structure of periodic waveguide arrays is investigated in the linear and the nonlinear regimes. Excitation of array modes belonging to high bands is demonstrated. Floquet-Bloch solitons are demonstrated experimentally and shown to be a generalization of discrete solitons.