We present a simple method, using constant pinnings, to suppress spatiotemporal chaos and achieve global control in coupled map lattice models under different situations, e.g., for uniform pinning, nonuniform pinning with regular or random distributions, and lattices with spatial heterogeneity in local dynamics and coupling strength. The method is easy to implement and does not require any a priori information of the system dynamics or explicit changes in its parameters. This method can also be used for local control of spatiotemporal dynamics, an aspect that has crucial importance in many natural systems.

The idea of the linear combination of atomic orbitals method, well known from the study of electrons, is extended to the classical wave case. The Mie resonances of the isolated scatterer in the classical wave case are analogous to the atomic orbitals in the electronic case. The matrix elements of the two-dimensional tight-binding (TB) Hamiltonian are obtained by fitting to ab initio results. The transferability of the TB model is tested by reproducing accurately the band structure of different 2D lattices, with and without defects, and at two different dielectric contrasts.

We report the experimental observation of a polarization kink or domain wall soliton by mixing two intense counterpropagating laser beams in a nonlinear isotropic dielectric. This soliton represents the switching of the state of polarization of light between two domains where both waves are circularly polarized and corotating. Good agreement is obtained with the theoretical description of the effect.

We report an experimental study of sound propagation in the bulk of a homogeneous flow made of a single intense vortex in air. By using an adaptive-coherent average technique, the mean amplitude and phase of the distorted wave fronts are reconstructed. A large phase shift is observed on the wave fronts on either side of the “shadow” region behind the vortex. The shape of the averaged amplitude, as a function of space coordinates, shows that caustics are also formed in the acoustic field. In a nonstationary flow, these effects make it possible to monitor the vortex strength and position.

We report experimental measurements of the velocity, vorticity, and thickness fields of turbulent flowing soap films using a modified particle-image velocimetry technique. These data yield the turbulent energy and enstrophy of the two-dimensional flows with microscale Reynolds numbers of about 100 and demonstrate the effects of compressibility arising from variations in film thickness. Despite the compressibility of the flow, real-space correlations of velocity, vorticity, and enstrophy flux are consistent with theoretical predictions for two-dimensional turbulence.

The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by these same instabilities in stripe patterns in a vertically oscillated granular layer. Molecular dynamics simulations show that the mechanism of the skew-varicose instability in granular patterns is similar to that in convection. These results suggest that pattern formation in granular media can be described by continuum models analogous to those used in fluid systems.

In this Letter we investigate the response of a confined chain to a harmonic driving force. A model is introduced which mimics recent measurements on friction using surface forces apparatus. The model predicts a critical driving amplitude below which the response is linear. For higher amplitudes the system exhibits a nonlinear behavior and shear thinning. A novel origin for the thinning is proposed which stems from energy dissipation due to stick-slip motion and the transition to smooth sliding. We establish relationships between the microscopic parameters of the system and phenomena observed in rheology and tribology.

The response of a periodically driven nonlinear oscillator slowly passing through resonance has long been suspected but never been shown to be dramatically affected by noise. The slow passage in the presence of noise is studied analytically and experimentally using a periodically modulated laser. Hysteresis in the magnitude of the oscillations of the laser output intensity is produced by sweeping back and forth the modulation frequency near resonance with the laser relaxation oscillations. The area of the hysteresis loop at first increases with the amplitude of the modulation but then exhibits a plateau determined by the noise level.

We consider the nonlinear optics models describing nascent optical bistability and the optical parametric oscillator and study a pattern formation mechanism which relies on the existence of an unstable band of modes which includes the homogeneous or zero mode and originates from the interaction of a Turing (modulational) instability with a saddle-node bifurcation. We identify three regimes in the evolution from an initial unstable field distribution to a final localized stationary pattern which is a unique stripe in the transverse profile of the field inside the cavity. This kinetics has analogies with that of the spinodal decomposition in immiscible mixtures.

Nonlinear Rayleigh waves are considered that propagate along the surface of a homogeneous solid medium covered by a thin film. Their dynamics is described by an evolution equation containing dispersion of the Benjamin-Ono type and a nonlocal nonlinearity. Periodic nonlinear wave solutions are found which become solitary waves in the limit of infinite periodicity. It is shown that these solitary solutions are stable, but unlike the Korteweg–de Vries solitons, they do not survive collisions with each other and therefore are no real solitons.

A novel convection experiment is conducted in a cell with rough upper and lower surfaces. The heat transport across the rough cell is found to be increased by more than 76%. Flow visualization and near-wall temperature measurements reveal new dynamics for the emission of thermal plumes. The discovery of the enhanced heat transport has important applications in engineering and atmospheric convection.

We introduce a new kind of soliton-impurity interaction by examining the phenomena generated by colliding multiple-wave solitons in quadratic nonlinear media with localized perturbations. We examine different models for the impurities and find regimes of soliton self-bouncing, tunneling, and trapping, depending on the impurity type. We show that the transition between the different regimes is governed, e.g., by the soliton energy, and in one of the models we derive a Snell-type law for the process. We propose an optical setting to observe the soliton bouncing predicted.

Experiments for simultaneous horizontal $\left(h\right)$ and vertical $\left(v\right)$ vibration of granular materials show novel flow dynamics. We focus on moderate dimensionless accelerations $0<\mathrm{}{\Gamma }_{h,v}<1.6\mathrm{}$. Phenomena include the spontaneous formation of a static heap at ${\Gamma }_{\mathrm{hs}}\left({\Gamma }_v\right)$ when ${\Gamma }_v<1\mathrm{}$, convective flow for ${\Gamma }_{\mathrm{hc}}>{\Gamma }_{\mathrm{hs}}$, and a novel switching state for frequencies ${\omega }_v\ne {\omega }_h$. A simple friction model provides an approximate, but not exact, description of the steady states and the transition to convection.

Two open containers filled with fluids of different density and connected by a vertical capillary tube can approach their thermodynamical equilibrium via an oscillatory flow. The temporal evolution of flow velocities was measured quantitatively. Data on the critical values determining the flow reversal are extracted yielding a simple dependence of the critical level of heavy fluid as a function of the density ratio and the length of the capillary. A novel theoretical description of the system is presented which is based on a one-fluid model and a steady-state approximation for a two-dimensional flow. Theoretical results are in good agreement with the experimental data.

In a series of recent works it was proposed that shell models of turbulence exhibit inertial range scaling exponents that depend on the nature of the dissipative mechanism. If true, and if one could imply a similar phenomenon to Navier-Stokes turbulence, this finding would cast strong doubts on the universality of scaling in turbulence. In this Letter we propose that these “nonuniversalities” are just corrections to scaling that disappear when the Reynolds number goes to infinity.

We present experimental results for Rayleigh-Bénard convection with rotation about a vertical axis at dimensionless rotation rates $0\le \Omega \le 250$ and $\epsilon \equiv \Delta T/\Delta T_c-1\mathrm{}\lesssim 0.2$. Critical Rayleigh numbers and wave numbers agree with predictions of linear-stability analysis. For $\Omega \gtrsim 70$ and small $\epsilon$ the patterns are cellular with local fourfold coordination and differ from the theoretically expected Küppers-Lortz unstable state. Stable as well as intermittent defect-free square lattices exist over certain parameter ranges. Over other ranges defects dynamically disrupt the lattice but cellular flow and local fourfold coordination is maintained.

Numerical simulations have been carried out for a pair of unidirectionally coupled identical pendula under the action of a common external ac torque. Both the master pendulum and the slave pendulum were in chaotic states. The only form of persistent locking appeared to be a computational artifact; otherwise the synchronization of slave to master was found to be intermittent.

Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable, along with a novel method to identify and model such systems, if a single variable is fed back. Making use of special properties of the feedback structure, we can understand the structure of the system by constructing equivalent equations of motion in spaces with dimensions which can be much smaller than the dimension of the chaotic attractor. We verify our method using both numerical and experimental data.

For controlling periodic orbits with delayed feedback methods the periodicity has to be known a priori. We propose a simple scheme, how to detect the period of orbits from properties of the control signal, at least if a periodic but nonvanishing signal is observed. We analytically derive a simple expression relating the delay, the control amplitude, and the unknown period. Thus, the latter can be computed from experimentally accessible quantities. Our findings are confirmed by numerical simulations and electronic circuit experiments.

We consider the energy conservation problem for nonlinear-optical three-wave mixing processes at the surface and in the bulk of semi-infinite centrosymmetric lossless media. Because of the intrinsic nonlocality of these processes, the corresponding Manley-Rowe relations differ from those of noncentrosymmetric media. The ensuing restrictions link the surface and bulk nonlinear susceptibility components and may be used to test theories of nonlinear response. Our analysis permits a clear separation of the intrinsic surface contribution that contains the information about the surface structure.