The coupling between a resonant excitation and a nonresonant parametric process in a nonlinear system is studied experimentally under non-phase-matched conditions. Our study performed in the context of anti-Stokes stimulated Raman scattering provides a clear observation of the self-induced phase matching of a parametric process. A close agreement with theoretical predictions is observed.

A closed loop learning control concept is introduced for teaching lasers to manipulate quantum systems for the purpose of optimally identifying Hamiltonian information. The closed loop optimal identification algorithm operates by revealing the distribution of Hamiltonians consistent with the data. The control laser is guided to perform additional experiments, based on minimizing the dispersion of the distribution. Operation of such an apparatus is simulated for two model finite dimensional quantum systems.

We propose a method for the determination of a characteristic oscillation frequency for a broad class of chaotic oscillators generating complex signals. It is based on the locking of standard periodic self-sustained oscillators by an irregular signal. The method is applied to experimental data from chaotic electrochemical oscillators, where other approaches of frequency determination (e.g., based on Hilbert transform) fail. Using the method we characterize the effects of phase synchronization for systems with ill-defined phase by external forcing and due to mutual coupling.

We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dynamics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of impurities in tubular vortical structures, the detachment of particles from fluid trajectories near hyperbolic invariant lines, and the formation of nontrivial three-dimensional structures in the distribution of particles are predicted.

Compaction from a random-loose-packed to a random-close-packed phase is observed when monodisperse granular beds are shaken, but beyond this packing, the system freezes up in a jammed structure. Here we report a technique to grow large hard-sphere granular crystals, with perfect stacking and no defects by means of a “gas phase” epitaxial procedure. We study the growth mechanism and provide evidence that the observed granular crystallization is driven by gravity and energy dissipation.

Ultrashort laser pulse propagation in a generalized nonconservative system is considered. Slopes appearing in the form of the third-order time derivative for narrow pulse widths, nonlinear dispersion, and self-frequency shift arising from stimulated Raman scattering are taken into account. An exact analytical solitonlike solution is presented for a femtosecond solitary laser pulse. The stability of the latter has been shown numerically by applying perturbations in amplitude and chirp, as well as adding white noise. The results indicate stability in a broad parameter range. In addition, we have also found that the solution acts as an attractor when starting with a quite arbitrary Gaussian pulse as an initial condition.

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum $f(\alpha ,\lambda )$ gives the Hausdorff dimension of the points where the potential scales with distance $r$ as $H\sim r^{\alpha }$ while the curve logarithmically spirals with a rotation angle $\phi =\lambda \ln r$. It obeys the scaling law $f(\alpha ,\lambda )=(1+{\lambda }^2)f(\overline{\alpha })-b{\lambda }^2$ with $\overline{\alpha }=\alpha /(1+{\lambda }^2)$ and $b=(25-c)/12$, and where $f(\alpha )\equiv f(\alpha ,0)$ is the pure harmonic measure spectrum, and $c$ the conformal central charge. The results apply to $O(N)$ and Potts models, as well as to stochastic Löwner evolution.

A new experiment can create small scale barchan dunes under water: some sand is put on a tray moving periodically and asymmetrically in a water tank, and barchans rapidly form. We measure basic morphological and dynamical properties of these dunes and compare them to field data. These favorable results demonstrate experimentally the relevance of the so-called “saturation length” for the control of the dunes physics.

We consider nonequilibrium probabilistic dynamics in logisticlike maps $x_{t+1}=1-a|x_t{|}^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W\gg 1$ intervals partitioning the phase space and focus on the unique value $q_{\mathrm{s}\mathrm{e}\mathrm{n}}<1$ for which the entropic form $S_q\equiv (1-\sum _{i=1}^W{p}_i^q)/(q-1)$ linearly increases with time. We then verify that $S_{q_{\mathrm{s}\mathrm{e}\mathrm{n}}}(t)-S_{q_{\mathrm{s}\mathrm{e}\mathrm{n}}}(\infty )$ vanishes like $t^{-1/[q_{\mathrm{r}\mathrm{e}\mathrm{l}}(W)-1]}$ [$q_{\mathrm{r}\mathrm{e}\mathrm{l}}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{\mathrm{r}\mathrm{e}\mathrm{l}}(\infty )-q_{\mathrm{r}\mathrm{e}\mathrm{l}}(W)\propto W^{-|q_{\mathrm{s}\mathrm{e}\mathrm{n}}|}$. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Domain walls with oscillatory tails are commonplace in models of spatially extended nonlinear optical devices. Their interaction and locking at discrete distances lead to asymptotically stable spatial disorder. We show that noise in the presence of domain walls with oscillatory tails can suppress spatial disorder by privileging highly correlated dynamical states consisting of arrays of spatial solitons.

Using a new experimental technique, based on the scattering of ultrasounds, we perform a direct measurement of particle velocities, in a fully turbulent flow. This allows us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that is extremely long range correlated in time. Theoretically, a Langevin equation is proposed and shown to account for the observed one- and two-point statistics. This approach connects intermittency to the dynamics of the flow.

Velocity fluctuations and particle concentrations are studied in a liquid fluidized bed to investigate the origin of steady state sedimentation. Both the velocity fluctuations and the particle concentrations are found to strongly depend on height. A flux balance model shows why the bed is stable: velocity fluctuations drive a downward particle flux that is compensated by an upward particle flux stemming from an excess flow velocity due to the stratification in concentration. Our results show that in steady state the magnitudes of the fluctuations are related to the degree of stratification.

We report the first experimental demonstration of a Ni-like optical-field ionization collisional soft x-ray laser. The amplifying medium is generated by focusing a circularly polarized 760 mJ, 30 fs, 10-Hz Ti:sapphire laser beam in a few mm cell filled with krypton. We have measured a gain coefficient of $78{\mathrm{c}\mathrm{m}}^{-1}$ on the $3d^{9}4d$ ${}^{1}S_0\mathrm{\text{−}}3d^{9}4p^1{P}_1$ transition at 32.8 nm, which is here amplified for the first time. This radiation source represents the shortest wavelength optical-field ionization collisional soft x-ray laser ever produced. The influence of the gas pressure and the pumping energy on the lasing output are also presented.

We experimentally demonstrate that by longitudinally pumping 2 mm long molybdenum preformed plasma with high-intensity 475 fs duration laser pulse, a highly directive soft-x-ray laser at 18.9 nm wavelength is generated. The divergence of the beam is evaluated to be of the submilliradian order, and only requires a pump laser energy of 150 mJ.

We study the effects of noise on the Lorenz equations in the parameter regime admitting two stable fixed point solutions and a strange attractor. We show that noise annihilates the two stable fixed point attractors and evicts a Hopf-bifurcation-like sequence and transition to chaos. The noise-induced oscillatory motions have very well defined period and amplitude, and this phenomenon is similar to stochastic resonance, but without a weak periodic forcing. When the noise level exceeds certain threshold value but is not too strong, the noise-induced signals enable an objective computation of the largest positive Lyapunov exponent, which characterize the signals to be truly chaotic.

The propagator for molecular displacements $P(\zeta ,t)$ and its first three cumulants were measured for Stokes flow in monodisperse bead packs with different sphere sizes $d$ and molecular diffusion coefficients $D_m$. We systematically varied the normalized mean displacement $⟨\zeta ⟩/d$ and diffusion length $L_D=\sqrt{2D_{m}t}/d$. The experimental results map onto each other with this scaling. For $L_D/d<0.2$ the propagator remains non-Gaussian, and thus an advection diffusion equation is not obeyed, for mean displacements measured up to $⟨\zeta ⟩>10d$. A Gaussian shape is approached for large mean displacements when $L_D>0.3d$.

Realistic optical fields are never completely monochromatic and the interpretation of the concept of phase is not straightforward. It has been pointed out by Wolf that, if a strict condition of spatial coherence is imposed, the statistically averaged behavior of a polychromatic field can be described by an associated monochromatic wave. We show that, for spatially coherent polychromatic optical fields, the measurement of the phase of the second-order correlations determines the phase of this associated, spatially coherent field. We verify this prediction using a novel interferometric technique for measuring the cross-spectral density of a steady-state optical field.

We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. An order parameter for the segregated domains is defined and the effect of the variation of the combined filling fraction, $\mathcal{C}$, of the mixture on the observed pattern formation is systematically studied. We find that there is a critical event associated with the onset of segregation, at ${\mathcal{C}}_c=0.647\pm 0.049$, which has the characteristics of a continuous phase transition, including critical slowing down.

Using molecular dynamics simulations, we study the motion of a closely fitting nanometer-size solid sphere in a fluid-filled cylindrical nanochannel at low Reynolds numbers. At early times, when the particle is close to the middle of the tube, its velocity is in agreement with continuum calculations, despite large thermal fluctuations. At later times, partially wetting fluids exhibit novel adsorption phenomena: the sphere meanders away from the center of the tube and adsorbs onto the wall, and subsequently either sticks to the wall and remains motionless on average, or separates slightly from the tube wall and then either slips parallel to the mean flow or executes an intermittent stick-slip motion.

It is shown that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for different systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by $1/f$ noise.