Exact (to all orders in Knudsen number) equations of linear hydrodynamics are derived from the Boltzmann kinetic equation with the Bhatnagar-Gross-Krook collision integral. The exact hydrodynamic equations are cast in a form which allows us to immediately prove their hyperbolicity, stability, and existence of an $H$ theorem.

We report experimental evidence of spatial clustering of dense particles in homogenous, isotropic turbulence at high Reynolds numbers. The dissipation-scale clustering becomes stronger as the Stokes number increases and is found to exhibit similarity with respect to the droplet Stokes number over a range of experimental conditions (particle diameter and turbulent energy dissipation rate). These findings are in qualitative agreement with recent theoretical and computational studies of inertial particle clustering in turbulence. Because of the large Reynolds numbers a broad scaling range of particle clustering due to turbulent mixing is present, and the inertial clustering can clearly be distinguished from that due to mixing of fluid particles.

Measurements of the velocity profile of water flowing on a glass surface using fluorescent nanoparticles and single fluorescent molecules as velocity probes show that the no slip boundary condition holds down to at least 10 nm from the surface. For water flowing on a hydrophobic solid surface, silanized glass, the no slip boundary condition fails, and a slip length of 45 nm is measured. These velocity measurements are complemented with atomic force microscopy measurements of dissipation on a small sphere oscillating near the surface with results in agreement with the velocity profiles.

We predict that interfaces of periodically curved waveguide arrays can support a novel type of surface states which exist in a certain region of modulation parameters associated with the band flattening. Such linear surface states appear in truncated but otherwise perfect (defect-free) lattices as a direct consequence of the periodic modulation of the lattice potential. We show that the existence of these modes in different band gaps can be flexibly controlled by selecting the modulation profile, with no restrictions on Bloch-wave symmetries characteristic of Shockley states.

In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of other states couple to each other which sensitively affects the strength function. The recently measured superscars in the barrier billiard provide an ideal model for an in-depth investigation of this mechanism. We introduce two new statistical observables: the full distribution of the maximum coupling coefficient to the doorway and directed spatial correlators. Using random matrix theory and random plane waves, we obtain a consistent understanding of the experimental data.

The 3D structure of randomly polarized light fields is exemplified by its polarization singularities: lines along which the polarization is purely circular ($C$ lines) and surfaces on which the polarization is linear ($L$ surfaces). We visualize these polarization singularities experimentally in vector laser speckle fields, and in numerical simulations of random wave superpositions. Our results confirm previous analytical predictions [M. R. Dennis, Opt. Commun. 213, 201 (2002)] regarding the statistical distribution of types of $C$ points and relate their 2D properties to their 3D structure.

Ultrahigh frequency acoustic resonances ($\backsim 2\mathrm{GHz}$) trapped within the glass core ($\backsim 1\mu \mathrm{m}$ diameter) of a photonic crystal fiber are selectively excited through electrostriction using laser pulses of duration 100 ps and energy 500 pJ. Using precisely timed sequences of such driving pulses, we achieve coherent control of the acoustic resonances by constructive or destructive interference, demonstrating both enhancement and suppression of the vibrations. A sequence of 27 resonantly-timed pulses provides a 100-fold increase in the amplitude of the vibrational mode. The results are explained and interpreted using a semianalytical theory, and supported by precise numerical simulations of the complex light-matter interaction.

A technique is proposed to generate attosecond pulse trains of radiation from a free-electron laser amplifier. The optics-free technique synthesizes a comb of longitudinal modes by applying a series of spatiotemporal shifts between the copropagating radiation and electron bunch in the free-electron laser. The modes may be phase locked by modulating the electron beam energy at the mode spacing frequency. Three-dimensional simulations demonstrate the generation of a train of 400 as pulses at gigawatt power levels evenly spaced by 2.5 fs at a wavelength of 124 Å. In the x-ray at wavelength 1.5 Å, trains of 23 as pulses evenly spaced by 150 as and of peak power up to 6 GW are predicted.

We present an effective technique for suppressing the vortex-induced vibrations of bluff bodies by eliminating the von Kármán street formed in their wake. Specifically, we find that small amounts of combined windward suction and leeward blowing around the body modify the wake instability and lead to suppression of the fluctuating lift force. Three-dimensional simulations and stability analysis are employed to quantify our findings for the flow past fixed and flexibly mounted circular cylinders.

A novel photonic monolithic integrated device consisting of a distributed feedback laser, a passive resonator, and active elements that control the optical feedback properties has been designed, fabricated, and evaluated as a compact potential chaotic emitter in optical communications. Under diverse operating parameters, the device behaves in different modes providing stable solutions, periodic states, and broadband chaotic dynamics. Chaos data analysis is performed in order to quantify the complexity and chaoticity of the experimental reconstructed attractors by applying nonlinear noise filtering.

We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.

With examples of two parallel dielectric gratings and two arrays of thin parallel dielectric cylinders, it is shown that the interaction between trapped electromagnetic modes can lead to scattering resonances with practically zero width. Such resonances are the bound states in the radiation continuum first discovered in quantum systems by von Neumann and Wigner. Potential applications of such photonic systems include: large amplification of electromagnetic fields within photonic structures and, hence, enhancement of nonlinear phenomena, biosensing, as well as perfect filters and waveguides for a particular frequency, and impurity detection.

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.

Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincaré recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.

We analyze the semiclassical evolution of Gaussian wave packets in chaotic systems. We show that after some short time a Gaussian wave packet becomes a primitive WKB state. From then on, the state can be propagated using the standard time-dependent WKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is $l_{\overline{B}}\propto S^{-1/2}$ and the growth rate is $\gamma \propto S$, where $S$ is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.

A sinusoidal temperature perturbation is superimposed on the bottom plate of a cylindrical convection cell, and its decay is measured at the cell midheight. Rayleigh numbers up to $\mathrm{Ra}={10}^{13}$ and aspect ratios 1 and 4 are considered. The technique allows a dynamic measurement of the height of the layer interposed between the superconducting core and the boundary. This deduced height is in good agreement with results from recent numerical simulations.

We report fine-tuning of nonlinear interactions in a solid-state ring laser gyroscope by vibrating the gain medium along the cavity axis. We demonstrate both experimentally and theoretically that nonlinear interactions vanish for some values of the vibration parameters, leading to quasi-ideal rotation sensing. We eventually point out that our conclusions can be mapped onto other subfields of physics such as ring-shaped superfluid configurations, where nonlinear interactions could be tuned by using Feshbach resonance.

Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical properties of oscillator networks are affected when some nodes are merged together to form a coarse-grained network. Moreover, we show that there exists a way of grouping nodes preserving as much as possible some crucial aspects of the network dynamics. This coarse graining approach provides a useful method to simplify complex oscillator networks, and more generally, networks whose dynamics involves a Laplacian matrix.

The Lagrangian velocity structure functions in the inertial range of fully developed fluid turbulence are for the first time derived based on the Navier-Stokes equation. For time $\tau$ much smaller than the correlation time, the structure functions are shown to obey the scaling relations $K_n(\tau )\propto {\tau }^{{\zeta }_n}$. The scaling exponents ${\zeta }_n$ are calculated analytically without any fitting parameters. The obtained values are in amazing agreement with the experimental results of the Bodenschatz group. A new relation connecting the Lagrangian structure functions of different orders analogously to the extended self-similarity ansatz is found.