We report development of generators for periodic, satellite-free fluxes of monodisperse drops with diameters down to $10\mu \mathrm{m}$ from cryogenic liquids such as ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, and Xe (and, as a reference fluid, water). While the break up of water jets can be described well by Rayleigh’s linear theory, we find jet regimes for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ which reveal deviations from this behavior. Thus, Rayleigh’s theory is inappropriate for thin jets that exchange energy and/or mass with the surrounding medium. Moreover, at high evaporation rates, the axial symmetry of the dynamics is lost. When the drops pass into vacuum, frozen pellets form due to surface evaporation. The narrow width of the pellet flux paves the way towards various industrial and scientific applications.

We present both experimental and theoretical evidence for uncertainty-limited turnstile transport in deformed microcavities. As the degree of cavity deformation was increased, a secondary peak gradually emerged in the far-field emission patterns to form a double-peak structure. Our observation can be explained in terms of the interplay between turnstile transport and its suppression by the quantum mechanical uncertainty principle.

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.

We experimentally corroborate the core analytical deductions of Thomson’s 124-year-old theorem, vis-à-vis the stability of a ring of $N$ vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular $N$-gons are stable for $N\le 6$ and unstable for $N\ge 8$. The $N\le 6$ equilibria are exceptionally resilient. When destroyed, they reemerge in their original form. We reason that the heptagonal system either survives in an exceedingly narrow band of disk speeds or is in theory critically stable. Contrary to the results with a rotating bottom reported by Jansson et al. [Phys. Rev. Lett. 96, 174502 (2006)], we show the interfacial axial symmetry does not break spontaneously but through spectral development, the functional relationship amongst the polygon rotation and disk speed is surprisingly simple, and the pattern to disk frequency ratio depends on both Froude and wave numbers.

We put forward a method that allows the experimental determination of the entire spatial mode spectrum of any arbitrary monochromatic wave field in a plane normal to its propagation direction. For coherent optical fields, our spatial spectrum analyzer can be implemented with a small number of benchmark refractive elements embedded in a single Mach-Zehnder interferometer. We detail an efficient setup for measuring in the Hermite-Gaussian mode basis. Our scheme should also be feasible in the context of atom optics for analyzing the spatial profiles of macroscopic matter waves.

We obtain a description of the Poincaré recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by leaking the system and taking a special initial ensemble. This ensemble is atypical in terms of the natural measure of the leaked system, the conditionally invariant measure. Accordingly, for general initial ensembles, the average recurrence and escape times are different. However, we show that the decay rate of these distributions is always the same. Our results remain valid for Hamiltonian systems with mixed phase space and validate a split of the chaotic saddle in hyperbolic and nonhyperbolic components.

Using the surface-specific vibrational technique of vibrational sum-frequency generation, we reveal that the double-peaked structure in the vibrational spectrum of hydrogen-bonded interfacial water molecules originates from vibrational coupling between the stretch and bending overtone, rather than from structural effects. This is demonstrated by isotopic dilution experiments, which reveal a smooth transition from two peaks to one peak, as ${\mathrm{D}}_{\mathbf{2}}\mathrm{O}$ is converted into HDO. Our results show that the water interface is structurally more homogeneous than previously thought.

The problem of a nonperturbative description of unsteady 2D premixed flames with arbitrary gas expansion is addressed. By considering the flame as a surface of discontinuity with an arbitrary local burning rate and gas velocity jumps, we show that the flame front evolution can be determined without having to solve the flow equations in the bulk. A system of integro-differential equations is obtained, which relates fresh gas velocity at the front and the front position, thus yielding a closed nonperturbative description of the spontaneous flame dynamics.

Simulations of over ${10}^3$ hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel accelerated Stokesian-dynamics algorithm relies on simplifications associated with the Hele-Shaw asymptotic far-field form of the flow scattered by the particles. The simulations reveal propagation of particle-displacement waves, deformation, and rearrangements of a particle lattice, propagation of dislocation defects in ordered arrays, and long-lasting coexistence of ordered and disordered regions.

We analyze second order parametric processes in a silica microsphere coated with radially aligned nonlinear optical molecules. In a high-$Q$ nonlinear microsphere, we discover that it is possible to achieve ultralow threshold parametric oscillation that obeys the rule of angular momentum conservation. Based on symmetry considerations, one can also implement parametric processes that naturally generate quantum entangled photon pairs. Practical issues regarding implementation of the nonlinear microsphere are also discussed.

We describe the synthesis of periodic waveforms consisting of a train of pulses that are 0.83 cycles long and have an electric field pulse width of 0.44 fs using 7 Raman sidebands generated by molecular modulation in ${\mathrm{H}}_2$. We verify by optical correlation that the carrier-envelope phase is constant in these waveforms when they are synthesized from commensurate sidebands. The estimated overall shift of the carrier-envelope phase is less than 0.18 cycles from the first to the last pulse of nearly ${10}^6$ pulses in the pulse train.

New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. Quite naturally, the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet. Elements missing from random plane wave modeling of chaotic eigenstates lead surprisingly to significant errors, which can be corrected within a purely semiclassical approach.

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.

For soft-mode turbulence, which is essentially the spatiotemporal chaos caused by the nonlinear interaction between convective modes and Goldstone modes in electroconvection of homeotropic nematics, a type of order-disorder phase transition was revealed, in which a new order parameter was introduced as pattern ordering. We calculated the spatial correlation function and the anisotropy of the convective patterns as a 2D $XY$ system because the convective wave vector could freely rotate in the homeotropic system. We found the hidden order in the chaotic patterns observed beyond the Lifshitz frequency $f_{\mathrm{L}}$, and a transition from a disordered to a hidden ordered state occurred at the $f_{\mathrm{L}}$ with the increase of the frequency of the applied voltages.

When a dilute polymer solution experiences capillary thinning, it forms an almost uniformly cylindrical thread, which we study experimentally. In the last stages of thinning, when polymers have become fully stretched, the filament becomes prone to instabilities, of which we describe two: a novel breathing instability, originating from the edge of the filament, and a sinusoidal instability in the interior, which ultimately gives rise to a blistering pattern of beads on the filament. We describe the linear instability with a spatial resolution of 80 nm in the disturbance amplitude. For sufficiently high polymer concentrations, the filament eventually separates out into a “solid” phase of entangled polymers, connected by fluid beads. A solid polymer fiber of about 100 nm thickness remains, which is essentially permanent.

We obtain quantitative phase reconstructions from differential phase contrast images obtained with a scanning transmission x-ray microscope and 2.5 keV x rays. The theoretical basis of the technique is presented along with measurements and their interpretation.

We study the optical trapping of highly elongated linear nanostructures in the focal region of a high-numerical aperture lens (optical tweezers). The radiation torque and trapping force on these nanostructures that are modeled as chains of identical spherical scatterers are calculated by means of multipole field expansions in the framework of the transition matrix approach. We investigate both orientational and trapping stability and calculate force constants and trap parameters in order to clarify the role of the linear geometry in the optical trapping mechanism. Furthermore, we calculate optical trapping of nanowires of different materials and compare our theoretical findings with available experimental results.

We study nonlinear Čerenkov radiation generated from a nonlinear photonic crystal waveguide where the nonlinear susceptibility tensor is modulated by the ferroelectric domain. Nonlinear polarization driven by an incident light field may emit coherently harmonic waves at new frequencies along the direction of Čerenkov angles. Multiple radiation spots with different azimuth angles are simultaneously exhibited from such a hexagonally poled waveguide. A scattering involved nonlinear Čerenkov arc is also observed for the first time. Čerenkov radiation associated with quasi-phase matching leads to these novel nonlinear phenomena.

The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid flow at the microscale controlled by external heating. This novel thermomechanical effect is investigated for a thin fluid chamber by a numerical solution of the Navier-Stokes equations and analytically by a perturbation expansion. A demonstration experiment confirms the basic mechanism and quantitatively validates our theoretical analysis.

Predictions and measurements of a multimode waveguide interferometer operating in a fiber-coupled, “dual-mode” regime are reported. With a $1.32\mu \mathrm{m}$ source, a complete switching cycle of the output beam is produced by a 10.0 nm incremental change in the $8.0\mu \mathrm{m}$ width of the hollow planar mirror waveguide. This equates to a fringe spacing of $\sim \lambda /130$. This is an order of magnitude smaller than previously reported results for this form of interferometer.