An analytical model of the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers $\left(A_T\right)$ is presented. The model is based on an extension of Layzer's theory [Astrophys. J. 122, 1 (1955)] previously applied only to the fluid-vacuum interfaces $(A_T=1\mathrm{})$. The model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime when the bubble velocity saturates at $U_b=\sqrt{{2A}_T/\left({1+A}_T\right)\left({g/C}_{g}k\right)}$, where $k$ is the perturbation wave number, $g$ is the interface acceleration, and $C_g=3\mathrm{}$ and $C_g=1\mathrm{}$ for the two-dimensional and three-dimensional geometries, respectively.

A solution is suggested for a persistent mystery in the physics of turbulent flows: cumulus clouds rise to towering heights, practically without entraining the ambient medium, while apparently similar turbulent jets quickly lose their identity through entrainment and mixing. Dynamical system computations on a model vortical flow show that entrainment due to coherent structures depends sensitively on relative speeds of fluid parcels. Local heating, for example, can alter drastically the sizes of Kolmogorov-Arnol'd-Moser tori and chaotic mixing regions. The entrainment rate and, hence, the lifetime of a turbulent shear flow show a universal, nonmonotone dependence on the heating.

The phase link between signal, idler, and pump waves in a parametric interaction allows generation of an idler pulse with a phase independent of that of the input pulse. We suggest the use of a white-light seeded optical parametric amplifier as a self-stabilized source of few-cycle pulses, in which the phase of the electric field is exactly reproduced in each laser shot.

We report an experimental study of the secondary modulational instability of a one-dimensional nonlinear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatiotemporal defects are linked to the convective and absolute nature of the instability. Both transitions appear to be subcritical. The spatiotemporal defects control the global mode structure.

We consider situations where, in a continuous-time dynamical system, a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window. Under the influence of noise, chaos can arise. We investigate the fundamental dynamical mechanism responsible for the transition and obtain a general scaling law for the largest Lyapunov exponent. A striking finding is that the topology of the flow is fundamentally disturbed after the onset of noisy chaos, and we point out that such a disturbance is due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.

We introduce the concept of degree of polarization for electromagnetic near fields. The approach is based on the generalized Stokes parameters that appear as expansion coefficients of the $3\times 3$ coherence matrix in terms of the Gell-Mann matrices. The formalism is applied to optical near fields of thermally fluctuating half-space sources with particular interest in fields that are strongly polarized owing to resonant surface plasmons or phonons. This novel method is particularly useful when assessing the full vectorial characteristics of random evanescent fields, e.g., for near-field spectroscopy and polarization microscopy.

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known “Brazil nut” fashion, i.e., with the larger particles rising to the top, but also in reverse “Brazil nut” fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.

The absence of self-averaging in mesoscopic systems is a consequence of long-range intensity correlations. Microwave measurements suggest, and diagrammatic calculations confirm, that the correlation function of the normalized intensity with displacement of the source and detector, $\Delta R$ and $\Delta r$, respectively, can be expressed as the sum of three terms, with distinctive spatial dependences. Each term involves only the sum or the product of the square of the field correlation function, $F\equiv F_E^2$. The leading-order term is the product, $F\left(\Delta R\right)F\left(\Delta r\right)$; the next term is proportional to the sum, $F\left(\Delta R\right)+F\left(\Delta r\right)$; the third term is proportional to $F\left(\Delta R\right)F\left(\Delta r\right)+\left[F\right(\Delta R)+F(\Delta r\left)\right]+1\mathrm{}$.

We report on an ultrafast longitudinal time measurement by a nonresonant Rayleigh-type nondegenerate four-wave mixing (NFWM). We investigated the field-correlation effects on Rayleigh-type NFWM by examining the time-delayed dependence of the NFWM spectra. Based on the field-correlation effects, a time-delayed method is proposed to suppress the thermal effect, and ultrafast relaxation time can be measured even in an absorbing medium.

We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new criterion for quantum chaos is provided by the statistics of the wave functions, which complements the well-established criterion based on spectral statistics.

Nodal domains are regions where a function has definite sign. In [[1]] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolationlike model for description of these nodal domains which permits us to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way to deeper understanding of the structure of chaotic wave functions.

Our velocity measurements on quasi-two-dimensional turbulent flow in a rapidly rotating annulus yield self-similar (scale-independent) probability distribution functions for longitudinal velocity differences, $\delta v\left(\ell \right)=v(x+\ell )-v\left(x\right)$. These distribution functions are strongly non-Gaussian, suggesting that the coherent vortices play a significant role. The structure functions $〈\left[\delta v\right(\ell ){]}^p〉\sim {\ell }^{{\zeta }_p}$ exhibit anomalous scaling: ${\zeta }_p=\frac{p}{2}$ rather than the expected ${\zeta }_p=\frac{p}{3}$. Correspondingly, the energy spectrum is described by $E\left(k\right)\sim k^{-2\mathrm{}}$ rather than the expected $E\left(k\right)\sim k^{-5/3\mathrm{}}$.

We have observed transverse pattern formation leading to highly regular structures in both the near and far fields when a near-resonant laser beam propagates without feedback through an atomic sodium vapor. One example is a regular far-field honeycomb pattern, which results from the transformation of the laser beam within the vapor into a stable three-lobed structure with a uniform phase distribution and highly correlated power fluctuations. The predictions of a theoretical model of the filamentation process are in good agreement with these observations.

We report the study of ultrasound tunneling in 3D phononic crystals, consisting of fcc arrays of close-packed tungsten carbide beads in water. The transmission coefficient, phase velocity, and group velocity were measured along the [111] direction, allowing us to systematically investigate the tunneling of ultrasound at frequencies in the lowest band gap. Our experimental data are interpreted using multiple scattering theory, which provides a good explanation of our results. The effect of absorption and the difference between the tunneling of classical waves and quantum waves are discussed.

We propose and theoretically analyze a new approach for generating and shaping 1-fs pulses. It combines the ideas of strong-field molecular optics and optimal control to manipulate light generation in a pump-probe Raman regime. Flexible phase control over the generated spectrum of about 3 eV width is achieved by controlling the input pulses and maximizing the coherence of medium excitation by adiabatically aligning molecules in the medium with a specially shaped pump pulse. The generated pulse is optimized for an output window, precompensating for its dispersion to all orders.

The dark core of an optical vortex was used to detect on-axis, forward-scattered light from a colloidal solution in the single and multiple scattering regimes. Using no adjustable parameters we obtain good agreement with a concentration-dependent scattering model.

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, $K\left(\tau \right)$, of a generic quantum graph with mixing classical dynamics and time-reversal symmetry. We calculate the contribution from pairs of self-intersecting orbits that differ from each other only in the orientation of a single loop. In the limit of large graphs, these pairs produce a contribution $-2\mathrm{}{\tau }^2$ to the form factor which agrees with random-matrix theory.

A near-field effect has been discovered experimentally in thermal radio emission of an absorbing dielectric medium. It is related to a specific character of the distribution of a quasistationary field component near a radiating surface. The effect consists of the fact that the effective depth of the received emission formation appears to be less than the skin-layer depth and depends on the size of the receiver antenna and its height above the surface. It can be considered as a new source of information about depth temperature distribution. A theory has been developed that allows for determining the relative contribution of wave and quasistationary components to the Plank emission received near the surface.

A numerical simulation of attosecond harmonic pulse generation in a three-dimensional field-ionizing gas is presented. Calculated harmonic efficiencies quantitatively reproduce experimental findings. This allows a quantitative characterization of attosecond pulse generation revealing information currently not accessible by experiment. The rapid phase variation and spatiotemporal distortions of harmonics are smaller than anticipated, allowing focusing of 30-nm, 750-as pulses to intensities in excess of ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. Feasibility of such pulses brings novel applications such as extreme ultraviolet nonlinear optics and attosecond pump probe spectroscopy within reach.

We study lasing emission from asymmetric resonant cavity GaN microlasers. By comparing far-field intensity patterns with images of the microlaser we find that the lasing modes are concentrated on three-bounce unstable periodic ray orbits; i.e., the modes are scarred. The high-intensity emission directions of these scarred modes are completely different from those predicted by applying Snell’s law to the ray orbit. This effect is due to the process of “Fresnel filtering” which occurs when a beam of finite angular spread is incident at the critical angle for total internal reflection.