We measure the velocities of the mean flows that are driven by curved rolls in a pattern formation system. Curved rolls in Faraday waves are generated in experimental cells consisting of channels with varying widths. The mean flow magnitudes are found to scale linearly with roll curvatures and squares of wave amplitudes, agreeing with the prediction from the analysis of phase dynamics expansion. The effects of the mean flows on reducing roll curvatures are also seen.

We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice and also describe novel coherent states where the populations of clockwise and anticlockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems, including optically induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.

It is shown that the statistical properties of the magnitude of the magnetic field in turbulent electrically conducting media resemble, in the inertial range, those of passive scalars in fully developed three-dimensional fluid turbulence. This conclusion, suggested by the data from the Advanced Composition Explorer, is supported by a brief analysis of the appropriate magnetohydrodynamic equations.

We report on a new random laser phenomenon that gives rise to narrow emission modes without requiring optical cavities. Sharp emission peaks are observed experimentally over a broad range of scattering strengths and analyzed in numerical calculations. We find that the introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are rare and often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.

We investigate the classical motion of three charged particles with both attractive and repulsive interactions. The triple collision is a main source of chaos in such three-body Coulomb problems. By employing the McGehee scaling technique, we analyze here for the first time in detail the three-body dynamics near the triple collision in 3 degrees of freedom. We reveal surprisingly simple dynamical patterns in large parts of the chaotic phase space. The underlying degree of order in the form of approximate Markov partitions may help in understanding the global structures observed in quantum spectra of two-electron atoms.

Heterostructure arrangements of uniaxial bicrystals have been discovered to produce electromagnetic fields with asymmetric distributions in guide wave structures. The property behind this remarkable phenomenon is the broken crystalline symmetry which allows the new physics to be seen in unsymmetric distributions. Here the theory behind this phenomenon is presented, numerical calculations are performed using an anisotropic Green’s function approach, and the results provided at 10 GHz for a realistic crystal system with nominal permittivity of . Asymmetric distributions seen here are one facet of the broken symmetry property which generates negative refraction for impinging waves on a bicrystal.

The perturbation analysis of an ideal acoustical duct was first made by Rayleigh in 1878 and the result has since stood in the literature. However, the analysis is based on the assumption of potential and kinetic energy densities that remain constant as a change in cross section occurs, whereas, in fact, they may fluctuate significantly in comparison to the slowly varying “wave function,” $\Psi (x,t)$, of the acoustical Klein-Gordon equation. The square of the time-independent eigenfunction, ${\psi }^2(x)$, is directly proportional to the potential energy per unit length of fluid, and it is shown that it is precisely the perturbation in potential energy that defines correctly the eigenvalue shifts.

We experimentally investigate light propagation in a disordered two-dimensional array of mutually coupled optical fibers. In the linear case light either spreads in a diffusive manner or localizes at a few sites. For high excitation power diffusive spreading is arrested by the focusing nonlinearity, i.e., forming a discrete soliton. By contrast, fields, which are localized in the linear regime, can experience both spreading and contraction caused by the nonlinearity.

We study a new variant of electroconvection using a homeotropically aligned nematic liquid crystal. The novelty of this system is a direct transition to roll- or square-type patterns controlled by the frequency of the applied voltage with a rich crossover scenario and strong influence of the zigzag instability even at onset. From the weakly nonlinear theory and simulations of an adapted Swift-Hohenberg model one can understand essential features of the phase diagram. In particular we find a quasiperiodic pattern with square symmetry.

We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and monofractal 3D fractional Brownian vector fields. We report the results of some application to the velocity and vorticity fields issued from 3D isotropic turbulence simulations. This study reveals the existence of an intimate relationship between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.

We report on specific signatures of self-phase-locking in a cw frequency divide-by-three optical parametric oscillator subject to two competing ${\chi }^{\left(2\right)}$ nonlinear processes that couple the signal and idler subharmonic waves. The self-phase-locked pair appears as a broad fringe dip within the mode-pair cluster. We have also observed Hopf instabilities of the zero-detuning case at $\sim 4\times$ the pump threshold. These results open the path to experimental investigation of quantum entanglement and phase-locked transverse mode structures in this novel class of parametric oscillators.

The speed of light, a fundamental physical constant and thought to be independent of frequency, is tested here with naturally occurring radio waves in the atmosphere at extremely low frequencies. It is shown that the speed of light in the frequency range 5–50 Hz is known with an accuracy determined by perturbations of the ionospheric reflection height associated with space weather phenomena, which place an upper limit on the photon rest mass $m_{\gamma }\lesssim 4\times {10}^{-52}\mathrm{k}\mathrm{g}$ to date.

We use symmetry considerations to investigate control of a class of resonant three-wave interactions relevant to pattern formation in weakly damped, parametrically forced systems near onset. We classify and tabulate the most important damped, resonant modes and determine how the corresponding resonant triad interactions depend on the forcing parameters. The relative phase of the forcing terms may be used to enhance or suppress the nonlinear interactions. We compare our symmetry-based predictions with numerical and experimental results for Faraday waves. Our results suggest how to design multifrequency forcing functions that favor chosen patterns in the lab.

We present a general finite element mapping procedure for defining spring network representations of solid mechanics. The procedure is rigorous and equally suitable for setting regular and unstructured spring network models of generally anisotropic solids. We use the procedure to define close-packed triangular and simple cubic lattice spring models of isotropic 2D and 3D elastic media, respectively. We extend the study to heterogeneous solids and show that the mapped spring network approach constitutes an appealing route for incorporating subelement level constitutive equations.

Fascinating dynamics is known to result when the flow rate $Q$ at which water drips from a faucet varies. Starting with simple (period-1) dripping, the system transitions as $Q$ increases to complex dripping, where it exhibits period-$n$ ($n=2,4,\dots$) and chaotic responses, and then jets once $Q$ exceeds a threshold. New experiments and simulations show that high viscosity ($\mu$) liquids, e.g., syrup, transition directly from simple dripping to jetting as $Q$ increases. Phase diagrams showing transitions between simple and complex dripping and jetting in $(Q,\mu )$ space are developed. Values of $Q$ for transition from dripping to jetting are estimated from scaling arguments and shown to accord well with simulations.

We report the critical effects the deformational stress from the elastic nature of a confined polymer layer has during the relaxation process on the buckling of thin metal-polymer bilayer systems (less than 100 nm) even above the temperature at which the polymer is in the liquid flow region. In contrast with what is generally believed, the dispersion force does not play a significant role in the buckling. We also find that the final wrinkled waves take on the shape of wormlike islands. The coarsening leading to the island structure is driven by the growth in amplitude of the dominant wave at the expense of less dominant ones.

Dynamical properties of discrete solitons in nonlinear Schrödinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site ($A$) and between two neighboring sites ($B$), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating strong implications on the stability and dynamics of the localized modes. Besides a stable propagation of mode $A$, a stable propagation of mode $B$ is also possible. The enhanced ability of the large power solitons to move across the lattice is pointed out and numerically verified.

We propose an iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution. The new technique requires an aperture that is scanned to two or more positions over the object wave function. A simple implementation of the method is modeled and demonstrated, showing how the algorithm uses overlapping data in real space to resolve ambiguities in the solution. The technique opens up the possibility of practical transmission lensless microscopy at subatomic resolution using electrons, x rays, or nuclear particles.

We calculate the low-frequency index of refraction of a medium which is homogeneous along axis $z$ and possesses a periodic dependence of the permittivity $\varepsilon \left(\mathbf{r}\mathbf{\right)}$ and permeability $\mu \left(\mathbf{r}\mathbf{\right)}$ in the $x\mathrm{\text{−}}y$ plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector $\mathbf{E}$ or $\mathbf{H}$ polarized along axis $z$ are obtained. We show that, unlike nonmagnetic photonic crystals where the $E$ mode is ordinary and the $H$ mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, $\omega \to 0$ and $\varepsilon \to \infty$.

It was recently demonstrated [P. B. Weichman, Phys. Rev. Lett. 91, 143908 (2003)] that the scattered electric field from highly conducting targets following a rapidly terminated electromagnetic pulse displays a universal $t^{-1/2}$ power law divergence at early time. It is now shown that for strongly permeable targets, ${\mu }_c/{\mu }_b\gg 1$, where ${\mu }_b$ is the background magnetic permeability, the early-time regime separates into two distinct power law regimes, with the early-early time $t^{-1/2}$ behavior crossing over to $t^{-3/2}$ at late-early time, reflecting a spectrum of magnetic surface modes. The latter is confirmed by data from ferrous targets where ${\mu }_c/{\mu }_b=O\left({10}^2\right)$, and for which the early-early-time regime is invisibly narrow.