A negative ion irradiated by a laser provides a coherent source of electrons propagating out from the location of the negative ion. The total escape rates of the electrons when the negative ion is placed inside an open cavity in the shape of a wedge are studied. It is shown that the wedge induces significant oscillations in the total escape rates because of quantum interference effects. In particular, it is shown that, for a wedge with an opening angle of $\pi /N$, where $N$ is an arbitrary positive integer, there are $(2N-1)$ induced oscillations in the rates. As a demonstration, the case for a wedge with an opening angle $\pi /5$ is calculated and analyzed in detail.

We present local temperature measurements of turbulent Rayleigh-Bénard convection with rotation about a vertical axis. The fluid, water with Prandtl number about 6, was confined in a cell with a square cross section of $7.3\times 7.3$ cm${}^2$ and a height of 9.4 cm. Temperature fluctuations and boundary-layer profiles were measured for Rayleigh numbers $1\times {10}^7<\mathrm{Ra}<5\times {10}^8$ and Taylor numbers $0<\mathrm{Ta}<5\times {10}^9$. We present statistics of the temperature field measured by a single thermistor located along the vertical centerline of the cell or by an array of thermistors distributed laterally from that centerline. The statistics include the mean temperature, standard deviation, skewness, and the probability distribution functions at various locations in the cell, especially near and inside the thermal boundary layer. The effects of rotation on these quantities are discussed including the presence of a rotation-dependent mean vertical temperature gradient, the negative skewness of temperature fluctuations in the boundary layer, and the horizontal homogenization of temperature.

Parametric shape instability of sonoluminescing argon bubbles in water and aqueous ${\mathrm{H}}_2$SO${}_4$ was numerically analyzed considering gas and liquid density variations. The employed model couples Gilmore, Tait (liquid) and van der Waals (gas) equations to simulate radial dynamics and density changes, respectively. Shape stability-instability zones in the $P_{\mathrm{a}}-R_0$ space resulted from a linear stability analysis. For the argon-water and argon-water-acid systems, numerical results indicate a rapid rise in both gas and liquid densities during final stages of bubble implosion which result in a stabilizing effect on the parametric instability.

Analytical solutions to the (3 $+$ 1)-dimensional Gross-Pitaevskii equation in the presence of chirp and for different diffraction and potential functions are found. We utilize a method we formulated to solve the Riccati equation for the chirp function that arises when the $F$-expansion technique and the homogeneous balance principle are applied to the Gross-Pitaevskii equation. Three specific examples of physical interest are considered in some detail.

When a small radiating or scattering object is placed near a multilayer array of plasmonic nanospheres, on the other side the optical near field is enhanced due to the excitation of resonant modes in the layers. For some particular frequencies, the field behind the array is concentrated in a subwavelength region, creating a super resolution effect. Resonating layers are able to reproduce (transport) part of the evanescent spectrum to the other side of these layers which otherwise would decay rapidly. We explore the mechanism of evanescent field transport and subwavelength field concentration on the other side of the layered material and show the relationship between near-field enhancement, field concentration, and modal dispersion characteristics. A detailed investigation of these phenomena is carried out by using an effective numerical model based on the array scanning method (ASM) combined with the Ewald method to accelerate the convergence of the dyadic Green function calculation. The subwavelength-sized spheres forming the arrays are represented as single dipole radiators, and the model of their interactions takes into account all the radiative and reactive field components.

The structure of nematic liquid crystals formed by bent-core mesogens (BCMs) is studied in the context of Monte Carlo simulations of a simple molecular model that captures the symmetry, shape, and flexibility of achiral BCMs. The results indicate the formation of (i) clusters exhibiting local smectic order, orthogonal or tilted, with strong in-layer polar correlations and antiferroelectric juxtaposition of successive layers and (ii) large homochiral domains through the helical arrangement of the tilted smectic clusters, while the orthogonal clusters produce achiral (untwisted) nematic states.

A Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach are considered. From this Fokker-Planck equation a class of exact solutions with the same spatial drift and diffusion coefficients is obtained. Furthermore, some details of this system are analyzed by using the spatial diffusion coefficient $D\left(x\right)=\sqrt{D}{\left|x\right|}^{-\theta /2}$.

In a recent publication [Phys. Rev. E 83, 011301 (2011)], Vollmayr-Lee et al. have determined by computer simulations the thermal diffusivity and the longitudinal viscosity coefficients of a driven granular fluid of hard spheres at intermediate volume fractions. Although they compare their simulation results with the predictions of kinetic theory, they use the dilute expressions for the driven system and the modified Sonine approximations for the undriven system. The goal here is to carry out this comparison by proposing a modified Sonine approximation to the Enskog equation for driven granular fluids that leads to a better quantitative agreement.

We provide physical insight into how a small hovering bird attains stabilized vision during downstroke. A passerine generates a lift force greater than its body weight during downstroke, leading to a substantial swing of the bird body, but the bird's eyes are nearly stable. Employing digital particle-image velocimetry, we demonstrate that a hovering passerine generates a lift force acting dorsal to the center of mass, concurrently resulting in rotational and translational displacements of the bird's body. The most notable finding is that the rotational and translational displacements at the bird's eyes almost cancel each other; the displacement of the eye is ∼8% that of the trailing tip of the tail. This aerodynamic trick enables a bird to attain stabilized vision beneficial for the inspection of the environment.

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents $h_{xy}$ extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order $q<0$ and underperforms when $q>0$. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of $h_{xy}\left(q\right)$ since its $h_{xy}\left(2\right)$ is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler’s oscillator. We show that spirals associated with periodicity hubs emerge and accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic bifurcations of a common saddle-focus equilibrium. The specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor.

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without losing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green’s function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.

The opening of a leaflet by one flow pulsation is studied here in an ideal system made of a rigid door, initially vertical, mounted on a horizontal wall. The dependence of the fluid-structure interaction on the leaflet inertia and flow parameters has been analyzed. The system has been solved by numerical integration of the Navier-Stokes equations coupled with the body dynamics. The behavior of the movable leaflet and resulting vortex formation has been conditioned through the range of Strouhal numbers and body inertia. When inertia is relatively large, the flow pulsation is unable to significantly move the leaflet. When inertia is relatively low, the degree of opening smoothly increases with lowering the Strouhal number (that corresponds, for example, to either a longer pulsation period or a higher flow velocity). The analysis also demonstrated the existence of a critical intermediate range where the body opens completely and impacts onto the lower wall at high speed.

We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,\cdots ,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an occupation probability $p$ increases, the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase, and back to a monodisperse one in the supercritical phase. We show analytically that $H$ diverges algebraically, approaching the percolation critical point $p_c$ as $H\sim |p-p_c{|}^{-1/\sigma }$ with the critical exponent $\sigma$ associated with the characteristic cluster size. Interestingly, its finite-size-scaling behavior is governed by a new exponent ${\nu }_H=(1+d_f/d)\nu$, where $d_f$ is the fractal dimension of the critical percolating cluster and $\nu$ is the correlation length exponent. The corresponding scaling variable defines a singular path to the critical point. All results are confirmed by numerical simulations.

We studied the structural and optical properties of scales in the longhorn beetle Sphingnotus mirabilis. Structural characterizations revealed that the scale interior possesses a disordered bicontinuous macroporous structure, resembling a phase-separated structure obtained by spinodal decomposition. Its optical response was investigated both experimentally and theoretically. Our results show that this structure has interesting optical properties due to the existence of only short-range order and the lack of well-defined local structures.

In this paper, we demonstrate that nontrivial interactions between steric effect and electrical-double-layer (EDL) overlap phenomena may augment the effective extent of EDL overlap in narrow fluidic confinements to a significant extent by virtue of rendering the channel centerline potential tending to the ζ potential in a limiting sense as the steric effect progressively intensifies. Such a behavior may result in a virtually uniform (undiminished) magnitude of the EDL potential across the entire channel height and may cause lowering of the total charge within the EDL.

Anomalous dispersion in heterogeneous environments describes the anomalous growth of the macroscopic characteristic sizes of scalar fields. Here we show that this phenomenon is closely related to the persistence of local scale incomplete mixing. We introduce the mixing scale $\epsilon$ as the length for which the scalar distribution is locally uniform. We quantify its temporal evolution due to the competition of shear action and diffusion and compare it to the evolution of the global dispersion scale $\sigma$. In highly heterogeneous flow fields, for which the temporal evolution of $\sigma$ is superdiffusive, we find that $\epsilon$ evolves subdiffusively. The anomalous evolutions of the dispersion and mixing scales are complementary, $\epsilon \sigma \propto t$. This result relates anomalous global dispersion to the dynamics of local mixing.

We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a wormlike micellar gel formed by surfactant cetyltrimethylammonium tosylate. At sufficiently high Weissenberg numbers the shear rate, and hence the injected power $p\left(t\right)$, at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of $p\left(t\right)$ and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian PDFs can be well described by a universal, large deviation functional form given by the generalized Gumbel distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.

Coupled oscillators can be heterogeneous in the sense that parameter values of constituent oscillators are not uniform for various reasons. Here it is discussed how such a system behaves in the strong-coupling limit. A theory is developed under certain assumptions and then used to quite generally explain an empirical law about a phase transition boundary in a class of heterogeneous populations of coupled oscillators such that bifurcation parameters are distributed. Results obtained here will be useful as a starting point for studying the behavior of such systems for moderate coupling strengths.