The reference wave solution for a two-frequency wave propagating in a random medium

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.     

The Cross-Entropy Method for Continuous Multi-Extremal Optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.      

Enhanced fluorescence from arrays of nanoholes in a gold film

Arrays of sub-wavelength holes (nanoholes) in gold films were used as a substrate for enhanced fluorescence spectroscopy. Seven arrays of nanoholes with distinct periodicities (distances between the holes) were fabricated. The arrays were then spin-coated with polystyrene films containing different concentrations of the fluorescent dye oxazine 720. The dye was excited via resonant extraordinary transmission of the laser source through the nanoholes. Enhanced fluorescence was observed when the geometric characteristics of the arrays allowed for an enhancement in the transmitted excitation. This enhancement occurred via surface plasmon excitation by the laser and a consequential increase in the local electromagnetic field in a sub-wavelength region at the metal-film interface. It was demonstrated that the sensitivity of the fluorescence measurement (change in signal vs change in dye concentration in the polymer film) is significantly larger at the surface plasmon resonance conditions than that obtained from equivalent films on glass substrates. Enhancement factors for the fluorescence emission were calculated for each array, with a maximum enhancement of close to 2 orders of magnitude as compared to the emission of films on glass. The results presented here indicate that arrays of nanoholes are interesting substrates for the development of fluorescence sensors based on surface plasmon resonance, as they provide a platform that allows both spatial confinement and enhancement of excitation light. Moreover, the collinear characteristics of the present optical setup, due to the resonant extraordinary transmission through the nanohole arrays, are more conducive to miniaturization and chip integration than more traditional experimental geometries.     

Comments on the electronic properties of cyclopropane,cyclobutane, and cyclohexane

Spectral quantities of cyclopropane, cyclobutane, cyclohexane, and of several derivatives, have been calculated by a semiempirical all-valence electron SCF-CI MO method. In cyclopropane, HOMO is practically localized in the carbon-frame, and LVMO is purely so. In cyclobutane, these two MO's are based on C-H bonds, while cyclohexane holds an intermediate position. Despite the overall similarity-experimental and computed-of the spectra of these molecules, assignments are non-parallel. Like cyclopropane, cyclobutane can extend conjugation, but to a diminished degree; cyclohexane behaves in this respect like an acyclic alkane. An interpretation of this gradation, in terms of the nature of high-lying MO's, is proposed.     

Limited path percolation in complex networks

We study the stability of network communication after removal of a fraction q=1-p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than al(ij)(a> or =1) where l(ij) is the shortest path before removal. For a large class of networks, we find analytically and numerically a new percolation transition at p(c)=(kappa(0)-1)((1-a)/a), where kappa(0) [triple bond] / and k is the node degree. Above p(c), order N nodes can communicate within the limited path length al(ij), while below p(c), N(delta) (delta<1) nodes can communicate. We expect our results to influence network design, routing algorithms, and immunization strategies, where short paths are most relevant.     

Periodic solitons in nonlocal nonlinear media

We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.