A family of Alltop functions that are EA-inequivalent to the cubic function

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (\emph{IEEE Trans. Inf. Theory} 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called \emph{Alltop functions}. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.

Constructing commutative semifields of square order

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semi-fields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187{196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.

The high-eccentricity asymmetric expansion of the disturbing function for non-planar resonant problems

In this paper we present an extension to the nonplanar case of the asymmetric expansion of the averaged resonant disturbing function of Ferraz-Mello & Sato (1989, A&A 225, 541-547). Comparions with the exact averaged disturbing function are also presented. The expansion gives a good approximation of the exact function in a wide region around the center of expansion.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

Planar silver nanowire, carbon nanotube and PEDOT:PSS nanocomposite transparent electrodes

Highly conductive, transparent and flexible planar electrodes were fabricated using interwoven silver nanowires and single-walled carbon nanotubes (AgNW:SWCNT) in a PEDOT:PSS matrix via an epoxy transfer method from a silicon template. The planar electrodes achieved a sheet resistance of 6.6 ± 0.0 Ω/squ and an average transmission of 86% between 400 and 800 nm. A high figure of merit of 367 Ω−1 is reported for the electrodes, which is much higher than that measured for indium tin oxide and reported for other AgNW composites. The AgNW:SWCNT:PEDOT:PSS electrode was used to fabricate low temperature (annealing free) devices demonstrating their potential to function with a range of organic semiconducting polymer:fullerene bulk heterojunction blend systems.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Analysis of the evanescent field coupling between a fiber and a planar waveguide using the explicit finite difference method with a nonuniform mesh (Journal Paper)

We investigate an optical waveguide system consisting of an unclad fiber core suspended at a constant distance parallel to the surface of a planar waveguide. The coupling and propagation of light in the combined system is studied using the three-dimensional explicit finite difference beam propagation method with a nonuniform mesh configuration. The power loss in the fiber and the field distribution in the waveguide are studied as a function of various parameters, such as index changes, index profile, and propagation distance, for the combined system.

Mean-field results of the multiple-band extended Hubbard model for the square-planar CuO2 lattice

We obtain metal-insulator phase diagrams at half-filling for the five-band extended Hubbard model of the square-planar CuO2 lattice treated within a Hartree-Fock mean-field approximation, allowing for spiral spin-density waves. We indicate the existence of an insulating phase (covalent insulator) characterized by strong covalency effects, not identified in the earlier Zaanen-Sawatzky-Allen phase diagram. While the insulating phase is always antiferromagnetic, we also obtain an antiferromagnetic metallic phase for a certain range of interaction parameters. Performing a nonperturbative calculation of J(eff), the in-plane antiferromagnetic interaction is presented as a function of the parameters in the model. We also calculate the band gap and magnetic moments at various sites and discuss critically the contrasting interpretation of the electronic structure of high-T(c) materials arising from photoemission and neutron-scattering experiments.

Exact N-Wave Solutions for the Non-Planar Burgers Equation

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).

Filtered density function for large eddy simulation of turbulent reacting flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results. © 1998 American Institute of Physics.

EFFECT OF OFF-STOICHIOMETRY AND TERNARY ADDITIONS ON PLANAR FAULT ENERGIES IN Ni3Al

First principles calculations were done to evaluate the lattice parameter, cohesive energy and stacking fault energies of ordered gamma' (Ll(2)) precipitates in superalloys as a function of composition. It was found that addition of Ti and Ta lead to an increase in lattice parameter and decrease in cohesive energy, while Ni antisites had the opposite effect. Ta and Ti addition to stoichiometric Ni3Al resulted in an initial increase in the energies of APB((111)), CSF(111), APB((001)) and SISF(111). However, at higher concentrations, the fault energies decreased. Addition of Ni antisites decreased the energy of all four faults monotonically. A model based on nearest neighbor bonding was used for Ni-3(Al, Ta), Ni-3(Al, Ti) and Ni-3(Al, Ni) pseudo-binary systems and extended to pseudo- ternary Ni-3(Al, Ta, Ni) and Ni-3(Al, Ti, Ni) systems. Recipes were developed for predicting lattice parameters, cohesive energies and fault energies in pseudo- ternary systems on the basis of coefficients derived from simpler pseudobinary systems. The model predictions were found to be in good agreement with first principles calculations for lattice parameters, cohesive energies, and energies of APB((111)) and CSF(111).

Relativistic force between fast electrons and planar targets

The full retarded electromagnetic force experienced by swift electrons moving parallel to planar boundaries is revisited, for both metallic and dielectric targets, with special emphasis on the consequences in electron microscopy experiments. The focus is placed on the sign of the transverse force experienced by the electron beam as a function of the impact parameter. For point probes, the force is found to be always attractive. The contribution of the induced magnetic field and the causality requirements of the target dielectric response, given by the Kramers-Kronig (K-K) relations, prove to be crucial issues at small impact parameters. For spatially extended probes, repulsive forces are predicted for close trajectories, in agreement with previous works. The force experienced by the target is also explored, with the finding that in insulators, the momentum associated to Cherenkov radiation (CR) is relevant at large impact parameters.

Effect of processing parameters on the optical properties of TiO2/ormosil planar waveguide

Hybrid TiO2/ormosil waveguiding films have been prepared by the sol-gel method at low thermal treatment temperature of 150&DEG; C. The influence of processing parameters including the molar ratios of titanium butoxide (Ti(OBu)(4))/3-glycidoxypropyltrimethoxysilane (GLYMO) and H2O/Ti(OBu)(4) (expressed as R), especially aging of sot on the optical properties was investigated. The optical properties of films were measured with scanning electron microscope (SEM), UV/VIS/NIR spectrophotometer (UV-Vis), m-line and the scattering-detection method. The results indicate that the film thickness increases with the increase of sol aging time, but the variation of refractive index as a function of sot aging time depends on the relative ratios of GLYMO to Ti(OBu)(4). Higher transmittance and lower attenuation of the planar waveguide can be obtained in the sol with lower Ti(OBu)(4) contents and shorter aging time.

SCATTERING AND RESONANT-TUNNELING THEORY FOR A CYLINDRICAL WELL IN PLANAR STRUCTURES

A two-dimensional atomic scattering theory is developed for scattering of electrons by a circularly symmetric quantum structure in the two-dimensional electron gas. It is found that the scattering cross section oscillates as a function of ka where k is the electron wave vector and a is the radius of the cylindrical potential barrier. If there is a quantum well inside the potential barrier, there appears a series of sharp resonant-tunneling peaks superposed on the original scattering-cross-section curves. The width of the resonant-tunneling peak depends sensitively on the thickness, the height of the potential barrier, and the electron energy.