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.

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Low-pressure planar magnetron discharge for surface deposition and nanofabrication

Current-voltage characteristics of the planar magnetron are studied experimentally and by numerical simulation. Based on the measured current-voltage characteristics, a model of the planar magnetron discharge is developed with the background gas pressure and magnetic field used as parameters. The discharge pressure was varied in a range of 0.7-1.7 Pa, the magnetic field of the magnetron was of 0.033-0.12 T near the cathode surface, the discharge current was from 1 to 25 A, and the magnetic field lines were tangential to the substrate surface in the region of the magnetron discharge ignition. The discharge model describes the motion of energetic secondary electrons that gain energy by passing the cathode sheath across the magnetic field, and the power required to sustain the plasma generation in the bulk. The plasma electrons, in turn, are accelerated in the electric field and ionize effectively the background gas species. The model is based on the assumption about the prevailing Bohm mechanism of electron conductivity across the magnetic field. A criterion of the self-sustained discharge ignition is used to establish the dependence of the discharge voltage on the discharge current. The dependence of the background gas density on the current is also observed from the experiment. The model is consistent with the experimental results. © 2010 American Institute of Physics.

Standing surface waves in a dust-contaminated large-area planar plasma source

The effect of charged particulates or dusts on surface wave produced microwave discharges is studied. The frequencies of the standing electromagnetic eigenmodes of large-area flat plasmas are calculated. The dusts absorb a significant amount of the plasma electrons and can lead to a modification of the electromagnetic field structure in the discharge by shifting the originally excited operating mode out of resonance. For certain given proportions of dusts, mode conversion is found to be possible. The power loss in the discharge is also increased because of dust-specific dissipations, leading to a decrease of the operating mode quality factor.

Discharge parameters and dominant electron conductivity mechanism in a low-pressure planar magnetron discharge

Parameters of a discharge sustained in a planar magnetron configuration with crossed electric and magnetic fields are studied experimentally and numerically. By comparing the data obtained in the experiment with the results of calculations made using the proposed theoretical model, conclusion was made about the leading role of the turbulence-driven Bohm electron conductivity in the low-pressure operation mode (up to 1 Pa) of the discharge in crossed electric and magnetic fields. A strong dependence of the width of the cathode sputter trench, associated with the ionization region of the magnetron discharge, on the discharge parameters was observed in the experiments. The experimental data were used as input parameters in the discharge model that describes the motion of secondary electrons across the magnetic field in the ionization region and takes into account the classical, near-wall, and Bohm mechanisms of electron conductivity.

A model of a large-area planar plasma producer based on surface wave propagation in a plasma-metal structure with a dielectric sheath

A theoretical model of a large-area planar plasma producer based on surface wave (SW) propagation in a plasma-metal structure with a dielectric sheath is presented. The SW which produces and sustains the microwave gas discharge in the planar structure propagates along an external magnetic field and possesses an eigenfrequency within the range between electron cyclotron and electron plasma frequencies. The spatial distributions of the produced plasma density, electromagnetic fields, energy flow density, phase velocity and reverse skin depth of the SW are obtained analytically and numerically.

Self-action of high-frequency surface waves in a magnetoactive planar plasma waveguide

The self-modulation process of a high-frequency surface wave (SW) in a wave-guiding structure - a semibounded magnetoactive plasma and perfectly conducting metal wall - is considered for the weak nonlinearity approximation. Estimates are given for the contributions to the nonlinear frequency shift of the SW from the two principal self-action channels: via the generation of a signal of the doubled frequency and of static surface perturbations, arising as the result of the action of a ponderomotive force. Solutions for the field envelope of the nonlinear wave are examined with regard to their stability with respect to longitudinal and transverse perturbations.

Self-interaction of high-frequency surface waves in magnetoactive plasma planar waveguide

The nonlinear effect of hf surface waves self-interaction in a magnetoactive planar plasma waveguide is studies. The waveguide structure under consideration can be formed by gaseous or semiconducting homogeneous plasma, which is limited by a perfectly conducting metal surface. The surface (localized near the surface) wave perturbations propagating on the plasma-metal boundary perpendicular to the constant external magnetic field, are investigated. The nonlinear frequency shift connected with interaction of the second harmonic and static surface perturbations with the main frequency wave, is determined using the approximation of weak nonlinearity. It is shown that the process of double-frequency signal generation is the dissipative one as a result of bulk wave excitation on the surface wave second harmonic.

Compensation for higher order mode coupling between inclined coupling slots and radiating slots in planar slotted waveguide arrays

Summary form only given. Geometric simplicity, efficiency and polarization purity make slot antenna arrays ideal solutions for many radar, communications and navigation applications, especially when high power, light weight and limited scan volume are priorities. Resonant arrays of longitudinal slots have a slot spacing of one-half guide wavelength at the design frequency, so that the slots are located at the standing wave peaks. Planar arrays are implemented using a number of rectangular waveguides (branch line guides), arranged side-by-side, while waveguides main lines located behind and at right angles to the branch lines excite the radiating waveguides via centered-inclined coupling slots. Planar slotted waveguide arrays radiate broadside beams and all radiators are designed to be in phase.

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.

Bias-dependent effects in planar perovskite solar cells based on CH3NH3PbI3−xClx films

A unique bias-dependent phenomenon in CH3NH3PbI3−xClx based planar perovskite solar cells has been demonstrated, in which the photovoltaic parameters derived from the current–voltage (I–V) curves are highly dependent on the initial positive bias of the I–V measurement. In FTO/CH3NH3PbI3−xClx/Au devices, the open-circuit voltage and short-circuit current increased by ca. 337.5% and 281.9% respectively, by simply increasing the initial bias from 0.5 V to 2.5 V.

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.

A 13C-NMR study of non-planar distortions in amides

The technique of 13C-NMR spectroscopy of oriented systems to problems of biological importance has been suggested and used to investigate non-planar distortions in substituted amides—models for peptides. The studies in conjunction with the proton magnetic resonance data on 5N-[13C]methyl[13C]formamide oriented in a nematic solvent provide all the direct dipolar couplings between the interacting nuclei in the system. When the 13C- and the 1H-NMR experiments are performed under non-identical conditions, 22 different direct dipolar couplings are obtained. It is demostrated that they can be used to determine unambiguously non-planar distortions around the nitrogen atom together with other geometrical data and the molecular order.

Approximation algorithm for maximum independent set in planar traingle-free graphs

The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.