Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality

     

Current and frequency modulation characteristics for continuous-wave quantum cascade lasers at 9.06 μm

We report the characteristics of current induced frequency modulation (FM) for two continuous-wave quantum cascade lasers (QCLs) at 9.06 μm. Both the frequency tuning rate and the phase shift between intensity modulation and FM are measured at different modulation frequencies from 10 Hz to 200 kHz. The frequency tuning rate of the QCLs depends on both the modulation frequency and amplitude. The tested QCL has been used to detect ambient water vapor with wavelength modulation spectroscopy for validation with a numerical model.     

High‐mobility solution‐processed zinc oxide thin films on silicon nitride

A high effective electron mobility of 33 cm² V^–1 s^–1 was achieved in solution‐processed undoped zinc oxide (ZnO) thin films. The introduction of silicon nitride (Si₃N₄) as growth substrate resulted in a mobility improvement by a factor of 2.5 with respect to the commonly used silicon oxide (SiO₂). The solution‐processed ZnO thin films grown on Si₃N₄, prepared by low‐pressure chemical vapor deposition, revealed bigger grain sizes, lower strain and better crystalline quality in comparison to the films grown on thermal SiO₂. These results show that the nucleation and growth mechanisms of solution‐processed films are substrate dependent and affect the final film structure accordingly. The substantial difference in electron mobilities suggests that, in addition to the grain morphology and crystalline structure effects, defect chemistry is a contributing factor that also depends on the particular substrate. In this respect, interface trap densities measured in high‐κ HfO₂/ZnO MOSCAPs were about ten times lower in those fabricated on Si₃N₄ substrates. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

     

Multiscale data sampling and function extension

We introduce a multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nyström interpolation method. The multiscale extension (MSE) method is based on mutual distances between data points. It uses a coarse-to-fine hierarchy of the multiscale decomposition of a Gaussian kernel. It generates a sequence of subsamples, which we refer to as adaptive grids, and a sequence of approximations to a given empirical function on the data, as well as their extensions to any newly-arrived data point. The subsampling is done by a special decomposition of the associated Gaussian kernel matrix in each scale in the hierarchical procedure.     

Molecular dynamics simulation of gas adsorption on defected graphene

Gas sensing is one of the most promising applications for graphene. Using molecular dynamics simulation method, adsorption isotherm of xenon (Xe) gas on defected and perfect graphene is studied in order to investigate sensing properties of graphene for Xe gas. In this method, first generation of Brenner many-body potential is used to simulate the interaction of carbon–carbon (C) atoms in graphene, and Lennard–Jones two-body potential is used to simulate interaction of Xe–Xe and Xe–C atoms. In the simulated systems, adsorption coverage, radial distribution function, heat of adsorption, binding energy and specific heat capacity at constant volume are calculated for several temperatures between 90 K and 130 K, and various pressures. It was found that both of the defected and perfect graphene could be introduced as very good candidates for adsorption of Xe gas.     

A note on simultaneous preconditioning and symmetrization of non‐symmetric linear systems

Motivated by the theory of self‐duality that provides a variational formulation and resolution for non‐self‐adjoint partial differential equations (Ann. Inst. Henri Poincaré (C) Anal Non Linéaire 2007; 24 :171–205; Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non‐symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well‐known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill‐conditioned, and highly non‐symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved photonic crystal directional coupler with short length

We investigate a photonic crystal (PC) waveguide coupler which is formed by two closely spaced linear waveguides in a two-dimensional triangular lattice of air holes. Our study shows that shifting one row of the air holes between the waveguides affects the dispersion curves of the guided modes and if the triangular lattice of air holes between the waveguides is replaced by a rectangular lattice, this modification results in an ultra-short coupling structure with coupling length less than 3a, where a is the lattice constant. Also, we investigate the effect of changing the radii of air holes that are adjacent to or between the waveguides on the coupling length and show that increasing the radius of air holes between the waveguides decreases the coupling length. We analyze the output spectrum of an ultra-short channel drop filter designed based on this structure.