Mode-medium instability and its correction with a Gaussian reflectivity mirror

A high power CO2 laser beam is known to deteriorate after a few microseconds due to a mode-medium instability (MMI) which results from an intensity dependent heating rate related to the vibrational-to-translational decay of the upper and lower CO2 lasing levels. An iterative numerical technique is developed to model the time evolution of the beam as it is affected by the MMI. The technique is used to study the MMI in an unstable CO2 resonator with a hard-edge output mirror for different parameters like the Fresnel number and the gas density. The results show that the mode of the hard edge unstable resonator deteriorates because of the diffraction ripples in the mode. A Gaussian-reflectivity mirror was used to correct the MMI. This mirror produces a smoother intensity profile which significantly reduces the effects of the MMI. Quantitative results on peak density variation and beam quality are presented

Virtual Enriching Operators

We construct bounded linear operators that map $H^1$ conforming Lagrange finite element spaces to $H^2$ conforming virtual element spaces in two and three dimensions. These operators are useful for the analysis of nonstandard finite element methods

Virtual Element Methods on Meshes with Small Edges or Faces

We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).Comment: 36 page

Land use/land cover mapping (1:25000) of Taiwan, Republic of China by automated multispectral interpretation of LANDSAT imagery

Three methods were tested for collection of the training sets needed to establish the spectral signatures of the land uses/land covers sought due to the difficulties of retrospective collection of representative ground control data. Computer preprocessing techniques applied to the digital images to improve the final classification results were geometric corrections, spectral band or image ratioing and statistical cleaning of the representative training sets. A minimal level of statistical verification was made based upon the comparisons between the airphoto estimates and the classification results. The verifications provided a further support to the selection of MSS band 5 and 7. It also indicated that the maximum likelihood ratioing technique can achieve more agreeable classification results with the airphoto estimates than the stepwise discriminant analysis

Scattering measurements on natural and model trees

The acoustical back scattering from a simple scale model of a tree has been experimentally measured. The model consisted of a trunk and six limbs, each with 4 branches; no foliage or twigs were included. The data from the anechoic chamber measurements were then mathematically combined to construct the effective back scattering from groups of trees. Also, initial measurements have been conducted out-of-doors on a single tree in an open field in order to characterize its acoustic scattering as a function of azimuth angle. These measurements were performed in the spring, prior to leaf development. The data support a statistical model of forest scattering; the scattered signal spectrum is highly irregular but with a remarkable general resemblance to the incident signal spectrum. Also, the scattered signal's spectra showed little dependence upon scattering angle

Internal Stresses and Formation of Switchable Nanowires at Thin Silica Film Edge

At vertical edges, thin films of silicon oxide (SiO_{2-x}) contain semiconductive c-Si layered nanocrystals (Si NC) embedded in and supported by an insulating g-SiO2 matrix. Tour et al. have shown that a trenched thin film geometry enables the NC to form switchable nanowires (SNW) when trained by an applied field. The field required to form SNW decreases rapidly within a few cycles, or by annealing at 600 C in even fewer cycles, and is stable to 700C. Here we describe the intrinsic evolution of Si NC and SNW in terms of the competition between internal stresses and electro-osmosis. The analysis relies heavily on experimental data from a wide range of thin film studies, and it explains why a vertical edge across the planar Si-SiOx interface is necessary to form SNW. The discussion also shows that the formation mechanisms of Si NC and Si/SiO_{2-x} SNW are intrinsic and result from optimization of nanowire conductivity in the presence of residual host misfit stresses

Kondo and charge fluctuation resistivity due to Anderson impurities in graphene

Motivated by experiments on ion irradiated graphene, we compute the resistivity of graphene with dilute impurities. In the local moment regime we employ the perturbation theory up to third order in the exchange coupling to determine the behavior at high temperatures within the Kondo model. Resistivity due to charge fluctuations is obtained within the mean field approach on the Anderson impurity model. Due to the linear spectrum of the graphene the Kondo behavior is shown to depend on the gate voltage applied. The location of the impurity on the graphene sheet is an important variable determining its effect on the Kondo scale and resistivity. Our results show that for chemical potential nearby the node the charge fluctuations is responsible for the observed temperature dependence of resistivity while away from the node the spin fluctuations take over. Quantitative agreement with experimental data is achieved if the energy of the impurity level varies linearly with the chemical potential.Comment: 17 pages, 15 figures, published versio