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Articles 1 - 6 of 6
Full-Text Articles in Mathematics
Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang
Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report a cheap and scalable bottom-up technique for fabricating wafer-scale, subwavelength-structured antireflection coatings on single-crystalline silicon substrates. Spin-coated monolayer colloidal crystals are utilized as shadow masks to generate metallic nanohole arrays. Inverted pyramid arrays in silicon can then be templated against nanoholes by anisotropic wet etching. The resulting subwavelength gratings greatly suppress specular reflection at normal incidence. The reflection spectra for flat silicon and the templated gratings at long wavelengths agree well with the simulated results using a rigorous coupled wave analysis model. These subwavelength gratings are of great technological importance in crystalline silicon solar cells.
Self-Assembled Biomimetic Antireflection Coatings, Nicholas C. Linn, Chih-Hung Sun, Peng Jiang, Bin Jiang
Self-Assembled Biomimetic Antireflection Coatings, Nicholas C. Linn, Chih-Hung Sun, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
The authors report a simple self-assembly technique for fabricating antireflection coatings that mimic antireflective moth eyes. Wafer-scale, nonclose-packed colloidal crystals with remarkable large hexagonal domains are created by a spin-coating technology. The resulting polymer-embedded colloidal crystals exhibit highly ordered surface modulation and can be used directly as templates to cast poly(dimethylsiloxane) (PDMS) molds. Moth-eye antireflection coatings with adjustable reflectivity can then be molded against the PDMS master. The specular reflection of replicated nipple arrays matches the theoretical prediction using a thin-film multilayer model. These biomimetic films may find important technological application in optical coatings and solar cells.
The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman
The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Given a pair of distinct points p and q in a metric space with distance d, the mediatrix is the set of points x such that d(x,p)=d(x,q). In this paper, we examine the topological structure of mediatrices in connected, compact, closed 2-manifolds whose distance function is inherited from a Riemannian metric. We determine that such mediatrices are, up to homeomorphism, finite, closed simplicial 1-complexes with an even number of incipient edges emanating from each vertex. Using this and results from [J.J.P. Veerman, J. Bernhard, Minimally separating sets, mediatrices and Brillouin spaces, Topology Appl., in press], we give the classification …
Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu
Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
Let Χ1, … Χn be independent random variables with Χᵢ having survival function Fλᵢ, i=1, … , n, and let Y₁, … , Yn be a random sample with common population survival distribution Fλ, where λ = Σᵢ=₁nλᵢl n. Let Χn:n and Yn:n denote the lifetimes of the parallel systems consisting of these components, respectively. It is shown that Xn:n is greater than Yn:n in terms of likelihood ratio order. It is also proved that the sample range Χn:n - Χ₁:n is larger than Yn n:n - Y₁:n according to reverse hazard rate ordering. These two results …
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
This paper reviews some recent results on stochastic orders and dependence among order statistics when the observations are independent and follow the proportional hazard rates model.
Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang
Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang
Mathematics and Statistics Faculty Publications and Presentations
The standard continuous Galerkin (CG) finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations, a much needed quantity in many applications. We show how to overcome this shortcoming by using a two step postprocessing. The first step is the computation of a numerical flux trace defined on element inter- faces and is motivated by the structure of the numerical traces of discontinuous Galerkin methods. This computation is non-local in that it requires the solution of a symmetric positive definite system, but the system is well conditioned independently of mesh size, so it …