Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Biomimicry (3)
- Finite element method (2)
- Mathematical physics (2)
- Optical coatings -- Design and construction (2)
- Sobolev spaces (2)
-
- Thin films -- Optical properties (2)
- Algebraic functions (1)
- Approximation theory (1)
- Asymptotic distribution (Probability theory) (1)
- Asymptotic expansions (1)
- Colloids -- Electric properties (1)
- Colloids -- Optical properties (1)
- Commutative algebra (1)
- Competing risks -- Mathematical models (1)
- Concentration functions (1)
- Decomposition (Chemistry) (1)
- Differential Geometry (1)
- Differential equations (1)
- Differential equations -- Study and teaching (Higher) (1)
- Discourse analysis (1)
- Electrostatics -- Study and teaching (1)
- Fluoropolymers (1)
- Gallium arsenide semiconductors -- Design and construction (1)
- Gallium compounds (1)
- Inquiry-based learning (1)
- Interaction analysis in education (1)
- Linear algebras (1)
- Linear orderings (1)
- Mathematical models (1)
- Mathematics -- Philosophy (1)
Articles 1 - 15 of 15
Full-Text Articles in Physical Sciences and Mathematics
Biomimetic Subwavelength Antireflective Gratings On Gaas, Chih-Hung Sun, Brian J. Ho, Bin Jiang, Peng Jiang
Biomimetic Subwavelength Antireflective Gratings On Gaas, Chih-Hung Sun, Brian J. Ho, Bin Jiang, Peng Jiang
Mathematics and Statistics Faculty Publications and Presentations
We have developed a simple and scalable bottom-up approach for fabricating moth-eye antireflective coatings on GaAs substrates. Monolayer, non-close-packed silica colloidal crystals are created on crystalline GaAs wafers by a spin-coating-based single-layer reduction technique. These colloidal monolayers can be used as etching masks during a BCl_3 dry-etch process to generate subwavelength-structured antireflective gratings directly on GaAs substrates. The gratings exhibit excellent broadband antireflective properties, and the specular reflection matches with the theoretical prediction using a rigorous coupled-wave analysis model. These bioinspired antireflection coatings have important technological applications ranging from efficient solar cells to IR detectors
How Students Use Mathematical Resources In An Electrostatics Context, Dawn C. Meredith, Karen A. Marrongelle
How Students Use Mathematical Resources In An Electrostatics Context, Dawn C. Meredith, Karen A. Marrongelle
Mathematics and Statistics Faculty Publications and Presentations
We present evidence that although students’ mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin’s symbolic forms. We find that students use notions of “dependence” and “parts-of-a-whole” to successfully guide their work, even in novel situations. We also present evidence that students’ naive conceptions of the limit may prevent them from viewing integrals as sums.
Bioinspired Broadband Antireflection Coatings On Gasb, Wei-Lun Min, Amaury P. Betancourt, Peng Jiang, Bin Jiang
Bioinspired Broadband Antireflection Coatings On Gasb, Wei-Lun Min, Amaury P. Betancourt, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report an inexpensive yet scalable templating technique for fabricating moth-eye antireflection gratings on gallium antimonide substrates. Non-close-packed colloidal monolayers are utilized as etching masks to pattern subwavelength-structured nipple arrays on GaSb. The resulting gratings exhibit superior broadband antireflection properties and thermal stability than conventional multilayer dielectric coatings. The specular reflection of the templated nipple arrays match with the theoretical predictions using a rigorous coupled-wave analysis model. The effect of the nipple shape and size on the antireflection properties has also been investigated by the same model. These biomimetic coatings are of great technological importance in developing efficient thermophotovoltaic cells.
Broadband Moth-Eye Antireflection Coatings On Silicon, Chih-Hung Sun, Peng Jiang, Bin Jiang
Broadband Moth-Eye Antireflection Coatings On Silicon, Chih-Hung Sun, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report a bioinspired templating technique for fabricating broadband antireflection coatings that mimic antireflective moth eyes. Wafer-scale, subwavelength-structured nipple arrays are directly patterned on silicon using spin-coated silica colloidal monolayers as etching masks. The templated gratings exhibit excellent broadband antireflection properties and the normal-incidence specular reflection matches with the theoretical prediction using a rigorous coupled-wave analysis (RCWA) model. We further demonstrate that two common simulation methods, RCWA and thin-film multilayer models, generate almost identical prediction for the templated nipple arrays. This simple bottom-up technique is compatible with standard microfabrication, promising for reducing the manufacturing cost of crystalline silicon solar cells.
Templated Biomimetic Multifunctional Coatings, Chih-Hung Sun, Adriel Gonzalez, Nicholas C. Linn, Peng Jiang, Bin Jiang
Templated Biomimetic Multifunctional Coatings, Chih-Hung Sun, Adriel Gonzalez, Nicholas C. Linn, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
We report a bioinspired templating technique for fabricating multifunctional optical coatings that mimic both unique functionalities of antireflective moth eyes and superhydrophobic cicada wings. Subwavelength-structured fluoropolymer nipple arrays are created by a soft-lithography-like process. The utilization of fluoropolymers simultaneously enhances the antireflective performance and the hydrophobicity of the replicated films. The specular reflectivity matches the optical simulation using a thin-film multilayer model. The dependence of the size and the crystalline ordering of the replicated nipples on the resulting antireflective properties have also been investigated by experiment and modeling. These biomimetic materials may find important technological application in self-cleaning antireflection coatings.
Multisymplectic Theory Of Balance Systems, I, Serge Preston
Multisymplectic Theory Of Balance Systems, I, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this paper we are presenting the theory of balance equations of the Continuum Thermodynamics (balance systems) in a geometrical form using Poincare-Cartan formalism of the Multisymplectic Field Theory. A constitutive relation C of a balance system BC is realized as a mapping between a (partial) 1-jet bundle of the configurational bundle π : Y ͢ X and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system BC is presented in three different forms and the space of admissible variations is defined and studied. Action of automorphisms …
Asymptotic And Numerical Techniques For Resonances Of Thin Photonic Structures, Jay Gopalakrishnan, Shari Moskow, Fadil Santosa
Asymptotic And Numerical Techniques For Resonances Of Thin Photonic Structures, Jay Gopalakrishnan, Shari Moskow, Fadil Santosa
Mathematics and Statistics Faculty Publications and Presentations
We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiting resonance problem as the thickness goes to zero, and for the case of a simple resonance, find a first order correction. The limiting problem and the correction are in one less space dimension, which can make the approach …
Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak
Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero. Then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number, providing an efficient solver for computing discrete approximations. Numerical experiments, while confirming the theory, …
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
Mathematics and Statistics Faculty Publications and Presentations
We study an indefinite metric G which was introduced by R. Mrugala and is defined on the contact phase space (P, θ) of a homogeneous thermodynamical system. We describe the curvature properties and the isometry group of the metric G. We established an isomorphism of the space (P, θ, G) with the Heisenberg Lie group Hn, endowed with the right invariant contact structure and the right invariant indefinite metric. The lift of the metric G to the symplectization of contact space (P, θ) and its properties are studied. Finally we introduce the "hyperbolic projectivization" of the space …
A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak
A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.
Order Restricted Inference For Comparing The Cumulative Incidence Of A Competing Risk Over Several Populations, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee
Order Restricted Inference For Comparing The Cumulative Incidence Of A Competing Risk Over Several Populations, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee
Mathematics and Statistics Faculty Publications and Presentations
There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this paper we propose an asymptotically distribution-free test when the alternative is that the incidence functions are linearly ordered, but not equal. The motivation stems from the fact that in many examples such a linear ordering seems reasonable intuitively and is borne out generally from empirical observations. These tests are more powerful when the ordering is justified. We also provide estimators of the incidence functions under …
Correction To "Stochastic Comparisons Of Parallel Systems When Components Have Proportional Hazard Rates", Subhash C. Kochar, Maochao Xu
Correction To "Stochastic Comparisons Of Parallel Systems When Components Have Proportional Hazard Rates", Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In the article "Stochastic comparisons of parallel systems when component have proportional hazard rates" we found a gap in the middle of the proof of Theorem 3.2. Therefore, we do not know whether Theorem 3.2 is true for the reverse hazard rate order. However, we could prove the following weaker result for the stochastic order.
Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Mathematics and Statistics Faculty Publications and Presentations
In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to introducing our new technique for constructing the extensions, and its application to the case of polynomial extensions from H½(∂K) into H¹(K), for any tetrahedron K.
Uniform Materials And The Multiplicative Decomposition Of The Deformation Gradient In Finite Elasto-Plasticity, Vincenzo Ciancio, Marina Dolfin, Mauro Francaviglia, Serge Preston
Uniform Materials And The Multiplicative Decomposition Of The Deformation Gradient In Finite Elasto-Plasticity, Vincenzo Ciancio, Marina Dolfin, Mauro Francaviglia, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we analyze the relation between the multiplicative decomposition F = F e F p of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations – total φ and the inelastic φ1. We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained for the configurations (φ, φ1) and the material …
Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park
Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park
Mathematics and Statistics Faculty Publications and Presentations
Researchers of mathematics education are increasingly interested in a teacher's discursive moves, which refer to deliberate actions taken by a teacher to participate in or influence debate and discussion in the mathematics classroom. This study explored one teacher's discursive moves in an undergraduate inquiry-oriented mathematics class. The data for this study come from four class sessions in which students investigated initial value problems as represented by the phase portrait of a system of differential equations. Through the analysis and a review of the literature, we identified four categories of a teacher's discursive moves: revoicing, questioning/requesting, telling, and managing. This report …