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Articles 1 - 15 of 15
Full-Text Articles in Physical Sciences and Mathematics
Self-Assembled Nanoparticle Antiglare Coatings, Khalid Askar, Blayne M. Phillips, Xuan Dou, Juan Lopez, Carl Smith, Bin Jiang, Peng Jiang
Self-Assembled Nanoparticle Antiglare Coatings, Khalid Askar, Blayne M. Phillips, Xuan Dou, Juan Lopez, Carl Smith, Bin Jiang, Peng Jiang
Mathematics and Statistics Faculty Publications and Presentations
Here we report a simple and scalable bottom-up technology for assembling close-packed nanoparticle monolayers on both sides of a glass substrate as high-quality antiglare coatings. Optical measurements show that monolayer coatings consisting of 110 nm silica nanoparticles can significantly reduce optical reflectance and enhance specular transmittance of the glass substrate for a broad range of visible wavelengths. Both experiments and numerical simulations reveal that the antiglare properties of the self-assembled colloidal monolayers are significantly affected by the size of the colloidal particles.
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Mathematics and Statistics Faculty Publications and Presentations
We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …
Some Unified Results On Comparing Linear Combinations Of Independent Gamma Random Variables, Subhash C. Kochar, Maochao Xu
Some Unified Results On Comparing Linear Combinations Of Independent Gamma Random Variables, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].
Convergence Analysis Of A Multigrid Algorithm For The Acoustic Single Layer Equation, Simon Gemmrich, Jay Gopalakrishnan, Nilima Nigam
Convergence Analysis Of A Multigrid Algorithm For The Acoustic Single Layer Equation, Simon Gemmrich, Jay Gopalakrishnan, Nilima Nigam
Mathematics and Statistics Faculty Publications and Presentations
We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise constant test functions and we make use of a weak inner product in the multigrid scheme as proposed in Bramble et al. (1994) . A full error analysis of the algorithm is presented. We also conduct a numerical study of the effect of the weak inner product on the oscillatory behavior of the eigenfunctions for the Laplace single layer operator.
On The Skewness Of Order Statistics With Applications, Subhash C. Kochar, Maochao Xu
On The Skewness Of Order Statistics With Applications, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
Order statistics from heterogenous samples have been extensively studied in the literature. However, most of the work focused on the effect of heterogeneity on the magnitude and dispersion of order statistics. In this paper, we study the skewness of order statistics from heterogeneous samples in the sense of star order. The main results extended the results in Kochar and Xu (2009, 2011). Examples and applications in statistical inference are highlighted.
Mixed Finite Element Approximation Of The Vector Laplacian With Dirichlet Boundary Conditions, Douglas N. Arnold, Richard S. Falk, Jay Gopalakrishnan
Mixed Finite Element Approximation Of The Vector Laplacian With Dirichlet Boundary Conditions, Douglas N. Arnold, Richard S. Falk, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We consider the finite element solution of the vector Laplace equation on a domain in two dimensions. For various choices of boundary conditions, it is known that a mixed finite element method, in which the rotation of the solution is introduced as a second unknown, is advantageous, and appropriate choices of mixed finite element spaces lead to a stable, optimally convergent discretization. However, the theory that leads to these conclusions does not apply to the case of Dirichlet boundary conditions, in which both components of the solution vanish on the boundary. We show, by computational example, that indeed such mixed …
Partial Expansion Of A Lipschitz Domain And Some Applications, Weifeng Qiu, Jay Gopalakrishnan
Partial Expansion Of A Lipschitz Domain And Some Applications, Weifeng Qiu, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated
Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.
Supporting Implementation Of The Common Core State Standards For Mathematics: Recommendations For Professional Development, Paola Sztajn, Karen A. Marrongelle, Peg Smith, Bonnie L. Melton
Supporting Implementation Of The Common Core State Standards For Mathematics: Recommendations For Professional Development, Paola Sztajn, Karen A. Marrongelle, Peg Smith, Bonnie L. Melton
Mathematics and Statistics Faculty Publications and Presentations
In 2010, the National Governor’s Association and the Council of Chief State School Officers published the Common Core State Standards for Mathematics (CCSSM) and to date, 44 states, the District of Columbia, and the U.S. Virgin Islands have adopted the document. These content and practice standards, which specify what students are expected to understand and be able to do in K-12 mathematics, represent a significant departure from what mathematics is currently taught in most classrooms and how it is taught. Developing teachers’ capacity to enact these new standards in ways that support the intended student learning outcomes will require considerable …
Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar
Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
We review some of the recent developments in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as nonidentically distributed. But most of the time we will be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters as well as the proportional hazard rate model is discussed in detail.
A Locking-Free Hp Dpg Method For Linear Elasticity With Symmetric Stresses, Jamie Bramwell, Leszek Demkowicz, Jay Gopalakrishnan, Weifeng Qiu
A Locking-Free Hp Dpg Method For Linear Elasticity With Symmetric Stresses, Jamie Bramwell, Leszek Demkowicz, Jay Gopalakrishnan, Weifeng Qiu
Mathematics and Statistics Faculty Publications and Presentations
We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov- Galerkin (DPG) framework. In this framework, both the stress and the displacement ap- proximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.
Instability In A Generalized Keller–Segel Model, Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr
Instability In A Generalized Keller–Segel Model, Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr
Mathematics and Statistics Faculty Publications and Presentations
We present a generalized Keller–Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although …
Wavenumber Explicit Analysis Of A Dpg Method For The Multidimensional Helmholtz Equation, Leszek Demkowicz, Jay Gopalakrishnan, Ignacio Muga, Jeffrey Zitelli
Wavenumber Explicit Analysis Of A Dpg Method For The Multidimensional Helmholtz Equation, Leszek Demkowicz, Jay Gopalakrishnan, Ignacio Muga, Jeffrey Zitelli
Mathematics and Statistics Faculty Publications and Presentations
We study the properties of a novel discontinuous Petrov Galerkin (DPG) method for acoustic wave propagation. The method yields Hermitian positive definite matrices and has good pre-asymptotic stability properties. Numerically, we find that the method exhibits negligible phase errors (otherwise known as pollution errors) even in the lowest order case. Theoretically, we are able to prove error estimates that explicitly show the dependencies with respect to the wavenumber ω, the mesh size h, and the polynomial degree p. But the current state of the theory does not fully explain the remarkably good numerical phase errors. Theoretically, comparisons are made with …
A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity, Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi
A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity, Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi
Mathematics and Statistics Faculty Publications and Presentations
We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts …
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A and are not ordered. If the systems fail the criterion, it does not follow they are ordered. Thus the theory only serves to avoid some a priori useless comparisons: when neither A nor can be said to be better than the other. The power of the theory lies in its wide potential applicability: the assumptions involve very weak estimates on the asymptotic behavior (as t→0 and as t→∞) of the constituent survival probabilities. We include examples.