Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae,
2010
Utah State University
Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …
Grading Practice Influence On The Value Of An Assigned Grade,
2010
Utah State University
Grading Practice Influence On The Value Of An Assigned Grade, Carrie Bala
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
This article presents results of a study of grading practice influence on the value of an assigned grade. The value of an assigned grade, as an indication of student achievement of learning goals, was measured using the Utah Criterion-Referenced Test (CRT) in the subjects of Geometry and Algebra 2. The grading policies of six mathematics teachers at the same high school were categorized according to grading practice and their combined 587 students' scores on the Utah CRT were collected and analyzed. The findings suggest that certain grading practices , such as the use of a 1-4 scale and a criterion-referenced …
A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data,
2010
Montclair State University
A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data, Steven Spero
Theses, Dissertations and Culminating Projects
This research applies time series methods to determine relationships among a set of weather variables which are continually monitored in the Hackensack Meadowlands region of northern New Jersey. Weather data includes chemical and atmospheric factors. Chemical factors are Nitrogen Oxide, atmospheric Ozone, Carbon Monoxide, and Carbon Dioxide. Weather factors are wind speed, barometric pressure, air temperature, humidity, and solar radiation. Additionally, traffic density and time of week are brought in as categorical factors. This research attempts to (a) introduce the reader to various time series methodologies, (b) find a significant and efficient model for forecasting Nitrogen Oxide levels, and (c) …
From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems,
2010
University of Nebraska - Lincoln
From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng
Department of Mathematics: Faculty Publications
The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …
Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory,
2010
Bulgarian Academy of Sciences
Multi–Component Nls Models On Symmetric Spaces: Spectral Properties Versus Representations Theory, Vladimir Gerdjikov, Georgi Grahovski
Articles
The algebraic structure and the spectral properties of a special class of multicomponent NLS equations, related to the symmetric spaces of BD.I-type are analyzed. The focus of the study is on the spectral theory of the associated Lax operator to these nonlinear evolutionary equations for different fundamental representations of the underlying simple Lie algebra g. Special attention is paid to the spinor representation of the orthogonal Lie algebras of B type.
A Projection-Based Error Analysis Of Hdg Methods,
2010
Portland State University
A Projection-Based Error Analysis Of Hdg Methods, Jay Gopalakrishnan, Bernardo Cockburn, Francisco-Javier Sayas
Mathematics and Statistics Faculty Publications and Presentations
We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG …
A Class Of Discontinuous Petrov–Galerkin Methods. Part I: The Transport Equation,
2010
University of Texas at Austin
A Class Of Discontinuous Petrov–Galerkin Methods. Part I: The Transport Equation, Leszek Demkowicz, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
Considering a simple model transport problem, we present a new finite element method. While the new method fits in the class of discontinuous Galerkin (DG) methods, it differs from standard DG and streamline diffusion methods, in that it uses a space of discontinuous trial functions tailored for stability. The new method, unlike the older approaches, yields optimal estimates for the primal variable in both the element size h and polynomial degree p, and outperforms the standard upwind DG method.
Hybridization And Postprocessing Techniques For Mixed Eigenfunctions,
2010
University of Minnesota - Twin Cities
Hybridization And Postprocessing Techniques For Mixed Eigenfunctions, Bernardo Cockburn, Jay Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, Jaume Peraire
Mathematics and Statistics Faculty Publications and Presentations
We introduce hybridization and postprocessing techniques for the Raviart–Thomas approximation of second-order elliptic eigenvalue problems. Hybridization reduces the Raviart–Thomas approximation to a condensed eigenproblem. The condensed eigenproblem is nonlinear, but smaller than the original mixed approximation. We derive multiple iterative algorithms for solving the condensed eigenproblem and examine their interrelationships and convergence rates. An element-by-element postprocessing technique to improve accuracy of computed eigenfunctions is also presented. We prove that a projection of the error in the eigenspace approximation by the mixed method (of any order) superconverges and that the postprocessed eigenfunction approximations converge faster for smooth eigenfunctions. Numerical experiments using …
Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics,
2010
Portland State University
Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, Dylan M. Copeland, Jay Gopalakrishnan, Minah Oh
Mathematics and Statistics Faculty Publications and Presentations
Consider the space of two-dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that if the original three-dimensional domain is convex then the multigrid Vcycle applied to the inner product in this space converges, provided certain modern smoothers are used. For the convergence analysis, we first prove several intermediate results, e.g., the approximation properties of a commuting projector in weighted norms, and a superconvergence estimate for a …
Symmetry And Stability Of Homogeneous Flocks,
2010
Portland State University
Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The study of the movement of flocks, whether biological or technological, is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological flock a large group of animals seek their course while moving in a more or less fixed formation. It seems reasonable that the immediate course is determined by leaders at the boundary of the flock. The others follow: what is their algorithm? The most popular technological application consists of cars on a one-lane road. The light turns green and the lead car …
A Class Of Discontinuous Petrov–Galerkin Methods. Ii. Optimal Test Functions,
2010
University of Texas at Austin
A Class Of Discontinuous Petrov–Galerkin Methods. Ii. Optimal Test Functions, Leszek Demkowicz, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes having test function spaces that are automatically computable to guarantee stability. Given a trial space, a DPG discretization using its optimal test space counterpart inherits stability from the well posedness of the undiscretized problem. Although the question of stable test space choice had attracted the attention of many previous authors, the novelty in our approach lies in the fact we identify a discontinuous Galerkin (DG) framework wherein test functions, arbitrarily close to the optimal ones, can be locally computed. The idea is presented abstractly and its feasibility illustrated through …
Linearly Ordered Topological Spaces And Weak Domain Representability,
2010
University of Dayton
Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn
Mathematics Faculty Publications
It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.
Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations,
2010
University of Dayton
Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik
Mathematics Faculty Publications
We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …
Temporal Scales For Transport Patterns In The Gulf Of Finland,
2010
Tallinn University of Technology
Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski
Publications
The basic time scales for current-induced net transport of surface water and associated time scales of reaching the nearshore in the Gulf of Finland, the Baltic Sea, are analysed based on Lagrangian trajectories of water particles reconstructed from three-dimensional velocity fields by the Rossby Centre circulation model for 1987–1991. The number of particles reaching the nearshore exhibits substantial temporal variability whereas the rate of leaving the gulf is almost steady. It is recommended to use an about 3 grid cells wide nearshore area as a substitute to the coastal zone and about 10–15 day long trajectories for calculations of the …
Waves In Materials With Microstructure: Numerical Simulation,
2010
Tallinn University of Technology
Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht
Publications
Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model.
Optimal Control And Nonlinear Programming,
2010
Louisiana State University and Agricultural and Mechanical College
Optimal Control And Nonlinear Programming, Qingxia Li
LSU Doctoral Dissertations
In this thesis, we have two distinct but related subjects: optimal control and nonlinear programming. In the first part of this thesis, we prove that the value function, propagated from initial or terminal costs, and constraints, in the form of a differential equation, satisfy a subgradient form of the Hamilton-Jacobi equation in which the Hamiltonian is measurable with respect to time. In the second part of this thesis, we first construct a concrete example to demonstrate conjugate duality theory in vector optimization as developed by Tanino. We also define the normal cones corresponding to Tanino's concept of the subgradient of …
Homogenization Of Nonlinear Partial Differential Equations,
2010
Louisiana State University and Agricultural and Mechanical College
Homogenization Of Nonlinear Partial Differential Equations, Silvia Jiménez
LSU Doctoral Dissertations
This dissertation is concerned with properties of local fields inside composites made from two materials with different power law behavior. This simple constitutive model is frequently used to describe several phenomena ranging from plasticity to optical nonlinearities in dielectric media. We provide the corrector theory for the strong approximation of fields inside composites made from two power law materials with different exponents. The correctors are used to develop bounds on the local singularity strength for gradient fields inside microstructured media. The bounds are multiscale in nature and can be used to measure the amplification of applied macroscopic fields by the …
Perverse Poisson Sheaves On The Nilpotent Cone,
2010
Louisiana State University and Agricultural and Mechanical College
Perverse Poisson Sheaves On The Nilpotent Cone, Jared Lee Culbertson
LSU Doctoral Dissertations
For a reductive complex algebraic group, the associated nilpotent cone is the variety of nilpotent elements in the corresponding Lie algebra. Understanding the nilpotent cone is of central importance in representation theory. For example, the nilpotent cone plays a prominent role in classifying the representations of finite groups of Lie type. More recently, the nilpotent cone has been shown to have a close connection with the affine flag variety and this has been exploited in the Geometric Langlands Program. We make use of the following important fact. The nilpotent cone is invariant under the coadjoint action of G on the …
Hamilton-Jacobi Theory For Optimal Control Problems On Stratified Domains,
2010
Louisiana State University and Agricultural and Mechanical College
Hamilton-Jacobi Theory For Optimal Control Problems On Stratified Domains, Richard Charles Barnard
LSU Doctoral Dissertations
This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz dynamics. This background gives the motivation for our results for systems over stratified domains, which is a system with non-Lipschitz dynamics that were introduced by Bressan and Hong. We provide an example that shows their attempt to derive a Hamilton-Jacobi characterization of the value function is incorrect, and discuss the nature of their error. A new construction of a multifunction is introduced that possesses properties similar to those of a Lipschitz multifunction, and is used …
Power Series Expansions For Waves In High-Contrast Plasmonic Crystals,
2010
Louisiana State University and Agricultural and Mechanical College
Power Series Expansions For Waves In High-Contrast Plasmonic Crystals, Santiago Prado Parentes Fortes
LSU Doctoral Dissertations
In this thesis, a method is developed for obtaining convergent power series expansions for dispersion relations in two-dimensional periodic media with frequency dependent constitutive relations. The method is based on high-contrast expansions in the parameter _x0011_ = 2_x0019_d=_x0015_, where d is the period of the crystal cell and _x0015_ is the wavelength. The radii of convergence obtained are not too small, on the order of _x0011_ _x0019_ 102. That the method applies to frequency dependent media is an important fact, since the majority of the methods available in the literature are restricted to frequency independent constitutive relations. The convergent series …
