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Articles 1 - 30 of 76
Full-Text Articles in Physical Sciences and Mathematics
An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones
An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …
Foundations Of Wave Phenomena: Complete Version, Charles G. Torre
Foundations Of Wave Phenomena: Complete Version, Charles G. Torre
Foundations of Wave Phenomena
This is the complete version of Foundations of Wave Phenomena. Version 8.3.1.
Please click here to explore the components of this work.
Introduction To Classical Field Theory, Charles G. Torre
Introduction To Classical Field Theory, Charles G. Torre
All Complete Monographs
This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.
Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton
Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
Downloads
This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.
Supplementary Files For "Creating A Universal Depth-To-Load Conversion Technique For The Conterminous United States Using Random Forests", Jesse Wheeler, Brennan Bean, Marc Maguire
Supplementary Files For "Creating A Universal Depth-To-Load Conversion Technique For The Conterminous United States Using Random Forests", Jesse Wheeler, Brennan Bean, Marc Maguire
Browse all Datasets
As part of an ongoing effort to update the ground snow load maps in the United States, this paper presents an investigation into snow densities for the purpose of predicting ground snow loads for structural engineering design with ASCE 7. Despite their importance, direct measurements of snow load are sparse when compared to measurements of snow depth. As a result, it is often necessary to estimate snow load using snow depth and other readily accessible climate variables. Existing depth-to-load conversion methods, each of varying complexity, are well suited for snow load estimation for a particular region or station network, but …
Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, Daniel D'Alessio
Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, Daniel D'Alessio
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Changes in the spatial distribution of vegetation respond to variations in the production and transportation mechanisms of seeds at different locations subject to heterogeneities, often because of soil characteristics. In semi-arid environments, the competition for water and nutrients pushes the superficial plant’s roots to obtain scarce resources at long ranges. In this report, we assume that vegetation biomass interacts with itself in two different ways, facilitation and inhibition, depending on the relative distances. We present a 1-dimensional Integro-difference model to represent and study the emergence of patterns in the distribution of vegetation.
Optimal Control Of Algae Biofilm Growth In Wastewater Treatment Using Computational Mathematical Models, Gerald Benjamin Jones
Optimal Control Of Algae Biofilm Growth In Wastewater Treatment Using Computational Mathematical Models, Gerald Benjamin Jones
Undergraduate Honors Capstone Projects
Microalgal biofilms are comprised of a syntrophic consortium of microalgae and other microorganisms embedded within an extracellular matrix. Despite significant processes in the application of microalgal biofilms in wastewater treatment, mechanistic understanding and optimization of microalgal biomass yield and productivity under environmental constraints is still lacking. This paper identifies theoretical insights on this challenging biological problem by leveraging novel mathematical and computational tools. In particular, through a computational mathematical model to advance the understanding of microalgal biofilm growth kinetics under environmental constraints through a systematic parameter study. Moreover, design of algae biofilm reactors for optimal biomass yield and productivity in …
Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight
Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the …
Methods In Modeling Wildlife Disease From Model Selection To Parameterization With Multi-Scale Data, Ian Mcgahan
Methods In Modeling Wildlife Disease From Model Selection To Parameterization With Multi-Scale Data, Ian Mcgahan
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The effects of emerging wildlife diseases are global and profound, resulting in loss of human life, economic and agricultural impacts, declines in wildlife populations, and ecological disturbance. The spread of wildlife diseases can be viewed as the result of two simultaneous processes: spatial spread of wildlife populations and disease spread through a population. For many diseases these processes happen at different timescales, which is reflected in available data. These data come in two flavors: high-frequency, high-resolution telemetry data (e.g. GPS collar) and low-frequency, low-resolution presence-absence disease data. The multi-scale nature of these data makes analysis of such systems challenging. Mathematical …
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Publications
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …
Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, Ashley B. Cromer
Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, Ashley B. Cromer
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
There has been little research conducted related to how school-based agricultural (SBAE) teachers perceive the utilization of volunteers in the classroom. The United States is facing a shortage of SBAE teachers, and with turnover rates that are not sustainable, solutions for support and reduction of the SBAE teachers’ workload must be sought with diligence. There is potential for volunteers to reduce some of the responsibilities that the SBAE teacher is faced with. The purposes of this study are to determine the demographic characteristics of the volunteers being utilized and of the SBAE teachers, determine the perceived benefits, barriers and beliefs …
Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang
Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang
Mathematics and Statistics Faculty Publications
We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …
How To Make Tetrads, Charles G. Torre
How To Make Tetrads, Charles G. Torre
How to... in 10 minutes or less
This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.
Symmetric Criticality In General Relativity, Charles G. Torre
Symmetric Criticality In General Relativity, Charles G. Torre
Research Vignettes
In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.
Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre
Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre
Tutorials on... in 1 hour or less
In this worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. I will restrict my attention to 4-dimensional spacetimes.
Applied Mathematical Programming, Man-Keun Kim, Bruce A. Mccarl, Thomas H. Spreen
Applied Mathematical Programming, Man-Keun Kim, Bruce A. Mccarl, Thomas H. Spreen
Textbooks
This book is intended to both serve as a reference guide and a text for a course on Applied Mathematical Programming for upper undergraduate and Master level students in Economics, Applied Economics, Agricultural and Resource Economics, and Management; primarily based on McCarl and Spreen (2013). The material presented in McCarl and Spreen (2013) concentrates upon conceptual issues, problem formulation, computerized problem solution, and results interpretation; it is designed for the advanced readers who are familiar with mathematical economics including linear and matrix algebra and also with advanced modeling skills. Upper level undergraduate and/or Master students may not be beneficial from …
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.
Prediction Of Stress Increase In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney
Prediction Of Stress Increase In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
While internal and external unbonded tendons are widely utilized in concrete structures, the analytic solution for the increase in unbonded tendon stress, Δ���, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. In this thesis, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on different sets of candidate variables, amongst the material and sectional properties from the database compiled by Maguire et al. [18]. Predictions of Δ��� are made via Principal Component Regression models, and the method …
A Stochastic Model For Water-Vegetation Systems And The Effect Of Decreasing Precipitation On Semi-Arid Environments, Shannon A. Dixon
A Stochastic Model For Water-Vegetation Systems And The Effect Of Decreasing Precipitation On Semi-Arid Environments, Shannon A. Dixon
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming these regions into deserts. Many mathematical models have been developed for purposes of analyzing vegetation-water interactions, particularly in semi-arid landscapes. Most models are based on the average behavior of the system as a whole, and how it is influenced by external changes. These models may be termed "macro-scale" models. Other models have concerned themselves with the interactions between individuals, in this case the interactions between individual plants …
Foundations Of Wave Phenomena, Charles G. Torre
Foundations Of Wave Phenomena, Charles G. Torre
Charles G. Torre
This is an undergraduate text on the mathematical foundations of wave phenomena. Version 8.2.
On The Propagation Of Atmospheric Gravity Waves In A Non-Uniform Wind Field: Introducing A Modified Acoustic-Gravity Wave Equation, Ahmad Talaei
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies.
We utilize the complete set of governing equations for a compressible atmosphere with non-uniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is simplified …
The Kretschmann Scalar, Charles G. Torre
The Kretschmann Scalar, Charles G. Torre
How to... in 10 minutes or less
On a pseudo-Riemannian manifold with metric g, the "Kretschmann scalar" is a quadratic scalar invariant of the Riemann R tensor of g, defined by contracting all indices with g. In this worksheet we show how to calculate the Kretschmann scalar from a metric.
Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link
Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link
All ECSTATIC Materials
The science and management of aquatic ecosystems is inherently interdisciplinary, with issues associated with hydrology, atmospheric science, water quality, geochemistry, sociology, economics, environmental science, and ecology. Addressing water resources issues in any one discipline invariably involves effects that concern other disciplines, and attempts to address one issue often have consequences that exacerbate existing issues or concerns, or create new ones (Jørgensen et al. 1992; Lackey et al. 1975; Straskraba 1994) due to the strongly interactive nature of key processes (Christensen et al. 1996). Thus, research and management of aquatic ecosystems must be interdisciplinary to be most effective, but such truly …
Rooted In Hell: Predicting Invasion Rates Of Phragmites Australis, Rachel Nydegger, Jacob P. Duncan, James A. Powell
Rooted In Hell: Predicting Invasion Rates Of Phragmites Australis, Rachel Nydegger, Jacob P. Duncan, James A. Powell
Browse All Undergraduate research
Across the estuaries of the east coast and wetlands of the Great Lakes, the invasive grass Phragmites australis outcompetes other vegetation and destroys local ecosystems. Because its roots are tolerant to salinity that other plants find hellish, Phragmites invasions begin with vegetative spread of genetic clones in brackish marshlands. This plant can grow over three meters tall at densities of 50 stems/m2, provides poor wildlife habitat, and is very difficult to eradicate.
A discrete life stage model on a yearly time step captures seed survivorship in a seed bank, sexual and asexual recruitment into a juvenile age class, and differential …
The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks
The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks
Presentations and Publications
The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the equivalence problem. These are the slides for a presentation at the Mathematics Association of America Spring 2015 conference at Brigham Young University.
Predicting Invasion Rates For Phragmites Australis, Rachel Nydegger, Jacob Duncan, James A. Powell
Predicting Invasion Rates For Phragmites Australis, Rachel Nydegger, Jacob Duncan, James A. Powell
Browse All Undergraduate research
In wetlands of Utah and southern Idaho as well as estuaries of the east coast, the ten-foot tall invasive grass Phragmites australis can be found near waterways, where it outcompetes native plants and degrades wildlife habitat. Phragmites australis is an obligate out-crossing plant that can spread sexually through seed disper- sal, or asexually via stolons and rhi- zomes (Kettenring and Mock 2012). Small patches are usually a single genetic individual, spreading vegetatively (and slowly) via runners; when patches become genetically diverse viable seeds are produced and invasion rates can be increase by an order of magnitude (Kettenring et al. 2011)
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
Tutorials on... in 1 hour or less
Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .