Active Polar Liquid Crystal Channel Flows: Analyzing The Roles Of Nematic Strength And Activation Parameter,
2022
Old Dominion University
Active Polar Liquid Crystal Channel Flows: Analyzing The Roles Of Nematic Strength And Activation Parameter, Lacey Schenk, Ruhai Zhou
College of Sciences Posters
Suspensions of active polar liquid crystalline polymers (APLC) exhibit complex phenomena such as spontaneous flows, pattern formations and defects. Using the Kinetic Model, which couples the Smoluchowski Equation and the Navier-Stokes Equations, we conduct numerical simulations of APLC in a microfluidic channel to investigate the competitive effect among different material constants, such as the nematic concentration (the strength of the potential for nematic order) and active strength (the individual nano-rods strength of their individual movement) with and without a pressure gradient. Both Dirichlet and Neumann boundary conditions on the mathematical model are employed. Steady states, including isotropic and nematic states, …
A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems,
2022
Old Dominion University
A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng
College of Sciences Posters
Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.
Factors That Relate To Academic Excellence,
2022
Louisiana Tech University
Factors That Relate To Academic Excellence, Matthew Lemoine
Mathematics Senior Capstone Papers
The American College Testing (ACT) provides university admissions offices a look into a student’s academic ability so that the university can determine admittance and scholarships. The premise of this study is to see whether this is the most effective way to determine academic ability, using the Logistic Regression Model. The data was collected from October 21, 2021 to December 31, 2021 at Louisiana Tech University. Using the Logistic Regression Model, predictions of academic excellence are obtained based on the parameters outlined in this paper. After the parameters for the Logistic Regression Model are calculated, conclusions can be drawn that the …
Predicting Box Office Revenues Using Differential Equation Models,
2022
Louisiana Tech University
Predicting Box Office Revenues Using Differential Equation Models, Brenden David
Mathematics Senior Capstone Papers
The growing popularity of the internet has increased exponentially in the past few decades. This sudden increase in popularity allows for users to gain access to more information than was thought possible in the past, including access to box-office movie revenues of previously released movies. Since we now have access to thousands of movie’s box office revenues, we can analyze some sort of trend within specific genres of movies. With these trends we develop a differential equations model that will predict the box office revenues of a movie that is in its early stages of the box office. This model …
Flood Risk Prediction In Southern Louisiana Using Support Vector Machines,
2022
Louisiana Tech University
Flood Risk Prediction In Southern Louisiana Using Support Vector Machines, Claire Dorsett
Mathematics Senior Capstone Papers
Flooding in Southern Louisiana is a growing concern as violent weather becomes more frequent. According to the Environmental Protection Agency (EPA), Louisiana soils have become drier and annual rainfall trends have increased, which may lead to more severe flooding in the coming years. In light of this change in weather trends, flood prediction has become increasingly important for the public’s safety. The focus of this paper is to apply the Support Vector Machine (SVM), a machine learning technique, to classify flood risks based on water gage height, wind speed and direction, and time of the year. In this paper, the …
A New Application Of The Central Limit Theorem,
2022
Southeastern University
A New Application Of The Central Limit Theorem, Kenneth Winters
Selected Honors Theses
This paper discusses the Central Limit Theorem (CLT) and its applications. The paper gives an introduction to what the CLT is and how it can be applied to real life. Additionally, the paper gives a conceptual understanding of the theorem through various examples and visuals. The paper discusses the applications of the CLT in fields such as computer science, psychology, and political science. The author then suggests a new mathematical theorem as an application of the CLT and provides a proof of the theorem. The new theorem relates to expected value and probabilities of random variables and provides a link …
A Uniform Chevalley Theorem For Direct Summands Of Polynomial Rings In Mixed Characteristic,
2022
Università di Genova
A Uniform Chevalley Theorem For Direct Summands Of Polynomial Rings In Mixed Characteristic, Alessandro De Stefani, Eloisa Grifo, Jack Jeffries
Department of Mathematics: Faculty Publications
We prove an explicit uniform Chevalley theorem for direct summands of graded polynomial rings in mixed characteristic. Our strategy relies on the introduction of a new type of differential powers that does not require the existence of a p-derivation on the direct summand.
Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode,
2022
Embry-Riddle Aeronautical University
Vertical Take-Off And Landing Control Via Dual-Quaternions And Sliding Mode, Joshua Sonderegger
Doctoral Dissertations and Master's Theses
The landing and reusability of space vehicles is one of the driving forces into renewed interest in space utilization. For missions to planetary surfaces, this soft landing has been most commonly accomplished with parachutes. However, in spite of their simplicity, they are susceptible to parachute drift. This parachute drift makes it very difficult to predict where the vehicle will land, especially in a dense and windy atmosphere such as Earth. Instead, recent focus has been put into developing a powered landing through gimbaled thrust. This gimbaled thrust output is dependent on robust path planning and controls algorithms. Being able to …
Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture,
2022
University of South Carolina
Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor
Senior Theses
Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to …
A Meshless Approach To Computational Pharmacokinetics,
2022
Embry-Riddle Aeronautical University
A Meshless Approach To Computational Pharmacokinetics, Anthony Matthew Khoury
Doctoral Dissertations and Master's Theses
The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless …
Obstructions To Shake Sliceness For Links,
2022
Andrews University
Obstructions To Shake Sliceness For Links, Anthony Bosman
Faculty Publications
Shake slice generalizes the notion of a slice link, naturally extending the notion of shake slice knots to links. There is also a relative version, shake concordance, that generalizes link concordance. We show that if two links are shake concordant, then their zero surgery manifolds are homology cobordant. Then we give several obstructions to a link being shake slice; for instance, the Arf invariants vanish for both the link and each component. Finally we show that a shake slice link bounds disjoint disks in a homology 4-ball and hence each component is algebraically slice.
Bistability And Switching Behavior In Moving Animal Groups,
2022
Lafayette College
Bistability And Switching Behavior In Moving Animal Groups, Daniel Strömbom, Stephanie Nickerson, Catherine Futterman, Alyssa Difazio, Cameron Costello, Kolbjørn Tunstrøm
Northeast Journal of Complex Systems (NEJCS)
Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching …
Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?,
2022
New Jersey Institute of Technology
Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?, Cristo Leon, James Lipuma, Michele Rittenhouse, Louis Wells, Edgar Meritano, Ricardo Morales-Carbajal, Miguel Angel Bastarrachea Magnani, Ten80 Education, Llc, New Jersey School Boards Association, International Stem League, Inc (Insl), Red De Investigadores De Juegos De Rol
STEM for Success Resources
Proceedings of the "State of STEM 2022: How does virtual hands-on STEM work?"
Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation,
2022
University of South Florida
Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation, Ahmed Ahmed
USF Tampa Graduate Theses and Dissertations
For many years, the study of integrable systems has been one of the most fascinating branches of mathematics and has been thought to be an interesting area for both mathematicians and physicists alike.Many natural phenomena can be predicted by using integrable systems, particularly by studying their different solutions, as well as analyzing and exploring their properties and structures. They are commonly found in nonlinear optics, plasmas, ocean and water waves, gravitational fields, and fluid dynamics. Typical examples of integrable systems include the Korteweg-de Vries (KdV) equation, the nonlinear Schrödinger (NLS) equation, and the Kadomtsev-Petviashvili (KP) equation. Solitons are intrinsic solutions …
Image Classification Based On Sparse Representation In The Quaternion Wavelet Domain,
2022
East Texas A&M University
Image Classification Based On Sparse Representation In The Quaternion Wavelet Domain, Long H. Ngo, Nikolay Metodiev Sirakov, Marie Luong, Emmanuel Viennet
Faculty Publications
In this study, we propose a novel sparse representation learning method in the Quaternion Wavelet (QW) domain for multi-class image classification. The proposed method takes advantages from: i) the QW decomposition, which promotes sparsity and provides structural information about the image data while allowing approximate shift-invariance, to extract meaningful features from low-frequency QW subbands, ii) the dimensionality reduction method using Principal Component Analysis (PCA) for reducing the complexity of the problem, and iii) the sparse representation of the generated QW features to efficiently learn and capture the meaningful and compact information of this data. After the QW decomposition, the features …
On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context,
2022
Dortmund University of Applied Sciences and Arts
On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, Flavius Guias
Spora: A Journal of Biomathematics
This paper presents a mathematically formalized approach which points out the relation between efficacy and effectiveness of vaccines. The first term denotes the relative degree of protection in clinical trials or under ideal conditions, while the latter is based on observed real-life data. We define the efficacy by a similar formula to the effectiveness, but the probabilities involved in the relative risk are conditional with respect to the exposure to the virus. If exposure and vaccination status are independent, the two quantities are equal. Otherwise, the observed value of the effectiveness is a biased one, as it could be seen …
Analysis Of Sir Epidemic Models With Sociological Phenomenon,
2022
University of Wisconsin-La Crosse
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Spora: A Journal of Biomathematics
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values.
Numerical Study Of Highly Efficient Centrifugal Cyclones,
2022
Ferghana Polytechnic Institute
Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev
Scientific-technical journal
Centrifugal cyclones have been developing for 100 years, while the efficiency of all cyclones for fine dust does not increase by 80%. The widespread use of cyclones in all branches of industrial production is determined by the simplicity of the design and sufficient reliability in operation. Along with this, the process carried out in a cyclone presents a complex scientific problem that has not been solved from the standpoint of aerohydromechanics. This is confirmed by various cyclone designs. Currently, the efficiency of cyclone cleaning of technological flows does not meet the requirements of sanitary standards and largely determines the level …
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium,
2022
California State Polytechnic University, Pomona
Human Impact On Planetary Temperature And Glacial Volume: Extending A Toy Climate Model To A New Millennium, Samantha Secor, Jennifer Switkes
CODEE Journal
Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions …
Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall,
2022
College of the Holy Cross
Translation Of: Dupin’Sche Hyperflächen, Doctoral Dissertation, Universität Freiburg (1981) By Ulrich Pinkall, Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
This is an unofficial translation of the original dissertation which was written in German. A few minor typographical errors have been corrected by the translator. All references should be made to the original dissertation. The classification of Dupin hypersurfaces in E4 contained in this dissertation is also contained in the journal article by Ulrich Pinkall, Dupin’sche Hyperflächen in E4, Manuscr. Math. 51 (1985), 89–119.
