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, …
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 …
Period Doubling Cascades From Data,
2022
William & Mary
Period Doubling Cascades From Data, Alexander Berliner
Undergraduate Honors Theses
Orbit diagrams of period doubling cascades represent systems going from periodicity to chaos. Here, we investigate whether a Gaussian process regression can be used to approximate a system from data and recover asymptotic dynamics in the orbit diagrams for period doubling cascades. To compare the orbits of a system to the approximation, we compute the Wasserstein metric between the point clouds of their obits for varying bifurcation parameter values. Visually comparing the period doubling cascades, we note that the exact bifurcation values may shift, which is confirmed in the plots of the Wasserstein distance. This has implications for studying dynamics …
Modeling And Analyses Of Mechanisms Underlying Network Synaptic Dynamics In Two Neural Circuits,
2022
William & Mary
Modeling And Analyses Of Mechanisms Underlying Network Synaptic Dynamics In Two Neural Circuits, Linda Ma
Undergraduate Honors Theses
In systems neuroscience, circuit models of cortical structures can be used to deconstruct mechanisms responsible for spike patterns that generate a variety of behaviors observed in the brain. In particular, mathematical simulations of these circuits can replicate complex dynamical behaviors that mirror not only macroscopically patterns observed in the brain, but also a significant amount of experimentally characterized minutiae. These models are capable of analyzing neural mechanisms by explicitly deconstructing connectivities between populations of neurons in ways that tend to be empirically inaccessible. This work presents two such models; one in the rat somatosensory barrel cortex, responsible for processing sensory …
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.
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.
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 …
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.
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 …
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 …
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?"
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 …
Decision-Analytic Models Using Reinforcement Learning To Inform Dynamic Sequential Decisions In Public Policy,
2022
University of Massachusetts Amherst
Decision-Analytic Models Using Reinforcement Learning To Inform Dynamic Sequential Decisions In Public Policy, Seyedeh Nazanin Khatami
Doctoral Dissertations
We developed decision-analytic models specifically suited for long-term sequential decision-making in the context of large-scale dynamic stochastic systems, focusing on public policy investment decisions. We found that while machine learning and artificial intelligence algorithms provide the most suitable frameworks for such analyses, multiple challenges arise in its successful adaptation. We address three specific challenges in two public sectors, public health and climate policy, through the following three essays. In Essay I, we developed a reinforcement learning (RL) model to identify optimal sequence of testing and retention-in-care interventions to inform the national strategic plan “Ending the HIV Epidemic in the US”. …
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 …
The Pursuit–Evasion Problems In A Differential Game With Ggr-Constraints On Controls,
2022
Namangan State University, Namangan, Uzbekistan
The Pursuit–Evasion Problems In A Differential Game With Ggr-Constraints On Controls, Bahrom Samatov, Bakhodirjon Juraev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In the present paper, we consider pursuit and evasion problems in a simple motion differential game when Pursuer's control is subjected to geometric constraint and Evader's control is subjected to Grönwall type constraint. In order to solve the pursuit problem, the parallel convergence strategy (the П-strategy) for the Pursuer is constructed, and sufficient conditions of pursuit are obtained. Also, we prove that the П-strategy is an optimal strategy of Pursuer. In solving of the evasion problem, we propose an admissible control function to the Evader, and we obtaine sufficient conditions of evasion. In addition, an estimation of the distance between …
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 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.
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer,
2022
University of California, Riverside
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Spora: A Journal of Biomathematics
Radiation therapy remains as one of the main cancer treatment modalities. Typical regimens for radiotherapy comprise a constant dose administered on weekdays, and no radiation on weekends. In this paper, we examine adaptive dosages of radiation treatment strategies for heterogeneous tumors using a dynamical system model that consist of radiation-resistant and parental populations with unique interactive properties, namely, PC3 and DU145 prostate cancer cell lines. We show that stronger doses of radiation given in longer time intervals, while keeping the overall dosage the same, are effective in PC3 cell lines, but not in DU145 cell lines. In addition, we tested …
