Universality And Synchronization In Complex Quadratic Networks (Cqns), 2022 State University of New York at New Paltz

#### Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Gene Drives And The Consequences Of Over-Suppression, 2022 Virginia Commonwealth University

#### Gene Drives And The Consequences Of Over-Suppression, Cole Butler

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, 2022 Georgia Institute of Technology

#### Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

The Butterfly Effect Of Fractals, 2022 Murray State University

#### The Butterfly Effect Of Fractals, Cody Watkins

*Honors College Theses*

This thesis applies concepts in fractal geometry to the relatively new field of mathematics known as chaos theory, with emphasis on the underlying foundation of the field: the butterfly effect. We begin by reviewing concepts useful for an introduction to chaos theory by defining terms such as fractals, transformations, affine transformations, and contraction mappings, as well as proving and demonstrating the contraction mapping theorem. We also show that each fractal produced by the contraction mapping theorem is unique in its fractal dimension, another term we define. We then show and demonstrate iterated function systems and take a closer look at ...

Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, 2021 Embry-Riddle Aeronautical University

#### Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov

*Publications*

A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow ...

A Connectivity Framework To Explore The Role Of Anthropogenic Activity And Climate On The Propagation Of Water And Sediment At The Catchment Scale, 2021 University of Tennessee, Knoxville

#### A Connectivity Framework To Explore The Role Of Anthropogenic Activity And Climate On The Propagation Of Water And Sediment At The Catchment Scale, Christos Giannopoulos

*Doctoral Dissertations*

Anthropogenic disturbance in intensively managed landscapes (IMLs) has dramatically altered critical zone processes, resulting in fundamental changes in material fluxes. Mitigating the negative effects of anthropogenic disturbance and making informed decisions for optimal placement and assessment of best management practices (BMPs) requires fundamental understanding of how different practices affect the connectivity or lack thereof of governing transport processes and resulting material fluxes across different landscape compartments within the hillslope-channel continuum of IMLs. However, there are no models operating at the event timescale that can accurately predict material flux transport from the hillslope to the catchment scale capturing the spatial and ...

An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival, 2021 University of Wisconsin - La Crosse

#### An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival, James Peirce, Greg Sandland

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, 2021 University of Richmond

#### Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, Michael Kerckhove, Shuheng Chen

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, 2021 Durango Institute of Technology, México

#### Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, 2021 Jarvis Christian College

#### Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Hyperbolicity And Certain Statistical Properties Of Chaotic Billiard Systems, 2021 University of Massachusetts Amherst

#### Hyperbolicity And Certain Statistical Properties Of Chaotic Billiard Systems, Kien T. Nguyen

*Doctoral Dissertations*

In this thesis, we address some questions about certain chaotic dynamical systems. In particular, the objects of our studies are chaotic billiards. A billiard is a dynamical system that describe the motions of point particles in a table where the particles collide elastically with the boundary and with each other.

Among the dynamical systems, billiards have a very important position. They are models for many problems in acoustics, optics, classical and quantum mechanics, etc.. Despite of the rather simple description, billiards of different shapes of tables exhibit a wide range of dynamical properties from being complete integrable to chaotic. A ...

On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, 2021 University of Sao Paulo

#### On The Rectilinear Motion Of Three Bodies Mutually Attracting Each Other, Sylvio R. Bistafa

*Euleriana*

This is an annotated translation from Latin of E327 --* De motu rectilineo trium corporum se mutuo attrahentium* (“On the rectilinear motion of three bodies mutually attracting each other”). In this publication, Euler considers three bodies lying on a straight line, which are attracted to each other by central forces inversely proportional to the square of their separation distance (inverse-square law). Here Euler finds that the parameter that controls the relative distances among the bodies is given by a quintic function.

Mapping Polynomial Dynamics, 2021 DePaul University

#### Mapping Polynomial Dynamics, Devin Becker

*DePaul Discoveries*

We explore the complex dynamics of a family of polynomials defined on the complex plane by f(z) = az^{m}(1+z/d)^{d} where a is a complex number not equal to zero, and m and d are at least 2. These functions have three finite critical points, one of which has behavior that differs as we change our parameter values. We analyze the dynamical behavior at this critical point, with a particular interest in the structures that appear in the filled Julia set K(f) and the basin of infinity A_{\infty}(f). The behavior of the family ...

Contributions To The Teaching And Learning Of Fluid Mechanics, 2021 Montclair State University

#### Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

*Department of Mathematics Facuty Scholarship and Creative Works*

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science and engineering ...

Lebesgue Measure Preserving Thompson Monoid And Its Properties Of Decomposition And Generators, 2021 Stanford University

#### Lebesgue Measure Preserving Thompson Monoid And Its Properties Of Decomposition And Generators, William Li

*Rose-Hulman Undergraduate Mathematics Journal*

This paper defines the Lebesgue measure preserving Thompson monoid, denoted by **G**, which is modeled on the Thompson group **F** except that the elements of **G** preserve the Lebesgue measure and can be non-invertible. The paper shows that any element of the monoid **G** is the composition of a finite number of basic elements of the monoid **G** and the generators of the Thompson group **F**. However, unlike the Thompson group **F**, the monoid **G** is not finitely generated. The paper then defines equivalence classes of the monoid **G**, use them to construct a monoid **H** that is finitely generated ...

Disjointness Of Linear Fractional Actions On Serre Trees, 2021 Brown University

#### Disjointness Of Linear Fractional Actions On Serre Trees, Henry W. Talbott

*Rose-Hulman Undergraduate Mathematics Journal*

Serre showed that, for a discrete valuation field, the group of linear fractional transformations acts on an infinite regular tree with vertex degree determined by the residue degree of the field. Since the p-adics and the polynomials over the finite field of order p act on isomorphic trees, we may ask whether pairs of actions from these two groups are ever conjugate as tree automorphisms. We analyze permutations induced on finite vertex sets, and show a permutation classification result for actions by these linear fractional transformation groups. We prove that actions by specific subgroups of these groups are conjugate only ...

Smooth Global Approximation For Continuous Data Assimilation, 2021 CUNY Hunter College

#### Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

*Theses and Dissertations*

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, 2021 CUNY Hunter College

#### Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

*Theses and Dissertations*

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

On The Structure Of The Essential Spectrum For Discrete Schrödinger Operators Associated With Three-Particle System, 2021 National University of Uzbekistan

#### On The Structure Of The Essential Spectrum For Discrete Schrödinger Operators Associated With Three-Particle System, Shukhrat Lakaev, Tirkash Radjabov, Nizomiddin Makhmasaitovich Aliev

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

We consider a family of discrete Schrödinger operators $H(K),\,K\in (-\pi,\pi]^5$ associated with a system of three quantum particles on the five-dimensional lattice ${\mathbb{Z}}^5$ interacting via short-range pair potentials and having arbitrary "dispersion functions" with not necessarily compact support.

We show that the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),\,K\in (-\pi,\pi]^5$ consists of a finitely many bounded closed intervals.

Stationary Probability Distributions Of Stochastic Gradient Descent And The Success And Failure Of The Diffusion Approximation, 2021 New Jersey Institute of Technology

#### Stationary Probability Distributions Of Stochastic Gradient Descent And The Success And Failure Of The Diffusion Approximation, William Joseph Mccann

*Theses*

In this thesis, Stochastic Gradient Descent (SGD), an optimization method originally popular due to its computational efficiency, is analyzed using Markov chain methods. We compute both numerically, and in some cases analytically, the stationary probability distributions (invariant measures) for the SGD Markov operator over all step sizes or learning rates. The stationary probability distributions provide insight into how the long-time behavior of SGD samples the objective function minimum.

A key focus of this thesis is to provide a systematic study in one dimension comparing the exact SGD stationary distributions to the Fokker-Planck diffusion approximation equations —which are commonly used in ...