Non-linear Dynamics Commons^™

Unconventional Computing With Photonic Oscillator Networks, Mostafa Honari Latifpour

Dissertations, Theses, and Capstone Projects

The ever-increasing demand for data processing and the challenges in scaling traditional computing architectures are driving intensive research into alternative computing paradigms. Optical computing has garnered renewed attention since the 2010s, driven by its potential to accelerate specialized computational tasks such as combinatorial optimization and neural networks.

Coherent light sources including lasers and parametric oscillators have been around for decades and become indispensable tools in modern technology, but these photonic oscillators are also nonlinear dynamical systems that can exhibit emergent, complex phenomena, especially when coupled in arrays. These nonlinear optical systems have recently been shown to be capable of doing …

A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Fast Information And Slow(Er) Disease Spreading: A Geometric Analysis, Iulia Martina Bulai, Mattia Sensi, Sara Sottile

Biology and Medicine Through Mathematics Conference

No abstract provided.

Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr

Biology and Medicine Through Mathematics Conference

No abstract provided.

Effect Of Recommending Users And Opinions On The Network Connectivity And Idea Generation Process, Sriniwas Pandey, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

The growing reliance on online services underscores the crucial role of recommendation systems, especially on social media platforms seeking increased user engagement. This study investigates how recommendation systems influence the impact of personal behavioral traits on social network dynamics. It explores the interplay between homophily, users’ openness to novel ideas, and recommendation-driven exposure to new opinions. Additionally, the research examines the impact of recommendation systems on the diversity of newly generated ideas, shedding light on the challenges and opportunities in designing effective systems that balance the exploration of new ideas with the risk of reinforcing biases or filtering valuable, unconventional …

Normrank Correlations For Testing Associations And For Use In Latent Variable Models, Daniel B. Wright

Educational Psychology, Leadership, and Higher Education Faculty Research

Pearson’s correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman’s p is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or for short the normrank transformation. Using the normrank transformation was more powerful than Pearson’s and Spearman’s procedures when the distributions have less than normal kurtosis (platykurtic), when the distributions have greater than normal kurtosis (leptokurtic), and when the distribution is skewed. This is examined for testing if there is an …

Exploration Of Characteristic Curve In Fox Float 3 Shock Dampers To Expedite Shock Damp Tuning., Joshua R. Moore

Honors College Theses

The shock absorber is an integral part of a vehicle suspension system and has a strong influence on its performance, especially in the case of motorsports. It is important to study the force versus velocity relationship, commonly known as the characteristic curve of the shock absorber both during compression and rebound. Vendor-supplied characteristics often reflect the behavior of the shock absorber in a particular setting. However, during the installation, the settings inside the shock absorber are adjusted to increase the human comfort level and performance of the vehicle. This may change the characteristic curve of the shock. The available data …

Generation, Dynamics, And Interaction Of Quartic Solitary Waves In Nonlinear Laser Systems, Sabrina Hetzel

Mathematics Theses and Dissertations

Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the …

Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi

Mathematics Dissertations - Archive

In this thesis, we employ optimal control frameworks in two distinct contexts: Human immunodeficiency virus (HIV) and esophageal cancer. For HIV, we introduce a comprehensive data-driven nonlinear optimization framework designed for personalized therapies. This framework utilizes a deterministic in-host nonlinear ordinary differential equation (ODE) model and formulates two optimization problems using individual patient data. The first problem focuses on estimating patient-specific parameters through constrained optimization, while the second problem determines optimal combination therapies to reduce viral load to undetectable levels. Several numerical experiments suggest that our framework can provide a robust and effective optimal dosages with lower toxicity levels to …

Hamiltonian Models For The Propagation Of Long Gravity Waves, Higher-Order Kdv-Type Equations And Integrability, Rossen Ivanov

Book chapter/book

A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation.

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

Mathematical Analysis Of Eukaryotic Pericentromere, Puranjan Ghimire

Theses and Dissertations

The centromere is crucial for chromosomal stability and their proper segregation during cell division in eukaryotes. Surrounding the centromere are pericentromeres, made of repetitive DNA elements called pericentromeric repeats, varying from 10 in fission yeast to thousands in humans. These repeats form densely packed heterochromatin, where genes are usually silenced. The silencing mechanism across different pericentromeric repeats remains unclear.

Despite variations in sequence and length, pericentromeric repeats are conserved across eukaryotes, indicating their functional importance. This dissertation presents mathematical models to quantify gene silencing in fission yeast and humans. In fission yeast, my model predicts that silencing occurs only with …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

All Dissertations

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Experimental Analysis Of Nonlinear Wave Propagation In Bistable Mechanical Metamaterials With A Defect, Samuel R. Harre

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Mechanical metamaterials built up of compliant units can support the propagation of linear and nonlinear waves. A popular architecture consists of a one-dimensional chain of bistable elements connected by linear springs. This type of chain can support nonlinear transition waves that switch each element from one stable state to the other as they propagate along the chain. One way to manipulate the propagation of such waves is via introduction of a local inhomogeneity, i.e., a defect in the otherwise periodic chain. Recent analytical and numerical work has shown that based on its initial velocity, a transition wave may be reflected, …

Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.