Non-linear Dynamics Commons^™

Information Theory Analysis Of Water Vapor Stable Isotopes From The Sail Campaign, Matthew John Rybecky

Earth and Planetary Sciences ETDs

Understanding the processes that control water vapor isotopic composition in mountain environ- ments is essential for interpreting isotope records and predicting water resource responses to cli- mate change. This thesis applies information theory to continuous, high-resolution water vapor stable isotope measurements from the Surface Atmosphere Integrated Field Laboratory (SAIL) campaign in the East River watershed of Colorado’s Upper Gunnison Basin, spanning the winter- to-spring transition of 2022–2023. The analysis employs Shannon entropy, mutual information, transfer entropy, and joint transfer en- tropy (JTE) to quantify how environmental variables, including surface meteorology, radiation, tur- bulent fluxes, and ERA5 reanalysis products, transfer information …

Derivation Of Adjoint Based Error Estimates For Nonlinear Ordinary Differential Equations With Application To Multistage Sir Models With Demographics, Daniel Alcala

Mathematics & Statistics ETDs

Ordinary Differential Equations (ODEs) are central to the mathematical modeling of various real-world phenomena, from mechanical systems governed by Newton’s laws to epidemic dynamics described by SIR-type ODEs. Since many ODEs do not admit closed-form analytic solutions, we approximate them numerically (e.g., with Euler’s, Runge–Kutta, or other such methods). This raises the key question: How accurate are these numerical solutions? In particular, reliably estimating the error in some quantity of interest (QoI) at time T without having an exact solution is of great scientific interest.

The first main contribution of this thesis is the development and analysis of adjoint-based error …

Theoretical And Experimental Investigation Of Liquid-Liquid Phase Separation: Characterizing Elastin-Like-Polypeptides, Adam D. Quintana

Chemical and Biological Engineering ETDs

This dissertation develops and validates a semi-empirical Flory–Huggins-based interaction model, combined with Cahn–Hilliard simulations, for predicting multi-component liquid–liquid phase separation (LLPS) in elastin-like polypeptide (ELP) systems. Equilibrium droplet compositions, measured using a PDMS-based microfluidic device, enabled direct parameterization of interaction coefficients. The model was applied to generate phase diagrams and assess composition dependence in ternary mixtures. Cahn–Hilliard simulations were conducted to explore potential phase morphologies under different interfacial conditions. Multi-component Lattice Boltzmann simulations were implemented to model droplet morphology evolution under varying interfacial and diffusive parameters, reproducing experimentally relevant morphologies. A three-phase wetting study revealed conditions for selective wetting and …

Parallel Multigrid In Time For Chaotic Dynamical Systems, David Alan Vargas

Mathematics & Statistics ETDs

Despite the fact that Parallel-in-Time (PinT) methods are predicted to become necessary to fully utilize next-generation exa- and zettascale machines, there are currently no known practical methods which scale well with the length of the time-domain for chaotic problems, due to exponential dependence of the condition number on the fastest chaotic timescale. I present modifications to the coarse-grid equations along with a novel rediscretization approach which together greatly improve convergence of the multigrid reduction in time (MGRIT) algorithm and allow the first known PinT speedup for a chaotic PDE. The novel Local Shadowing Relaxation (LSR) is presented as an alternative …

Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova

Mathematics & Statistics ETDs

The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …

One-Note-Samba Approach To Cosmology, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

Inspired by One Note Samba, a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology. Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also briefly discuss possible link with our previous paper which describes Newtonian Universe with Vortex in terms of Ermakov equation.

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to …

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Neutrosophic Operational Research - Vol. 2, Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Neutrosophic Theory And Its Applications : Collected Papers - Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every entity tends to be …

Collected Papers, Vol. V, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.