Applied Mathematics Commons^™

Modelling The Formation Of Unslanted Holographic Gratings In Hybrid Photopolymer Media, Jack Lyons, Dana Mackey, Izabela Naydenova

Articles

The theoretical modelling of holographic recording in photopolymers has been an important tool in their optimisation. More complex, hybrid organic/inorganic photopolymers have been developed in pursuit of materials with higher sensitivity, low shrinkage, high dynamic range and environmental stability. Recent attempts to augment the existing models for the redistribution of inorganic nanoparticles in holographic recording were successful but there is still a knowledge gap in regards to modelling optical losses, mutual cross-diffusion, the formation of slanted holographic gratings and polymerization induced shrinkage in hybrid photopolymer media. This paper will describe a novel approach to modelling the formation of unslanted holographic …

Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …

Modeling Of Light Filamentation For Nonlinear Imaging And Waveguiding, Nicholas Bagley

Mathematics Theses and Dissertations

Ultrashort pulses are capable of extremely high powers; in addition to enabling various applications in defense, sensing, and imaging, they provide a useful arena in which to study nonlinear optical phenomena that are observable only at high intensities. Due to these effects, which can include ionization and thermal blooming, simulation of ultrashort pulse propagation is a complicated multiphysics problem. We provide an overview of techniques used to simulate the propagation of ultrashort pulses in the nonlinear regime, including the formation of light filaments due to the competition of Kerr self-focusing and defocusing (e.g. via plasma generation). We discuss both carrier-resolved …

(R2111) Effect Of Stenotic-Aneurysmal Arterial Regime On Unsteady Magnetohydrodynamic Non-Newtonian Blood Flow With Heat Radiation, Babatunde A. Joseph, Dada M. Sunday, Bello A.J. Funsho, Akeem B. Disu, Alamu-Awoniran F., Danas James Y.

Applications and Applied Mathematics: An International Journal (AAM)

The study aims to investigate the effect of magneto-hydrodynamic on a non-Newtonian unsteady blood flow with internal heat energy in the presence of blood ironic properties characterized by stenosis. The formulated mathematical equations resulted in differential forms and were solved analytically by Differential Transform Method. The obtained solutions were displayed by graphs showing different flow physiognomies like blood velocity, temperature profile, Nusselt number, wall shear stress and stream function.

The results indicated that velocity profile increases as magnetic field, Darcy number and aneurysmal artery rise, while it decreases as heat radiation, Reynold number, and Casson parameter speedup. The temperature profile …

An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech

OUR Journal: ODU Undergraduate Research Journal

The Time-Independent Schrödinger Equation is a linear elliptic PDE that describes quantum-mechanical systems. Its significance in the science of submicroscopic phenomena, particularly quantum mechanics, is as central as Newton’s laws of motion are to classical mechanics. This study uses various methods, including novel neural networks and finite difference schemes, to solve the one-dimensional two-body equation.

A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, Nicholas J. Dubicki

Dissertations

Magnetic skyrmions are topologically protected, localized, nanoscale spin textures in non-centrosymmetric thin ferromagnetic materials and heterostructures. At present they are of great interest to physicists for potential applications in information technology due to their particle-like properties and stability. In a system of multiple thin ferromagnetic layers, the stray field interaction was typically treated with various simplifications and approximations. It is shown that extensive analysis of the micromagnetic equations leads to an exact representation of the stray field interaction energy in the form of layer interaction kernels, a so-called 'finite thickness' representation. This formulation reveals the competition between perpendicular magnetic anisotropy …

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

Accelerating The Efficiency Of Multiscale Hybridizable Discontinuos Galerkin Methods For Flows In Heterogeneous Media, Tony Charles Haines

Mathematics & Statistics Theses & Dissertations

A plethora of scientific and engineering problems encountered are multiscale in nature. This multiscale feature often influences simulation efforts wherever large disparities in spatial scales are experienced. Notable examples include composite materials, fluid flow through porous media and turbulent transport in high Reynolds number flow. Although there are promising results from the advancement of modern supercomputer, obtaining direct numerical solution of multiscale problems is very laborious. This difficulty stems from the tremendous amount of computer memory and CPU time required. Parallel computing may be one obvious choice in remedying this issue. However, the complexity and size of the discrete problem …

Parallel-In-Time Implicit Schemes For Nonlinear Pdes, Subhash Paudel

Mathematics & Statistics Theses & Dissertations

An accurate prediction of unsteady physical phenomena arising in various applications (e.g., rotorcraft and turbomachinery flows, fluid-structure interaction, maneuvering flight conditions, etc.) requires a very large number of time steps, thus considerably increasing the total computational time, because conventional time integrators are inherently sequential. Parallel-in-time methods offer a promising direction for drastically reducing the computational time and achieving such scalability that is required for solving these unsteady problems on modern supercomputers with hundreds of thousands of computing cores. The parallel performance of existing parallel-in-time algorithms for nonlinear equations especially of the hyperbolic or mixed type is far from being satisfactory. …

(R2085) Heat And Mass Transport Characteristics In Williamson Fluid Flow Over A Permeable Stretching Cylinder, Amala Olkha, Mukesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The intention of this research endeavor is to examine heat and mass transport in Williamson fluid flow induced by a permeable stretching cylinder in a porous medium. Various physical factors (like viscous dissipation, chemical reaction, etc.) affecting the relevant fields (flow, temperature and concentration) are incorporated in the investigation. The governing PDEs are turned into nondimensional ODEs using adequate similarity transformation relations, and then tackled numerically using MATLAB based Bvp4c technique along with shooting method. The impacts of various parameters arising in the problem are exhibited on fluid flow, temperature and concentration distribution by drawing portraits and discussed. Moreover, impressions …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Modeling Redistribution Of Nanozeolites In Holographic Recording, Dana Mackey, Jack Lyons Dr, Izabela Naydenova

Articles

Zeolite doped photopolymers have been studied experimentally due to their potential application in the develop- ment of optical sensors. It has been shown that dopant redistribution can be achieved by holographic recording and has a direct influence on the sensitivity of the recorded grating. To achieve better theoretical understanding of these processes, this paper proposes an extended photopolymerization-diffusion mathematical model for describing the dynamics of nanozeolite redistribution during recording in an acrylamide-based photopolymer. Using numerical simulations of this model, we investigate how recording conditions, dopant transport parameters, and initial load affect the refractive index modulation of the resulting photonic structure.

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 …

Nidus Idearum. Scilogs, Xiii: Structure / Neutrostructure / Antistructure, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies.

Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations and Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila

Faculty Publications

This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …

Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, William L. Blair

Graduate Theses and Dissertations

We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.

Predicting Biomolecular Properties And Interactions Using Numerical, Statistical And Machine Learning Methods, Elyssa Sliheet

Mathematics Theses and Dissertations

We investigate machine learning and electrostatic methods to predict biophysical properties of proteins, such as solvation energy and protein ligand binding affinity, for the purpose of drug discovery/development. We focus on the Poisson-Boltzmann model and various high performance computing considerations such as parallelization schemes.

Invariance Of Chsh Parameters When Projecting Weakly Signaling Distribution Into A No Signaling Subspace, Aaditya Paudel

LSU New Orleans Theses and Dissertations

The seminal 1935 paper by Einstein, Podolsky, and Rosen (EPR) sparked a fundamental debate in quantum mechanics about the completeness of physical reality through the EPR paradox. They questioned local realism by suggesting that particles could exhibit instantaneous correlations across any distance, challenging classical physics. Bell's theorem (1964) argued that no local hidden variable theory could replicate quantum predictions, introducing Bell's inequalities and their experimental tests. These tests, particularly through violations of Bell's inequalities, confirmed quantum predictions of non-local correlations that local realism could not account for. Quantum theory, while supporting such correlations, adheres to the no-signaling principle to prevent …

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 …

Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks

LSU Doctoral Dissertations

This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …

Analyzing The Influence Of Design And Operating Conditions On Combustion And Emissions In Premixed Turbulent Flames: A Comprehensive Review, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi, Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

Recently, premixed combustion has dominated the field of combustion research worldwide. The current work is a review that addresses the effects of design and operating regimes on the combustion and emission characteristics of premixed turbulent flames. The study accounts for recent developments aimed at overcoming combustor operability issues that influence emissions and flame stability. Various experimental setups have been utilized in investigations, with results pertaining to performance and emissions concerning premixed turbulent flames. Thus, the objective of this paper is to provide a comprehensive review of the effects of swirl vane angles and equivalence fuel-air ratios for tests conducted both …

Strengthen Establishment Of Application-Supported Major Science And Technology Infrastructure To Enhance Basic Capacity Of Science And Technology For High-Quality Development, Congli Huang, Feite Zhou, Xiang Xu, Lingling Zhang

Bulletin of Chinese Academy of Sciences (Chinese Version)

From “Two Bombs and One Satellite” to Five-hundred-meter Aperture Spherical Radio Telescope (FAST), from ground zero to the center stage of the world, China has unswervingly followed the path of independent innovation with distinctive characteristics. After the development of nearly half a century, breakthroughs have been made in several key areas. The position, implication, and classification of major scientific and technological infrastructures are constantly changing under the new situation. Based on an in-depth investigation of major scientific and technological infrastructure such as high-efficiency and low-carbon gas turbine research facility, it is believed that the construction of application-supported major scientific and …

Probing The Ising Model’S Thermodynamics Through Restricted Boltzmann Machines, Xiaobei (Emma) Zhang

HMC Senior Theses

This thesis explores the connection between physics and machine learning by using Restricted Boltzmann Machines (RBMs) to study the thermodynamic properties of the Ising model. The Ising model is a simple but realistic model that captures the magnetic behavior of a system, where spins occupy a lattice of sites and different spin configurations correspond to different energies. The model exhibits phase transitions between ferromagnetic and paramagnetic phases as a function of temperature. RBMs are two-layered neural networks that can learn probability distributions over binary spins. The study generates 2D Ising model data at different temperatures using Monte Carlo simulations, including …

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan

College of Graduate Studies: Theses & Dissertations

The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …

Weak-Strong Beam-Beam Simulation With Crab Cavity Noises For The Hadron Storage Ring Of The Electron-Ion Collider, Y. Luo, B. Gamage, C. Montag, D. Marx, D. Xu, F. Willeke, H. Huang, H. Lovelace Iii, J. Berg, M. Blaskiewicz, S. Peggs, T. Satogata, V. Ptitsyn, V. Morozov, Y. Hao

Mathematics & Statistics Faculty Publications

The Electron Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized high-energy electron beams with hadron beams, achieving luminosities of up to 1 X 10³⁴cm⁻²s⁻¹ in the center-mass energy range of 20-140 GeV. Crab cavities are employed to compensate for the geometric luminosity loss caused by a large crossing angle of 25 mrad in the interaction region. The phase noise in crab cavities will induce a significant emittance growth for the hadron beams in the Hadron Storage Ring (HSR). Various models have been utilized to study the effects of crab cavity …

Numerical Solution Of Hybrid Nanofluid And Its Stability Over Permeable Wedge Sheet With Heat Transfer Analysis, Aisha M. Alqahtani, Zeeshan, Waris Khan, Florentin Smarandache, Nidhal Becheikh, Roobaea Alroobaea, Taseer Muhammad

Branch Mathematics and Statistics Faculty and Staff Publications

The inclusion of nanoparticles has the potential to improve the thermal efficiency of the base fluid. The field of nanofluid (NF) dynamics has attracted important attention due to its extensive range of practical uses like fuel cells, solar energy, medication administration, heat transfer, microfabrication, coolant applications, and other related domains. The aim of this study is to scrutinize the impact of Lorentz force, thermal energy, joule heating, heat source and injection parameters, and Brownian and thermoporetic diffusions on the hybrid nanofluid over the moving wedge. The stability inquiry is reported for the existing work in order to confirm the stable …

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 …

Long-Wave Modeling Of Viscous Film Dynamics Inside A Tube With Time-Dependent Radius, Robert E. Hicks

Theses and Dissertations

Lung fluid dynamics is a well studied topic and relevant in the field of research surrounding patients with Chronic Obstructive Pulmonary Disease (COPD) and cystic fibrosis. However, the literature on the mathematical description of the net pulmonary fluid transport in the case of constricting and expanding airways is scarce. In this paper we aim to address how breathing contributes to airways clearance in patients with pulmonary diseases such as COPD and CF in which cilia do not function properly. We begin with the flow of a fluid-filled tube with rigid walls of fixed radius and the effects of gravity being …

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, …