Modeling Fluid Phenomena In The Context Of The Constrained Vapor Bubble System, 2020 Southern Methodist University

#### Modeling Fluid Phenomena In The Context Of The Constrained Vapor Bubble System, James Barrett

*Mathematics Theses and Dissertations*

This thesis focuses on the fluid phenomena observed within what is known as the constrained vapor bubble system. The constrained vapor bubble system is a closed system consisting of a quartz cuvette partially filled with liquid and used as a coolant device. Heat is applied to the heater end which causes the liquid to evaporate and condense on the cooled end of the cuvette. Liquid travels back to the heated end via capillary flow in the corners. A pure vapor bubble is formed in the center of the cuvette giving rise to the name of the experiment. The constrained vapor ...

Uncertainty Quantification Of Nonreflecting Boundary Schemes, 2020 Southern Methodist University

#### Uncertainty Quantification Of Nonreflecting Boundary Schemes, Brian Citty

*Mathematics Theses and Dissertations*

Numerical methods have been developed to solve partial differential equations involving the far-field radiation of waves. In addition, there has been recent interest in uncertainty quantification- a burgeoning field involving solving PDEs where random variables are used to model uncertainty in the data. In this thesis we will apply uncertainty quantification methodology to the 1D and 2D wave equation with nonreflecting boundary. We first derive a boundary condition for the 1D wave equation assuming several models of the random wave speed. Later we use our result to compare to an asymptotic SDE approach, and finally we repeat our analysis for ...

The Effect Of The Initial Structure On The System Relaxation Time In Langevin Dynamics, 2020 The University of Western Ontario

#### The Effect Of The Initial Structure On The System Relaxation Time In Langevin Dynamics, Omid Mozafar

*Electronic Thesis and Dissertation Repository*

In recent decades, computer experiments have allowed an accurate and fundamental understanding of molecular mechanisms at the microscopic level, such as the process of relaxation at a stable physical state. However, computer simulations may sometimes produce non-physical results or relations due to the incompleteness of mathematical models describing physical systems. In this thesis, we have investigated whether the initial structure in a computer simulation affects the system relaxation time, which is denoted by τ_{sys}, in the Langevin NVT ensemble. We found that for an initial structure, which is inhomogeneous in the number density of atoms, the system relaxation time ...

Introduction To Classical Field Theory, 2020 Department of Physics, Utah State University

#### Introduction To Classical Field Theory, Charles G. Torre

*All Complete Monographs*

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

The Revised Nim For Solving The Non-Linear System Variant Boussinesq Equations And Comparison With Nim, 2020 University of Mosul, Mosul

#### The Revised Nim For Solving The Non-Linear System Variant Boussinesq Equations And Comparison With Nim, Oday Ahmed Jasim

*Karbala International Journal of Modern Science*

This research aims to guide researchers to use a new method, and it is the Revised New Iterative Method (RNIM) to solve partial differential equation systems and apply them to solve problems in various disciplines such as chemistry, physics, engineering and medicine. In this paper, the numerical solutions of the nonlinear Variable Boussinesq Equation System (VBE) were obtained using a new modified iterative method (RNIM); this was planned by (Bhaleker and Datterder-Gejj). A numerical solution to the Variable Boussinesq Equation System (VBE) was also found using a widely known method, a new iterative method (NIM). By comparing the numerical solutions ...

Two New Finite Element Schemes And Their Analysis For Modeling Of Wave Propagation In Graphene, 2020 University of Nevada, Las Vegas

#### Two New Finite Element Schemes And Their Analysis For Modeling Of Wave Propagation In Graphene, Jichun Li

*Mathematical Sciences Faculty Publications*

© 2020 The Author(s) In this paper, we investigate a system of governing equations for modeling wave propagation in graphene. Compared to our previous work (Yang et al., 2020), here we re-investigate the governing equations by eliminating two auxiliary unknowns from the original model. A totally new stability for the model is established for the first time. Since the finite element scheme proposed in Yang et al. (2020) is only first order in time, here we propose two new schemes with second order convergence in time for the simplified modeling equations. Discrete stabilities inheriting exactly the same form as the ...

A Logical Method For Finding Maximum Compatible Subsystems Of Systems Of Boolean Equations, 2020 National University of Uzbekistan

#### A Logical Method For Finding Maximum Compatible Subsystems Of Systems Of Boolean Equations, Anvar Kabulov, Erkin Urunbaev, Mansur Berdimurodov

*Scientific Journal of Samarkand University*

The problem of finding the maximum joint subsystem of Boolean equation systems is solved. An algorithm for finding the maximum upper zero of a monotone Boolean function is proposed. An efficient procedure for calculating the values of monotone functions on sets of a - dimensional cube is investigated and developed. An algorithm for solving systems of Boolean equations based on the search for the maximum upper zero of monotone functions of the logic algebra is developed.

Rapid Implicit Diagonalization Of Variable-Coefficient Differential Operators Using The Uncertainty Principle, 2020 The University of Southern Mississippi

#### Rapid Implicit Diagonalization Of Variable-Coefficient Differential Operators Using The Uncertainty Principle, Carley Walker

*Master's Theses*

We propose to create a new numerical method for a class of time-dependent PDEs (second-order, one space dimension, Dirichlet boundary conditions) that can be used to obtain more accurate and reliable solutions than traditional methods. Previously, it was shown that conventional time-stepping methods could be avoided for time-dependent mathematical models featuring a finite number of homogeneous materials, thus assuming general piecewise constant coefficients. This proposed method will avoid the modeling shortcuts that are traditionally taken, and it will generalize the piecewise constant case of energy diffusion and wave propagation to work for an infinite number of smaller pieces, or a ...

Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, 2020 The University of Western Ontario

#### Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, Tarik Menkad

*Electronic Thesis and Dissertation Repository*

Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits.

The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic ...

Using Statistical Analysis To Examine Weather Variability In New York City, 2020 CUNY New York City College of Technology

#### Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang

*Publications and Research*

As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology ...

Parametric Art, 2020 CUNY New York City College of Technology

#### Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

*Publications and Research*

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations 𝑥=𝐴𝑐𝑜𝑠(𝑎𝑡) and 𝑦=𝐵𝑠𝑖𝑛(𝑏𝑡) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their ...

Spectral Properties Of A Non-Compact Operator In Ecology, 2020 University of Nebraska-Lincoln

#### Spectral Properties Of A Non-Compact Operator In Ecology, Matthew Reichenbach

*Dissertations, Theses, and Student Research Papers in Mathematics*

Ecologists have used integral projection models (IPMs) to study fish and other animals which continue to grow throughout their lives. Such animals cannot shrink, since they have bony skeletons; a mathematical consequence of this is that the kernel of the integral projection operator T is unbounded, and the operator is not compact. A priori, it is unclear whether these IPMs have an asymptotic growth rate λ, or a stable-stage distribution ψ. In the case of a compact operator, these quantities are its spectral radius and the associated eigenvector, respectively. Under biologically reasonable assumptions, we prove that the non-compact operators in ...

On Subdiagonal Rational Pade Approximations And The Brenner-Thomee Approximation Theorem For Operator Semigroups, 2020 Louisiana State Univ, Dept Math, Baton Rouge, LA

#### On Subdiagonal Rational Pade Approximations And The Brenner-Thomee Approximation Theorem For Operator Semigroups, Frank Neubrander, Koray Ozer, Lee Windsperger

*Faculty Publications*

The computational powers of Mathematica are used to prove polynomial identities that are essential to obtain growth estimates for subdiagonal rational Pade approximations of the exponential function and to obtain new estimates of the constants of the Brenner-Thomee Approximation Theorem of Semigroup Theory.

A Brief On Characteristic Functions, 2020 Missouri University of Science and Technology

#### A Brief On Characteristic Functions, Austin G. Vandegriffe

*Graduate Student Research & Creative Works*

Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs *always* exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust ...

Analytic Solutions For Diffusion On Path Graphs And Its Application To The Modeling Of The Evolution Of Electrically Indiscernible Conformational States Of Lysenin, 2020 Boise State University

#### Analytic Solutions For Diffusion On Path Graphs And Its Application To The Modeling Of The Evolution Of Electrically Indiscernible Conformational States Of Lysenin, K. Summer Ware

*Boise State University Theses and Dissertations*

Memory is traditionally thought of as a biological function of the brain. In recent years, however, researchers have found that some stimuli-responsive molecules exhibit memory-like behavior manifested as history-dependent hysteresis in response to external excitations. One example is lysenin, a pore-forming toxin found naturally in the coelomic fluid of the common earthworm *Eisenia fetida*. When reconstituted into a bilayer lipid membrane, this unassuming toxin undergoes conformational changes in response to applied voltages. However, lysenin is able to "remember" past history by adjusting its conformational state based not only on the amplitude of the stimulus but also on its previous its ...

Structure, Neutrostructure, And Antistructure In Science, 2020 University of New Mexico

#### Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives ...

A Collection Of Fast Algorithms For Scalar And Vector-Valued Data On Irregular Domains: Spherical Harmonic Analysis, Divergence-Free/Curl-Free Radial Basis Functions, And Implicit Surface Reconstruction, 2020 Boise State University

#### A Collection Of Fast Algorithms For Scalar And Vector-Valued Data On Irregular Domains: Spherical Harmonic Analysis, Divergence-Free/Curl-Free Radial Basis Functions, And Implicit Surface Reconstruction, Kathryn Primrose Drake

*Boise State University Theses and Dissertations*

This dissertation addresses problems that arise in a diverse group of fields including cosmology, electromagnetism, and graphic design. While these topics may seem disparate, they share a commonality in their need for fast and accurate algorithms which can handle large datasets collected on irregular domains. An important issue in cosmology is the calculation of the angular power spectrum of the cosmic microwave background (CMB) radiation. CMB photons offer a direct insight into the early stages of the universe's development and give the strongest evidence for the Big Bang theory to date. The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) grid ...

Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, 2020 Old Dominion University

#### Conical Orbital Mechanics: A Rework Of Classic Orbit Transfer Mechanics, Cian Anthony Branco

*Mechanical & Aerospace Engineering Theses & Dissertations*

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in ...

Inference And Estimation In Change Point Models For Censored Data, 2020 Old Dominion University

#### Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

*Mathematics & Statistics Theses & Dissertations*

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change ...

Sum Of Cubes Of The First N Integers, 2020 California State University, San Bernardino

#### Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

*Electronic Theses, Projects, and Dissertations*

In Calculus we learned that Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at ...