Numerical Analysis and Computation Commons^™

Profit Analysis Of A Two Unit Cold Standby System Operating Under Different Weather Conditions Subject T O Inspection, M. S. Barak, Neeraj _, Sudesh Kumari

Applications and Applied Mathematics: An International Journal (AAM)

A system, or unit, is said to be working under normal weather conditions if the system is working under prescribed conditions as defined/stated by the definition of reliability of system/unit, otherwise the system is said to be working in abnormal weather conditions. For example, if a car with the capacity for five persons is carrying more than five persons, it will be said to be working under abnormal weather conditions. Another example, if a hydraulic machine having the capacity to lift a maximum weight of 500 tons is lifting a weight of 600 tons, then the machine is working under …

United States Population Future Estimates And Long-Term Distribution, Sean P. Brogan

DePaul Discoveries

The population of the United States has always increased year over year. Even now with decreasing birth rates, the overall population continues to grow when looking at conventional models. The present study specifically examines what would happen to the U.S. population if we were to maintain the current birth and survival rates into the future. By 2050, our research shows that the U.S. population will become much older and cease to grow at all.

Recta: Regulon Identification Based On Comparative Genomics And Transcriptomics Analysis, Xin Chen, Anjun Ma, Adam Mcdermaid, Hanyuan Zhang, Chao Liu, Huansheng Cao, Qin Ma

School of Computing: Faculty Publications

Regulons, which serve as co-regulated gene groups contributing to the transcriptional regulation of microbial genomes, have the potential to aid in understanding of underlying regulatory mechanisms. In this study, we designed a novel computational pipeline, regulon identification based on comparative genomics and transcriptomics analysis (RECTA), for regulon prediction related to the gene regulatory network under certain conditions. To demonstrate the effectiveness of this tool, we implemented RECTA on Lactococcus lactis MG1363 data to elucidate acid-response regulons. A total of 51 regulons were identified, 14 of which have computational-verified significance. Among these 14 regulons, five of them were computationally predicted to …

Patient-Specific Multiscale Computational Fluid Dynamics Assessment Of Embolization Rates In The Hybrid Norwood: Effects Of Size And Placement Of The Reverse Blalock–Taussig Shunt, Ray Prather, John Seligson, Marcus Ni, Eduardo Divo, Alain J. Kassab, William Decampli

Publications

The hybrid Norwood operation is performed to treat hypoplastic left heart syndrome. Distal arch obstruction may compromise flow to the brain. In a variant of this procedure, a synthetic graft (reverse Blalock–Taussig shunt) is placed between the pulmonary trunk and innominate artery to improve upper torso blood flow. Thrombi originating in the graft may embolize to the brain. In this study, we used computational fluid dynamics and particle tracking to investigate the patterns of particle embolization as a function of the anatomic position of the reverse Blalock–Taussig shunt. The degree of distal arch obstruction and position of particle origin influence …

Risk Assessment Of Dropped Cylindrical Objects In Offshore Operations, Adelina Steven

LSU New Orleans Theses and Dissertations

Dropped object are defined as any object that fall under its own weight from a previously static position or fell due to an applied force from equipment or a moving object. It is among the top ten causes of injuries and fatality in oil and gas industry. To solve this problem, several in-house tools and guidelines is developed over time to assess the risk of dropped objects on the sub-sea structures. This thesis focuses on compiling and comparing those methods in hope to improve the recommended practices available in the market. A simple modification is done on the in-house tools …

The Auxiliary Space Preconditioner For The De Rham Complex, Jay Gopalakrishnan, Martin Neumüller, Panayot S. Vassilevski

Portland Institute for Computational Science Publications

We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of …

Godunov-Type Upwind Flux Schemes Of The Two-Dimensional Finite Volume Discrete Boltzmann Method, Leitao Chen, Laura Schaefer

Publications

A simple unified Godunov-type upwind approach that does not need Riemann solvers for the flux calculation is developed for the finite volume discrete Boltzmann method (FVDBM) on an unstructured cell-centered triangular mesh. With piecewise-constant (PC), piecewise-linear (PL) and piecewise-parabolic (PP) reconstructions, three Godunov-type upwind flux schemes with different orders of accuracy are subsequently derived. After developing both a semi-implicit time marching scheme tailored for the developed flux schemes, and a versatile boundary treatment that is compatible with all of the flux schemes presented in this paper, numerical tests are conducted on spatial accuracy for several single-phase flow problems. Four major …

Rapid Generation Of Jacobi Matrices For Measures Modified By Rational Factors, Amber Sumner

Dissertations

Orthogonal polynomials are important throughout the fields of numerical analysis and numerical linear algebra. The Jacobi matrix J for a family of n orthogonal polynomials is an n x n tridiagonal symmetric matrix constructed from the recursion coefficients for the three-term recurrence satisfied by the family. Every family of polynomials orthogonal with respect to a measure on a real interval [a,b] satisfies such a recurrence. Given a measure that is modified by multiplying by a rational weight function r(t), an important problem is to compute the modified Jacobi matrix Jmod corresponding to the new measure from knowledge of J. There …

Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Ashley Montiforte

Master's Theses

Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.

Power Corrections To Tmd Factorization For Z-Boson Production, I. Balitsky, A. Tatasov

Physics Faculty Publications

A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to the TMD factorization formula become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in N_c power corrections are expressed in …

Clark Measures And A Theorem Of Ritt, Isabelle Chalendar, Pamela Gorkin, Jonathan R. Partington, William T. Ross

Department of Math & Statistics Faculty Publications

We determine when a finite Blaschke product B can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for B. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute.

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different …

A Mathematical Analysis Of The Game Of Chess, John C. White

Selected Honors Theses

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle

Master's Theses

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing …

General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai

LSU Doctoral Dissertations

A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory to several …

Improving Annual Fixed Wing Maintenance Cost Estimates Through Cost Estimating Relationships, Kirsten Bunecke

Theses and Dissertations

The Air Force executes its mission primarily through the use of fixed-wing aircrafts. Maintaining these aircrafts represents approximately one-third of annual Operating and Support costs; which in turn, make up the majority of Life Cycle Costs. The current approach to estimating aircraft maintenance costs does not take into consideration programmatic data available in the Air Force Total Ownership Cost (AFTOC) database. The four maintenance cost subcategories researched in this thesis are Consumable Materials and Repair Parts, Depot Level Repairables (DLRs), Depot Maintenance, and Contractor Logistic Support. Each of these cost categories must first be standardized to be able to compare …

Analysis Of Temperature And Humidity Effects On Horizontal Photovoltaic Panels, Corey J. Booker

Theses and Dissertations

The United States Air Force seeks to address power grid vulnerability and bolster energy resilience through the use of renewable energy sources. Air Force Institute of Technology engineers designed and manufactured control systems to monitor power production from the most widely-used silicon-based solar cells at 38 testing locations around the globe spanning the majority of climate types. Researchers conducted multivariate regression analysis to establish a statistical relationship between photovoltaic power output, ambient temperature, and humidity pertaining to monocrystalline and polycrystalline photovoltaic panels. Formulated models first characterized power output globally, then by specific climate type with general inaccuracy. Location-specific models are …

Real Solution Of Dae And Pdae System, Zahra Mohammadi, Greg Reid

Western Research Forum

General systems of differential equations don't have restrictions on the number or type of equations. For example, they can be over or under-determined, and also contain algebraic constraints (e.g. algebraic equations such as in Differential-Algebraic equations (DAE) and Partial differential algebraic equations (PDAE). Increasingly such general systems arise from mathematical modeling of engineering and science problems such as in multibody mechanics, electrical circuit design, optimal control, chemical kinetics and chemical control systems. In most applications, only real solutions are of interest, rather than complex-valued solutions. Much progress has been made in exact differential elimination methods, which enable characterization of all …

Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski

Publications

Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (non-mechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasi-nil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also …