Applied Mathematics Commons^™

Mathematical Modeling Of Pipeline Features For Robotic Inspection, Yang Gao

Doctoral Dissertations

Underground pipeline systems play an indispensable role in transporting liquids in both developed and developing countries. The associated social and economic cost to repair a pipe upon abrupt failure is often unacceptable. Regular inspection is a preventative action that aims to monitor pipe conditions, catch abnormalities and reduce the chance of undesirable surprises. Robots with CCTV video cameras have been used for decades to inspect pipelines, yielding only qualitative information. It is becoming necessary and preferable for municipalities, project managers and engineers to also quantify the 3-D geometry of underground pipe networks. Existing robots equipped specialized hardware and software algorithms …

Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon

Doctoral Dissertations

As High Performance Computing (HPC) systems increase in size to fulfill computational power demand, the chance of failure occurrences dramatically increases, resulting in potentially large amounts of lost computing time. Fault Tolerance (FT) mechanisms aim to mitigate the impact of failure occurrences to the running applications. However, the overhead of FT mechanisms increases proportionally to the HPC systems' size. Therefore, challenges arise in handling the expensive overhead of FT mechanisms while minimizing the large amount of lost computing time due to failure occurrences.

In this dissertation, a near-optimal scheduling model is built to determine when to invoke a hybrid checkpoint …

The Search For An Optimal Means Of Determining The Minmax Control Parameter Using Sensitivity Analysis, John Teye Brown

Doctoral Dissertations

The use of computational methods for design and simulation of control systems allows for a cost-effective trial and error approach. In this work, we are concerned with the robust, real-time control of physical systems whose state space is infinite-dimensional. Such systems are known as Distributed Parameter Systems (DPS). A body whose state is heterogeneous is a distributed parameter. In particular, this work focuses on DPS systems that are governed by linear Partial Differential Equations, such as the heat equation. We specifically focus on the MinMax controller, which is regarded as being a very robust controller. The mathematical formulation of the …

Systems Of Nonlinear Wave Equations With Damping And Supercritical Sources, Yanqiu Guo

Department of Mathematics: Dissertations, Theses, and Student Research

We consider the local and global well-posedness of the coupled nonlinear wave equations

u_tt – Δu + g₁(u_t) = f₁(u, v)

v_tt – Δv + g₂(v_t) = f₂(u, v);

in a bounded domain Ω subset of the real numbers (Rⁿ) with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f₁(u, v) and f₂(u, v) are with supercritical exponents …

Random Number Generation: Types And Techniques, David F. Dicarlo

Senior Honors Theses

What does it mean to have random numbers? Without understanding where a group of numbers came from, it is impossible to know if they were randomly generated. However, common sense claims that if the process to generate these numbers is truly understood, then the numbers could not be random. Methods that are able to let their internal workings be known without sacrificing random results are what this paper sets out to describe. Beginning with a study of what it really means for something to be random, this paper dives into the topic of random number generators and summarizes the key …

Determining Angular Frequency From A Video With A Generalized Fast Fourier Transform, Lindsay N. Smith

Theses and Dissertations

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DFT) and as such, the two transforms have much in common. However, whereas the DFT is applied to a sequence of scalars, the GST can be applied to a sequence of vectors. …

Local Histograms For Per-Pixel Classification, Melody L. Massar

Theses and Dissertations

We introduce a rigorous mathematical theory for the analysis of local histograms, and study how they interact with textures that can be modeled as occlusions of simpler components. We first show how local histograms can be computed as a system of convolutions and discuss some basic local histogram properties. We then introduce a probabilistic, occlusion-based model for textures and formally demonstrate that local histogram transforms are natural tools for analyzing the textures produced by our model. Next, we characterize all nonlinear transforms which satisfy the three key properties of local histograms and consider the appropriateness of local histogram features in …

On Soliton Interactions For A Hierarchy Of Generalized Heisenberg Ferromagnetic Models On Su(3)/S(U(1) $\Times$ U(2)) Symmetric Space, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valchev

Articles

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In …

Preconditioning Visco-Resistive Mhd For Tokamak Plasmas, Daniel R. Reynolds, Ravi Samtaney, Hilari C. Tiedeman

Mathematics Research

No abstract provided.

Ball Remotality In Banach Spaces And Related Topics., Tanmoy Paul

Doctoral Theses

In this project we aim to study Ball Remotality and densely Ball Remotality of subspaces in Banach spaces. We study this property in many classical spaces of type c0, c,\\â„“p and C(K) where K is a compact Hausdorff space. The said problem also discussed for Banach spaces when considered as a subspace in its bidual. It is observed M-ideals in C(K) are densely ball remotal. It is shown that a particular type of M-ideal in A(K) where K is a Choquet simplex is densely ball remotal.

The Immersed Interface Method For Two-Fluid Problems, Miguel Uh, Sheng Xu

Mathematics Research

No abstract provided.

Numerical Solution Of Integral Equations In Solidification And Laser Melting, Elizabeth Case, Johannes Tausch

Mathematics Research

No abstract provided.

Heterogeneous Multiscale Modeling Of Advection-Diffusion Problems, David J. Gardner, Daniel R. Reynolds

Mathematics Research

No abstract provided.

Multilevel Schur Complement Preconditioner For Multi-Physics Simulations, Hilari Tiedeman, Daniel Reynolds

Mathematics Research

No abstract provided.

Effects Of Stochastic Freshwater Flux On The Atlantic Thermohaline Circulation, Alyssa Pampell, Alejandra Aceves

Mathematics Research

No abstract provided.

Block Preconditioning Of Stiff Implicit Models For Radiative Ionization In The Early Universe, Daniel R. Reynolds, Robert Harkness, Geoffrey So, Michael L. Norman

Mathematics Research

No abstract provided.

On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski

Publications

Abstract

The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.

Research highlights

The Mindlin-type microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlin-type microstructure model with weakly non-convex free energy resolves this discrepancy. It is shown that the improved model with weakly non-convex free energy is asymptotically stable for short waves.

Estimation Of Performance Indices For The Planning Of Sustainable Transportation Systems, Pankaj Maheshwari, Alexander Paz, Pushkin Kachroo

Graduate Publications & Presentations

What is sustainable transportation system?

Fulfill the needs of current generations without compromising the ability of future generations

Utilize resources without compromising their health and productivity Leads to development that improves quality of life

Assimilate economic, ecological, social, and bio-physical components of resource ecosystems

Minimize the use of renewable and non-renewable resources, provide affordability and equity between generations

A Local Radial Basis Function Method For The Numerical Solution Of Partial Differential Equations, Maggie Elizabeth Chenoweth

Theses, Dissertations and Capstones

Most traditional numerical methods for approximating the solutions of problems in science, engineering, and mathematics require the data to be arranged in a structured pattern and to be contained in a simply shaped region, such as a rectangle or circle. In many important applications, this severe restriction on structure cannot be met, and traditional numerical methods cannot be applied. In the 1970s, radial basis function (RBF) methods were developed to overcome the structure requirements of existing numerical methods. RBF methods are applicable with scattered data locations. As a result, the shape of the domain may be determined by the application …

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman

Mathematics Faculty Publications

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.