Other Physical Sciences and Mathematics Commons^™

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions.

As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

Espade: An Efficient And Semantically Secure Shortest Path Discovery For Outsourced Location-Based Services, Bharath K. Samanthula, Divyadharshini Karthikeyan, Boxiang Dong, K. Anitha Kumari

Department of Computer Science Faculty Scholarship and Creative Works

With the rapid growth of smart devices and technological advancements in tracking geospatial data, the demand for Location-Based Services (LBS) is facing a constant rise in several domains, including military, healthcare and transportation. It is a natural step to migrate LBS to a cloud environment to achieve on-demand scalability and increased resiliency. Nonetheless, outsourcing sensitive location data to a third-party cloud provider raises a host of privacy concerns as the data owners have reduced visibility and control over the outsourced data. In this paper, we consider outsourced LBS where users want to retrieve map directions without disclosing their location information. …

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Faculty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

3d Microwave Tomography Using The Soft Prior Regularization Technique: Evaluation In Anatomically-Realistic Mri-Derived Numerical Breast Phantoms, Amir H. Golnabi, Paul M. Meaney, Shireen D. Geimer, Keith D. Paulsen

Department of Mathematics Faculty Scholarship and Creative Works

Objective: Fusion of magnetic resonance imaging (MRI) breast images with microwave tomography is accomplished through a soft prior technique, which incorporates spatial information (from MRI), i.e. accurate boundary location of different regions of interest, into the regularization process of the microwave image reconstruction algorithm. Methods: Numerical experiments were completed on a set of 3D breast geometries derived from MR breast data with different parenchymal densities, as well as a simulated tumor to evaluate performance over a range of breast shapes, sizes and property distributions. Results: When the soft prior regularization technique was applied, both permittivity and conductivity relative root mean …

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Arizona's Vulnerable Populations, Jonathan G.S. Koppell, Warren Prostollo, Jay Kittle, Arlan Colton, Kim Demarchi, Darryl Dobras, Susan Goldsmith, Billie Fidlin, Jim Holoway, Tara Jackson, Rita Maguire, Elizabeth Mcnamee, Patrick Mcwhortor, Ray Newton, Pat Norris, Steve Pedigo, Scott Rhodes, Fred Rosenfed, Chad Sampson, David Snider, Bob Strain, Marissa Theisen, Devan Wastchak, Terri Wogan, Larry Woods, Antonia Adams-Clement, Nina Babich, Andrea Banks, Eric Bjorklund, Luke Black, Luis De La Cruz-Parra, Richard Fabes, Felicia Ganther, Joseph Garcia, Maria Harper-Marinick, Kevin Hengehold, Lane Kenworthy, Julie Knapp, Kelly Mcgowan, Ray Ostos, Kathleen Perales, Suzanne Pfister, Michael S. Shafer, Julia Grace Smith, Ed Strong, Cynthia Zwick

Publications from President Jonathan G.S. Koppell

Arizona’s vulnerable populations are struggling on a daily basis but usually do so in silence, undetected by traditional radar and rankings, often unaware themselves of their high risk for being pushed or pulled into a full crisis. Ineligible for financial assistance under strict eligibility guidelines, they don’t qualify as poor because vulnerable populations are not yet in full crisis. To be clear, this report is not about the “poor,” at least not in the limited sense of the word. It is about our underemployed wage earners, our single-parent households, our deployed or returning military members, our under-educated and unskilled workforce, …

Rollover, Drowning, And Discontinuous Retreat: Distinct Modes Of Barrier Response To Sea-Level Rise Arising From A Simple Morphodynamic Model, Jorge Lorenzo Trueba, Andrew Dale Ashton

Department of Earth and Environmental Studies Faculty Scholarship and Creative Works

We construct a simple morphodynamic model to investigate the long-term dynamic evolution of a coastal barrier system experiencing sea-level rise. Using a simplified barrier geometry, the model includes a dynamic shoreface profile that can be out of equilibrium and explicitly treats barrier sediment overwash as a flux. With barrier behavior primarily controlled by the maximum potential overwash flux and the rate of shoreface response, the modeled barrier system demonstrates four primary behaviors: height drowning, width drowning, constant landward retreat, and a periodic retreat. Height drowning occurs when overwash fluxes are insufficient to maintain the landward migration rate required to keep …