Applied Mathematics Commons^™

Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model …

Using Mathematical Modeling To Unmask The Concealed Nature Of Long Qt-3 Syndrome, Steven Poelzing, Amara Greer-Short, Seth H. Weinberg

Biology and Medicine Through Mathematics Conference

No abstract provided.

A General Framework Of Large-Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques, Soysal Degirmenci

McKelvey School of Engineering Graduate Student Theses & Dissertations

In a world where data rates are growing faster than computing power, algorithmic acceleration based on developments in mathematical optimization plays a crucial role in narrowing the gap between the two. As the scale of optimization problems in many fields is getting larger, we need faster optimization methods that not only work well in theory, but also work well in practice by exploiting underlying state-of-the-art computing technology.

In this document, we introduce a unified framework of large-scale convex optimization using Jensen surrogates, an iterative optimization method that has been used in different fields since the 1970s. After this general treatment, …

Developing A Risk Analysis Model To Improve Study Abroad Awareness, Tyler Spain

Industrial Engineering Undergraduate Honors Theses

As international education opportunities increase in popularity among U.S. college students (McMurtrie, 2007), it is becoming more and more necessary for study abroad organizations to be aware of the risks students face as they travel abroad. While some international cities are riskier than others, it can be difficult to distinguish between cities which truly carry a high degree of risk for visiting students, and which cities are only perceived to be risky based on various personal misconceptions. The University of Arkansas Office of Study Abroad & International Exchange currently lacks a way to quantifiably analyze the risk of study abroad …

Cfd Model For Ventilation In Broiler Holding Sheds, Christian Heymsfield

Biological and Agricultural Engineering Undergraduate Honors Theses

Broiler production in Arkansas was valued at over $3.6 billion in 2013 (University of Arkansas Extension of Agriculture). Consequently, improvement in any phase of the production process can have significant economic impact and animal welfare implications. From the time poultry leave the farm and until they are slaughtered, they can be exposed to harsh environmental conditions, both in winter and in summer. After road transportation, birds are left to wait in holding sheds once they arrive at the processing plant, for periods of approximately 30 minutes to two hours. This project was interested in this holding shed waiting time during …

Acoustic Firearm Discharge Detection And Classification In An Enclosed Environment, Lorenzo Luzi, Eric Gonzalez, Paul Bruillard, Matthew Prowant, James Skorpik, Michael Hughes, Scott Child, Duane Kist, John E. Mccarthy

Mathematics Faculty Research

Two different signal processing algorithms are described for detection and classification of acoustic signals generated by firearm discharges in small enclosed spaces. The first is based on the logarithm of the signal energy. The second is a joint entropy. The current study indicates that a system using both signal energy and joint entropy would be able to both detect weapon discharges and classify weapon type, in small spaces, with high statistical certainty.

On The Scattering Of An Acoustic Plane Wave By A Soft Prolate Spheroid, Joseph Michael Borromeo

UNLV Theses, Dissertations, Professional Papers, and Capstones

This thesis solves the scattering problem in which an acoustic plane wave of propagation number K1 is scattered by a soft prolate spheroid. The interior field of the scatterer is characterized by a propagation number K2, while the field radiated by the scatterer is characterized by the propagation number K3. The three fields and their normal derivatives satisfy boundary conditions at the surface of the scatterer. These boundary conditions involve six complex parameters depending on the propagation numbers. The scattered wave also satisfies the Sommerfeld radiation condition at infinity. Through analytical methods, series representations are constructed for the interior field …

Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation …

A Logistic Regression And Markov Chain Model For The Prediction Of Nation-State Violent Conflicts And Transitions, Nicholas Shallcross

Theses and Dissertations

Using open source data, this research formulates and constructs a suite of statistical models that predict future transitions into and out of violent conflict and forecasts the regional and global incidences of violent conflict over a ten-year time horizon. A total of thirty predictor variables are tested and evaluated for inclusion in twelve conditional logistic regression models, which calculate the probability that a nation will transition from its current conflict state, either In Conflict or Not in Conflict, to a new state in the following year. These probabilities are then used to construct a series of nation-specific Markov chain models …

Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in …

Supervised Learning-Based Explicit Nonlinear Model Predictive Control And Unknown Input Estimation In Biomedical Systems, Ankush Chakrabarty

Open Access Dissertations

Application of nonlinear control theory to biomedical systems involves tackling some unique and challenging problems. The mathematical models that describe biomedical systems are typically large and nonlinear. In addition, biological systems exhibit dynamics which are not reflected in the model (so-called 'un-modeled dynamics') and hard constraints on the states and control actions, which exacerbate the difficulties in designing model-based controllers or observers.

This thesis investigates the design of scalable fast explicit nonlinear model predictive controllers (ENMPCs). The design involves (i) the estimation of a feasible region using Lyapunov stability methods and support vector machines; and (ii) within the estimated feasible …

Signal Flow Graph Approach To Efficient Dst I-Iv Algorithms, Sirani M. Perera

Publications

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having (n�1) points signal flow graph for DST-I and n points signal flow graphs for DST II-IV.

Early Afternoon Concurrent Panel Sessions: Commercial Space Industry Snapshot: Presentation: Small Catapult-Assisted Horizontal-Launch Reusable Rbcc Ssto Spaceplane For Economical Short-Duration Leo Access, Nihad E. Daidzic,

Aviation / Aeronautics / Aerospace International Research Conference

This article discusses the conceptual design, flight trajectory calculations, and utilization of the possible future horizontally-launched reusable Single-Stage-to-Orbit (SSTO) spaceplane for small payload short-duration manned/unmanned access to Low-Earth-Orbit (LEO). The 10,000 lb spaceplane would use 5,000 ft catapult-assist horizontal-launch facility and conduct powered approach and landing on conventional horizontal paved runways following the gliding atmospheric re-entry. To increase the economy of operation, the launch facility located at high elevations (4,000+ ft) equatorial region is required, such as, the plateaus in Kenya and Tanzania in Africa and/or Ecuador in South America. A 500-lb payload, including pilot-commander, is envisioned. The propulsion cycle …

Effect Of Spalled Particles Thermal Degradation On A Hypersonic Flow Field Environment, Raghava S. C. Davuluri, Huaibao Zhang, Alexandre Martin

Mechanical Engineering Faculty Publications

Two-way coupling is performed between a spallation code and a hypersonic aerothermodynamics CFD solver to evaluate the effect of spalled particles on the flow field. Time accurate solutions are computed in argon and air flow fields. A single particle simulations and multiple particles simulations are performed and studied. The results show that the carbon vapor released by spalled particles tend to change the composition of the flow field, particularly the upstream region of the shock.

General Solution Of The Wind Triangle Problem And The Critical Tailwind Angle, Nihad E. Daidzic

Aviation Department Publications

A general analytical solution of the navigational wind-triangle problem and the calculation of the critical tailwind angle are presented in this study among other findings. Any crosswind component will effectively create a headwind component on fixed course tracks. The meaning of a route track is lost with excessive crosswinds representing the bifurcation point between the possible and the impossible navigational solutions. Any wind of constant direction and speed will effectively reduce groundspeed and increase time-of-flight on closed-loop multi-segment flights. Effective wind track component consists, in general, of true and induced components. The average groundspeed of multiple-leg flights is a harmonic …

Project Oasis: Optimizing Aquaponic Systems To Improve Sustainability, Siddharth Nigam, Paige Balcom

Honors Theses and Capstones

Started in Fall 2015, Project OASIS (Optimizing Aquaponic Systems to Improve Sustainability) is an interdisciplinary capstone project with the goal of designing a sustainable and affordable small-scale aquaponic system for use in developing nations to tackle the problems of malnutrition and food insecurity. Aquaponics is a symbiotic relationship between fish and vegetables growing together in a recirculating system. The project’s goals were to minimize energy consumption and construction costs while using universally available materials. The computational fluid dynamics (CFD) software OpenFOAM was used to create transient and steady-state models of fish tanks to visualize velocity profiles, streamlines, and particle movement. …

An Investigation Of Inital Shock Cell Formation In Turbulent Coanda Wall Jets, Caroline P. Lubert, Christian R. Schwantes, Richard J. Shafer

Department of Mathematics and Statistics - Faculty Scholarship

Turbulent Coanda wall jets are present in a multitude of natural and man-made applications. Their obvious advantages in terms of flow deflection are often outweighed by disadvantages related to the increased noise levels associated with these jets. Primary high-frequency noise sources are turbulent mixing noise (TMN) and shock-associated noise (SAN). Clearly, accurate modeling of these noise sources will facilitate better predictions of the behavior of such jet noise with physical characteristics. This paper, which focuses on SAN, shows how the Method of Characteristics can be applied to a steady two-dimensional axisymmetric supersonic flow to rewrite the three governing partial differential …

Methodology For Analyzing Epoxy-Cnt Phononic Crystals For Wave Attenuation And Guiding, Madhu Kolati

Dissertations, Master's Theses and Master's Reports

Phononic crystals (PhnCs) control, direct and manipulate sound waves to achieve wave guiding and attenuation. This dissertation presents methodology for analyzing nanotube materials based phononic crystals to achieve control over sound, vibration and stress mitigation. Much of the analytical work presented is in identifying frequency band gaps in which sound or vibration cannot propagate through these PhnCs. Wave attenuation and mitigation analysis is demonstrated using finite element simulation. Engineering principles from current research areas of solid mechanics, solid-state physics, elasto-dynamics, mechanical vibrations and acoustics are employed for the methodology. A considerable effort is put to show that these PhnCs can …

Heuristic And Exact Algorithms For The Two-Machine Just In Time Job Shop Scheduling Problem, Mohammed Al Salem, Leonardo Bedoya-Valencia, Ghaith Rabadi

Engineering Management & Systems Engineering Faculty Publications

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much …

Modeling Of Piezoelectric Traveling Wave Rotary Ultrasonic Motors With The Finite Volume Method, Ivan Arturo Renteria Marquez

Open Access Theses & Dissertations

In 1983 Toshiiku Sashida developed a new motor concept called Piezoelectric Traveling Wave Rotary Ultrasonic Motor (PTRUSM). The advantages of these motors include high torque at low speed, absence of a generated magnetic field, and high potential for miniaturization. Unfortunately PTRUSMs have some disadvantages that limit the areas of applications for these types of motors. The disadvantages are a short operating life (about 1000 hours), small output power, and the need of a complex motor controller.

On one hand, these motors have been used in satellites, mobile phones, photocopiers, robotic arms, telescopes, automobiles, and camera autofocusing. On the other hand, …

Diffusive Behavior Of Physically Cross-Linked Hydrogels, Morgan A. Stilke

Williams Honors College, Honors Research Projects

A hydrogel is a water swollen polymeric network that has the potential to transform a variety of biomedical applications because of its biocompatibility and water content. Unfortunately, hydrogels typically have poor mechanical robustness. The majority of the content is water, while the remaining structure consists of a physical network, a covalent network, or a combination of both, yielding strength and toughness. There are several strategies attempted to improve mechanical properties including double network hydrogels comprised of two interpenetrating networks: one being a highly crosslinked sacrificial network and the other being a weakly crosslinked network that maintains reversibility after deformation. However, …

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski

Publications

Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.

A Machine Learning Approach To Post-Market Surveillance Of Medical Devices, Jonathan Bates, Shu-Xia Li, Craig Parzynski, Ronald Coifman, Harlan Krumholz, Joseph Ross

Yale Day of Data

Post-market surveillance is a collection of processes and activities used by product manufacturers and regulators, such as the U.S. Food and Drug Administration (FDA) to monitor the safety and effectiveness of medical devices once they are available for use “on the market”. These activities are designed to generate information to identify poorly performing devices and other safety problems, accurately characterize real-world device performance and clinical outcomes, and facilitate the development of new devices, or new uses for existing devices. Typically, a device is monitored by comparing adverse events in the exposed population to a matched unexposed population. This research considers …

Factors Affecting Dimensional Precision Of Consumer 3d Printing, David D. Hernandez

International Journal of Aviation, Aeronautics, and Aerospace

This paper investigates the factors affecting dimensional precision of consumer-grade 3D printing, attempting to isolate and mitigate sources of error. The focus is on creating engineering prototypes of, tooling for, or finalized instances of mechanical devices. A specific fused deposition modeling printer – the Ultimaker 2 – is analyzed in terms of meeting precise physical dimensions, consistent shapes, and predictable surface finish. Extensive trial and error resulted in removal of several sources of bias, with square test articles exhibiting a lower-than-anticipated mean percentage error of -0.387% (SD = 0.559), a value comparable to other modern manufacturing techniques. A full …

Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu

LSU New Orleans Theses and Dissertations

The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.

Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes

Rose-Hulman Undergraduate Research Publications

From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …

Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,

International Journal of Aviation, Aeronautics, and Aerospace

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and …

On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo

Dissertations

Meshless methods utilizing Radial Basis Functions~(RBFs) are a numerical method that require no mesh connections within the computational domain. They are useful for solving numerous real-world engineering problems. Over the past decades, after the 1970s, several RBFs have been developed and successfully applied to recover unknown functions and to solve Partial Differential Equations (PDEs).
However, some RBFs, such as Multiquadratic (MQ), Gaussian (GA), and Matern functions, contain a free variable, the shape parameter, c. Because c exerts a strong influence on the accuracy of numerical solutions, much effort has been devoted to developing methods for determining shape parameters which provide …

Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link

All ECSTATIC Materials

The science and management of aquatic ecosystems is inherently interdisciplinary, with issues associated with hydrology, atmospheric science, water quality, geochemistry, sociology, economics, environmental science, and ecology. Addressing water resources issues in any one discipline invariably involves effects that concern other disciplines, and attempts to address one issue often have consequences that exacerbate existing issues or concerns, or create new ones (Jørgensen et al. 1992; Lackey et al. 1975; Straskraba 1994) due to the strongly interactive nature of key processes (Christensen et al. 1996). Thus, research and management of aquatic ecosystems must be interdisciplinary to be most effective, but such truly …