Trident Scholar Abstracts 2019
Samuel H. Baker
Midshipman First Class
United States Navy
Solving the Inverse Problem Using Combination Random Graph Models
We seek to determine if real-networks can accurately be represented by random graph models. To accomplish this task, we use a combination of three commonly-used random graph models: geometric, Chung-Lu, and preferential attachment. Each of these three models has unique properties that helps model certain characteristics of real-world networks, but using these random graph models individually has proven fruitless. Therefore, we combine multiple models in order to get a model that more accurately reflects these networks. Our method for determining if our combination random graph model successfully represents a real-world network consists of three main tests: edge counts, degree distributions, and triangle counts. This developed algorithm supports the idea that random graph models have potential in modeling real-world networks, and its output is further supported by statistical tests we develop. Although we find some faults in our method, it shows significant potential. We achieved some success with organically produced real-world networks like human and animal social networks and terrorist cells. However, we hypothesize that our model can be improved by adding more random graph models and testing it on larger networks.
FACULTY ADVISOR
Assistant Professor Franklin Kenter
Mathematics Department
Andrius V. Bernotas
Midshipman First Class
United States Navy
Electron Phonon Coupling in Superlattice and Multilayer Systems
Multilayer thin films are critical to microelectronics design (for example, as diffusion barriers between the silicon active layer and copper interconnects). However, work is needed to understand potential thermal bottlenecks that could arise from their use in transistors. A major source of thermal buildup in microelectronic devices is the interaction between electrons and the surrounding atomic species when they are in a state of thermal nonequilibrium, through electron-phonon (EP) coupling. In this project, we explore EP coupling in multilayer superlattices and oxide conductors. We use ultra-fast optical measurements of these systems, a numerical solution to the two temperature thermal model, and a graded multilayer thermoreflectance model to better understand the relationship between the EP coupling in these multilayer materials and the physical parameters of the system. We show in this project the validity of using a multilayer two temperature model in understanding thermal diffusion on the time and length scales associated with microelectronics, and we show that in superlattice configurations, the electron phonon interactions within the materials can vary greatly as compared to these interactions in the constituent materials. This change in behavior shows dependence on both the thicknesses of the layers within the superlattice and the individual properties of each layer's material. We additionally demonstrate a thorough method of processing thermoreflectance data, accounting for various changes in thermoreactance throughout the multiple layers of the system and depth of energy deposited. A greater understanding of these dynamics within multilayer systems will allow for greater control of the thermal properties as they relate to the design of the system, in turn leading to increased thermal efficiency in microelectronics in the future.
FACULTY ADVISOR
Assistant Professor Brian Donovan
Physics Department
Anderson S. Camp
Midshipman First Class
United States Navy
Design of a Hand Exoskeleton System Actuated Via Linear and Adaptive Control for Rehabilitation
A hand exoskeleton is designed and constructed to achieve five hand positions: (1) fully extended, (2) hook fist, (3) right angle to the palm, (4) straight fist, and (5) fully flexed. These hand orientations comprise the five positions defining a rehabilitation exercise known as tendon glide. The device is significant in its ability to move the two joints distal to the palm independently of the joint adjoining the palm, without requiring bulky, rigid hardware located on the finger. Movement of the finger is achieved through hydraulically activated fluidic artificial muscles (FAMs). FAMs are soft, biomimetic actuators consisting of an expandable bladder encased in a braided sheath. FAMs show improved force-to-weight ratios, cost, and alignment strategies over traditional, rigid hydraulic cylinders and allow forces to be applied across a flexed joint of the finger as it straightens. A direct model of the relationship between the volume transferred to the FAM by the hydraulic cylinder and the strain of the FAM is developed and validated through experiment. The strain-volume relationship remains constant regardless of load, enabling streamlined models and control algorithms. Position-based control of the FAMs is achieved, in both simulation and experiment, with a Proportional Integral (PI) controller and a Model Reference Adaptive Controller (MRAC). The PI controller is a linear algorithm characterized by constant controller gains. Alternatively, MRAC is an adaptive control algorithm characterized by time-varying controller gains, which can guarantee convergence of the actual system to a defined reference system. The resultant device is a wearable exoskeleton actuated by FAMs and governed by novel control architecture. The exoskeleton is capable of guiding a finger through all five positions of tendon glide. The exoskeleton aims to assist patients with at-home rehabilitation, particularly targeting patients who are typically unable to conduct their exercises without assistance from an occupational therapist.
FACULTY ADVISORS
Assistant Professor Paola Jaramillo Cienfuegos
Weapons, Robotics, and Control Engineering Department
LT Edward Chapman
Physics Department
Ψ Robert T. Chung
Midshipman First Class
United States Navy
The goal of this study was to develop novel ionic liquids (ILs) for the Natural Fiber Welding (NFW) process and use them to make advanced functional biocomposite materials with improved mechanical, chemical, and electrical properties. In this project, we synthesized three different classes of ILs containing either aromatic cations, cyclic (non-aromatic) cations, or polymerizable cations. These ILs were prepared to (i) evaluate their potential as novel NFW solvents to disrupt and reorganize biopolymer matrices, (ii) test their ability to polymerize ex-situ, and (iii) fiber-weld and subsequently polymerize within a biopolymer material to generate polyionic biocomposites.
After synthesizing nine different ILs and confirming their structure with nuclear magnetic resonance and infrared spectroscopies, we evaluated their welding potential through confocal fluorescence microscopy and scanning electron microscopy. These data confirmed that each class of ILs were viable NFW solvents. In this effort, we also developed a powerful, new method using atomic force microscopy (AFM) to map the nanomechanical properties of fiber-welded biomaterials. While evaluating each ILs’ ability to polymerize ex-situ, we discovered that the acetate anion inhibits polymerization of acetate based polymerizable-ILs (poly-ILs). However, poly-ILs with chloride anions could be polymerized using either photo or thermal initiators. We then synthesized a polyionic biocomposite containing 1-ethyl-3-vinylimidazolium chloride and microcrystalline cellulose within a welded cotton matrix. Our novel results show that poly-ILs can be applied to the NFW process to fabricate advanced fiber-welded polyionic biocomposites. Due to the ionic character added by embedding poly-ILs within a biopolymer material (e.g. silk, cotton, hemp), these biocomposites have the potential for applications in solid battery electrolytes, biosensor technologies, ion-exchange materials, smart textiles, and fuel cell membranes.
Professor Paul Trulove
Midshipman First Class
United States Navy
This paper analyzes the impact of foreign aid on institutional quality. While there is no clear definition for institutional quality, we define it to be an average measure of a country’s level of democracy, accountability of its government to the populace and ability provide public goods, as well as the government’s capacity to enforce the rule of law. The body of prior empirical literature fails to reach a consensus on the impact of aid on institutional quality. The heterogeneous nature of aid is widely recognized, but little understood. We suggest that there are underlying factors correlated with both the probability of receiving aid and aid’s effectiveness in promoting institutional quality that may be driving these varied results. Therefore, in order to mitigate and potentially quantify omitted variable bias concerns, we proxy for gender inequality through ancestral characteristics, specifically, the creation of the plow and practice of brideprice. Contemporaneous measures of gender inequality are riddled with problems of reverse causality and endogeneity concerns. The use of historic and unchanging ancestral traits allows us to employ fixed effects to alleviate these issues of reverse causality.
One may then ask how ancestral creation of the plow and the practice of brideprice relates to contemporaneous gender inequality? Alesina et al. (2011) show that adoption of the plow created the early division of labor along gender lines, which created gender divisions in society that persist today. We propose that countries that created the plow vs. adopted the plow had the resources necessary to sustain a plow economy and have the capacity for stronger economic institutions. Thus, the receipt of foreign aid has the potential to have larger positive effects on institutional quality. The ancestral practice of brideprice altered attitudes towards women in the past by creating a deep rooted view of women as property. While the ancestral practice of brideprice inclines these societies to have greater gender inequality today, Ashraf et al. (2016) show that the increased value of educated women in the brideprice market can induce spending on female education and incentivize policies that increase female education. Herz and Sperling (2004) show that greater female education is associated with various human capital gains, to include better- educated and more healthy children, more participation of females in the labor force and politics, as well as higher economic productivity of societies. In addition, brideprice also induces saving within societies, as the brideprice represents a significant expenditure of income. Therefore, brideprice societies potentially have a higher productive capacity and may be apt to receive greater institutional quality gains as a result of foreign aid.
Prior literature, most notably Acemoglu et al. (2001), shows that factors rooted in history shape comparative development of institutions. Ancestral characteristics shape contemporary institutions, but accidents of past fortune do not necessarily consign countries to permanent poverty. External assistance, foreign aid, reverses the misfortunes of the past. While contemporary societal characteristics have changed through time, many regions are “stuck” with inherited institutions from their progenitors. By shaping institutions, foreign aid benefits countries whose institutions are rooted in the past. Once underlying factors that can influence the impact of aid on institutional quality are understood, we can then begin to comprehend the true relationship between foreign aid and institutional quality.
FACULTY ADVISORS
Associate Professor Ahmed Rahman
Economics Department
Assistant Professor Alex McQuoid
Economics Department
Professor Katherine Smith
Economics Department
Megan L. Hanson
Midshipman First Class
United States Navy
Soft Skills and Soft Standards in a Sequential Learning Framework
This paper studies the effect of soft skills in higher education by analyzing how personality types and instructor tendencies affect student performance through six sets of sequential classes. To do this, we look at freshman students at the United States Naval Academy from the class years of 1998 to 2018. The Naval Academy offers an ideal environment to test the effects of soft skills due to the unique controls of the academic environment: all students take the same core courses their freshman year and are randomly placed in sections with no ability to select instructors or peers. We analyze instructor grading tendencies in a grade-distortion model while controlling for a variety of background characteristics and accounting for student personality types as captured by Myers-Briggs. We define “cushy” instructors as those who, on average, tend to give higher grades than students are projected to receive based on background characteristics. Similarly, we define “challenging” instructors as those who tend to give lower grades than we would expect a particular student to achieve.
We find that teachers have the most significant effect on subsequent student performance. Excessively “cushy” instructors hurt student performance in follow-on courses, especially in STEM courses. We also find that student personality measures matter for academic achievement overall and in a course-by-course analysis: most notably, we see that “judgers” outperform “perceivers” across all courses and lead to a higher overall grade point average over all four years. Finally, we see that the gender of the student and instructor may play a role in the ability of a student to succeed in a follow-on course regardless of the signal an instructor sends with a grade.
FACULTY ADVISORS
Associate Professor Ahmed Rahman
Economics Department
Professor Katherine Smith
Economics Department
Assistant Professor Alex McQuoid
Economics Department
Midshipman First Class
United States Navy
This project’s goal was to determine experimentally the effects of free stream turbulence on the near wake dynamics of a marine propeller. The experiments were conducted in the USNA Hydromechanics Laboratory recirculating water channel. A turbulence generating grid was placed at the opening of the channel, upstream from the propeller plane and perpendicular to the flow direction, to induce flow turbulence with 7% intensity and integral lengthscale of 0.2D (here, D is propeller diameter). Two and three-dimensional Particle Image Velocimetry (PIV) measurement techniques were used to analyze the flow domain for both unconditioned velocity measurements and phase locked measurements at a single phase of the propeller. Both sets of experiments were completed with and without the turbulence grid. The instantaneous velocity vector fields from the processed PIV data were used for analysis of multiple flow characteristics in both the unconditioned and phase-locked cases.
Spatial distributions of mean velocity profiles in the near wake (x/D<9) resemble an axisymmetric wake. Horizontal velocity of jet-type velocity profile exhibits a distinct dip at the propeller centerline due to the strong and persistent presence of the hub vortex. This vortex is clearly apparent on scaled velocity profiles when properly scaled with classical wake scaling. Tip vortices at the wake boundaries persist further downstream for the case with no turbulence generation in the free stream. Conditional sampling of velocity fluctuations showed the mechanisms of how mean flow energy is transported out of the wake core and into the less energetic free stream flow. The net transport of mean flow kinetic energy by means of random fluctuations was found to be 20% greater in the case with imposed free stream turbulence. The net transport by means of coherent fluctuations was greater in the quiescent case, however this net transport is smaller in magnitude by a factor of three.
FACULTY ADVISOR
Associate Professor Luksa Luznik
Mechanical Engineering Department
Thomas B. Imhoff
Midshipman First Class
United States Navy
Asymmetrically Loaded Gridshells: A Parametric Study on Bracing Methods and a Case Study for Use in Disaster Relief
From 1970 to 2000, 68 percent of United States naval operations were categorized as Humanitarian Assistance and Disaster Relief (HA/DR). These relief efforts identified a need for deployable, lightweight structures, capable of sheltering a large area. Large-span shelters are necessary in HA/DR because they provide space for community gathering, emergency services, educational facilities, and worship. Field work in Athens, Greece and input from external collaborators confirmed that this need is not only physical, but is both culturally and emotionally significant. Gridshells are a potential solution to this need because of their portability, sustainability, and efficiency. Formed from flat, linear members bent on-site into a curved surface, gridshells are relatively large structures that can be built without the use of heavy machinery. To broaden the use of gridshells, this paper quantifies the effect of asymmetric loading and bracing on their performance, as both are likely occurrences in HA/DR. The design requirements and constraints for the gridshell were established in Athens, Greece and with international building codes. The structural analysis included a parametric study that assessed the effect of the grid density, bracing patterns, and load cases (gravity, asymmetric, and point loads) on the failure load. These results, along with the design constraints, governed the design of the HA/DR gridshell. The results generated from this analysis will contribute to the overall design space of gridshells, specifically regarding the effects of bracing and the impact of asymmetric loads. This knowledge will broaden the design space by illustrating relationships between physical parameters and structural performance. The constructability was evaluated with small-scale models and a half-scale prototype. Having verified the structural performance, deployment mechanisms, storage schemes, and joint movements, gridshells were proven to be solutions that meet the distinct needs in HA/DR efforts.
FACULTY ADVISOR
Assistant Professor Samar Malek
Mechanical Engineering Department
Davis P. Katakura
Midshipman First Class
United States Navy
China's Export Effects: A Product-Level Analysis of Global Supply Chains, Comparative Advantage, and Crowding-Out
China's extraordinary economic growth has had a large impact on the world economy. Between 1995 and 2015, China's share in the world's total exports increased from 3.2% to 13.8%. The effect of China's sudden growth may have affected neighboring, developing economies that possessed a similar make-up to China in terms of labor resources and products produced. This paper attempts to address the effects of China's exports on the magnitude and composition of other countries' exports by analyzing a dataset of bilateral trade flows between countries, covering the period 1988-2016 at a highly disaggregated product level. Including the most recent data will include the exogenous shocks of the US Financial Crisis and the Great Trade Collapse of 2008-2009. Disaggregated products are classified by their sector of industry (e.g., electronics and clothing) and final usage in a global supply chain (e.g., intermediate inputs, final goods, and capital goods). Using a gravity model of trade, we quantitatively investigate both the crowding-out and crowding-in of trade due to China's exports. Standard trade theory of comparative advantage suggests if China is relatively good at exporting certain goods, trading partners will produce less (crowding-out), but those resources can be reallocated to new sectors and stages in global supply chains, increasing exports elsewhere (crowding-in). The results show that China's role exhibits a greater influence in crowding-in and crowding-out final goods relative to its effect on stimulating global supply chains. If China's exports remained constant at its 1988 levels, the rest of the world would have experienced around a 10% decrease in trade.
FACULTY ADVISORS
Assistant Professor Jacek Rothert
Economics Department
Professor Katherine Smith
Economics Department
Assistant Professor Douglas VanDerwerken
Mathematics Department
Yash D. Khatavkar
Midshipman First Class
United States Navy
Predicting Optimal Maneuvering Time Benefits for Satellite Attitude Control
A common goal of satellite control systems is to reduce the time required to change a spacecraft’s attitude, which maximizes its mission capability. Time- optimal attitude control algorithms increase the agility of satellites such as imaging spacecraft, thus allowing a greater frequency of image collection. Eigenaxis based maneuvering, though common in industry and academia, fails to produce the minimum-time solution for actual satellites. Solving the optimal control problem is often challenging and requires evaluating multiple maneuver paths to ensure the shortest path is found for each spacecraft configuration. One of the primary difficulties in predicting optimal control benefits stems from the wide range of satellite configurations and infinite variation in inertia. To mitigate this issue, this research aims to determine an analytical relationship between satellite inertia and the time savings of using optimal control rather than eigenaxis maneuvering on spacecraft with a NASA standard four reaction-wheel configuration. To accomplish this, the development of a script using DIDOR optimization software determines minimum-time paths for satellite maneuvers. Each path was independently verified and validated using Pontryagin’s minimization principle to ensure that they are physically feasible and that each solution is optimal. Additionally, this work demonstrates that inertia ratios can be used to characterize the attitude control performance of any spacecraft, allowing for the analysis of satellite inertias and their relationship to maneuver time reduction regardless of the scale of the spacecraft. The calculation of the agility envelope volume is then utilized in conjunction with the DIDOR script and various inertia ratios in order to investigate the mathematical relationship between satellite inertia and time savings from optimal control. The result of this work is a design-space tool that can be used by engineers to help determine whether or not to implement time-optimal control algorithms on any spacecraft in a simple and effective way.
FACULTY ADVISOR
CDR Jeffery King
Aerospace Engineering Department
Stefano Pineda
Midshipman First Class
United States Navy
Numerical Simulation of Laser-Induced Drop Evaporation
Despite the rapid development of naval laser weapon systems, applications used to model High-Energy Lasers (HEL) in maritime environments are still incomplete. When a high-energy laser interacts with raindrops, fog, or other aqueous aerosols, the laser propagation and drop thermodynamics are coupled through the absorption-dependent vaporization process. Experiments with small droplets have shown that laser-droplet interactions may fall in two regimes – a “slow heating” regime where the drop rapidly evaporates due to elevated surface temperature, and a “fast heating” regime where the drop explosively breaks apart due to the pressure wave from spontaneous vaporization. Related numerical studies have ignored internal drop dynamics, assuming either spatially isothermal drops or assuming that heat transfer is by diffusion only. Recent experiments with larger laser-irradiated drops have shown that temperature fluctuations and internal drop dynamics are not negligible when drop diameter is on the order of 1 mm, e.g. in rain or sea spray. These experiments measured drop surface temperatures during a “slow heating” regime, but were unable to measure temperatures on the interior of the drop, where spontaneous vaporization is most likely to occur. This research uses computer simulations to explore the laser heating, fluid dynamics, and evaporation of large water drops in order to determine internal drop temperatures and predict the onset of a “fast heating” regime. Simulations are run using COMSOL Multiphysics, a commercial solver based on the Finite Element Method. A geometric (ray) optics approach is used to generate internal volumetric heating distributions within a drop. This heating distribution is then applied to drops with different shapes and sizes, with increasing physical complexity to evaluate the effects each physical assumption has on the drop dynamics. The simulation is validated with experimental data on drop surface temperature, temperature variance, and vaporization rate, and is then extended to explore the effects of a range of parameters including laser irradiance and wavelength, drop shape, and external forcing. Dimensionless relationships between laser parameters and environmental conditions generated in this study can then be applied to laser propagation applications to enhance their predictive capabilities.
FACULTY ADVISORS
Associate Professor Cody Brownell
Mechanical Engineering Department
Associate Professor Evelyn Lunasin
Mathematics Department
CDR Stuart Blair
Mechanical Engineering Department
Dean N. Rye
Midshipman First Class
United States Navy
Many Body Systems of Coupled Dissipative Jaynes-Cummings Cavities
Open many body systems are difficult to solve because they obey non-equilibrium laws of physics. However, quantum many body systems are inherently coupled to the environment, necessitating a full understanding of non-equilibrium physics for real world applications. The Jaynes-Cummings model, consisting of a cavity with an atom interacting with a light field, provides a suitable platform to study many body non-equilibrium physics. In the single cavity, low photon states are achieved in the dispersive regime due to photon blockade, where the absorption of one photon blocks the absorption of a second. When open to the environment, the breakdown of this photon blockade sets in through dispersive bistability, where the cavity can reach two distinct stable solutions. We implement mean field theory to derive semiclassical equations which locate parameter regimes of bistability. Numerical solutions of the Lindblad master equation do not predict bistability directly, but unfolding the master equation into quantum trajectory calculations demonstrates switching between the semiclassical solutions. We then consider open systems of weakly interacting Jaynes-Cummings cavities. The bistability of the single cavity facilitates the emergence of symmetry-breaking states in multiple cavity systems, where the cavities achieve different steady states despite their coupling. Analysis of the two cavity system using quantum trajectories shows qualitative differences between symmetry-breaking and symmetry-preserving states. In the three cavity case, the symmetry-breaking bistability region extends past the critical point of typical symmetry-preserving bistability. The results for multiple Jaynes-Cummings cavities build towards a better understanding of open many body quantum physics.
FACULTY ADVISORS
Assistant Professor Seth Rittenhouse
Physics Department
Assistant Professor Joel Helton
Physics Department
Nicholas T. Vu
Midshipman First Class
United States Navy
The Effects of Nanostructuring on the Thermal Transport of Electronic Materials
Understanding the fundamental energy transport mechanisms in nanostructured materials is vital to the development of smaller, energy-dense systems. This is particularly important in materials used in high power density electronic systems and renewable energy platforms, where performance is directly tied to the thermal properties of constituent materials. By altering the nanostructure, the thermal properties can be tailored to meet various needs. Frequency Domain Thermoreflectance (FDTR), an optical pump-probe thermal characterization technique, is used to characterize the thermal properties of different electronic materials. An FDTR system was built as part of this project and validated with reference scans of known materials. This work thermally characterizes nickel titanium (NiTi), germanium telluride (GeTe), Bi 2Te 3/Bi 2(TeSe) 3 superlattices, and gallium nitride (GaN). NiTi is a candidate material for elastocaloric cooling and thermal energy storage applications. We show that increasing the grain size of NiTi significantly increases thermal conductivity on both sides of the phase change. We study the impact of film thickness on the thermal conductivity of the crystalline and amorphous phases of germanium telluride (GeTe). It was found that the mean free path of heat energy carriers is similar in both phases of the material. The application of a phonon scattering model to a thickness-dependent thermal conductivity dataset indicates that phonon boundary scattering is the predominant physical mechanism that limits thermal transport in thin-films of GeTe. Superlattices with alternating thin-films of Bi 2Te 3 and Bi 2(TeSe) 3 were thermally characterized. We find a large degree of thermal anisotropy and a significant increase in the in-plane thermal conductivity compared to bulk values, possibly due to a topological insulator effect. We report preliminary results of the thermal conductivity of seed-grown GaN films with a grain size gradient on partially etched substrates.
FACULTY ADVISORS
Assistant Professor Ronald Warzoha
Mechanical Engineering Department
Professor Andrew Smith
Mechanical Engineering Department
Assistant Professor Brian Donovan
Physics Department
Dakota L. Wenberg
Midshipman First Class
United States Navy
Development of Hybrid Robotic Controller for Autonomous, On-Orbit Spacecraft Assembly Applications
The use of robotics in the space environment has been common throughout the last half century of space exploration. However, robotic arms are rarely entrusted to perform large assembly tasks without a human in the loop because of the high cost of the hardware. As our presence in space grows, developing advanced autonomous robotic systems may be the way forward as time lags associated with teleoperation are expected to cripple future space missions beyond earth orbit.
This project focuses on the derivation of an autonomous control system for spacecraft assembly applications that blends Jacobian path following and visual servoing. Jacobian path following assumes the environment is well known and plans end effector trajectories whose performance for assembly may suffer in dynamic or uncertain environments. Visual servoing approaches use feedback from an effector attached camera and can avoid dynamic obstacles, but provides no guarantee of success if the sensor cannot keep the goal location in its field of view and often traverses inefficient manipulator trajectories. This work proposes a hybrid approach that combines both approaches to improve the performance of a robotic manipulator in both known and unknown environments.
The robotic systems are simulated using the proposed hybrid controller. The hybrid controller is developed in MATLAB using a kinematic simulation of a two degree of freedom robotic arm operating in a single plane with a simplified camera model. Following successful implementation of the simulation, a more complex robotic arm is simulated in 3D space. The controller is integrated into an existing robotic arm platform (UR5 Industrial Manipulator) for a proof of concept. The results of the testing highlights the path and final position of each controller to demonstrate the advantages of each controller individually and the advantages of the hybrid approach.
FACULTY ADVISORS
Assistant Professor Michael Kutzer
Weapons, Robotics, and Control Engineering Department
Assistant Professor Jin Kang
Aerospace Engineering Department
Assistant Professor Levi DeVries
Weapons, Robotics, and Control Engineering Department
Drew M. Weninger
Midshipman First Class
United States Navy
Quantum Singularities in Black Hole Spacetime Systems with Timelike Classical Singularities
General relativity is currently the best theory that describes gravitation, one of the four basic forces of nature. A thorough understanding of general relativity is essential for navigation systems reliant upon GPS to operate with accurate and precise measurements over time. Classical general relativity predicts the existence of irremovable singularities, points in space where a mathematical description of the spacetime “breaks down" due to geodesic incompleteness. These singularities are found in a host of relativistic spacetimes, including those of observable astrophysical objects such as black hole systems. In our study, timelike curvature singularities associated with a group of super-extremal spacetimes are analyzed with a quantum wave packet in place of geodesic incompleteness. In this case, these singularities may be “removed" or “healed" without imposing boundary conditions. The super-extremal spacetimes explored include overcharged and overspinning black hole systems with naked singularities and different assumptions such as penetration by a cosmic string, a higher dimensional universe background, or in expanding or contracting cosmologies.
The technique to determine quantum singularities focuses on analysis of the spatial segment of the minimally coupled, relativistic Klein Gordon wave operator for a massive scalar particle and whether it is essentially self-adjoint. Both, Weyl's limit-point, limit-circle criterion and deficiency indices are used to determine self-adjointness. By using self-adjointness properties, the spacetime can be characterized as quantum mechanically singular or non-singular. This method can help in determining the behavior of quantum particles, including the Higgs and other bosons found in spontaneous symmetry breaking models, near a black hole singularity. Our results indicate the quantum wave operator is not essentially self-adjoint for the spherically symmetric spacetimes and spacetimes with cosmic strings. Hence, they contain quantum singularities. Finally, for a wave packet in the vicinity of a rotating black hole's naked singularity, the wave operator is not essentially-self adjoint indicating quantum singularities exist and the ring singularity is not “healed".
FACULTY ADVISORS
Professor Deborah Konkowski
Mathematics Department
Professor Mitchell Baker
Mathematics Department
Professor Eyo Ita
Physics Department
Kathryn S. Wesdyk
Midshipman First Class
United States Navy
Towards a Sustainable Approach to Water Service Delivery in a Rural Context
According to the World Health Organization (WHO), over two billion people lack access to safely managed drinking water services, accounting for over one million deaths worldwide each year. To focus needed attention on this crisis, the United Nations’ Sustainable Development Goals call for universal, equitable, safe, and affordable water service. This global challenge has proved to be particularly difficult in a rural context. Governments in developing regions often lack the resources, capital, and capabilities to provide and manage public services, to include drinking water. Many have turned to the private sector, foreign donors, and aid organizations to supply safe water. Historically, these programs have struggled to do so sustainably, over-prioritizing short-term infrastructure development at the expense of the long-term operation of the systems. Many water providers and their donors have focused on the number of facilities built and the number of people with access, driving the performance of the Water, Sanitation, and Hygiene (WASH) sector by these metrics alone. Sustainability; however, cannot be described by system functionality or population coverage exclusively. The definition of the term should be expanded to include a wider variety of metrics that describe the long term operation and resiliency of the system, from the perspective of both the water suppliers and the communities they serve.
A more nuanced view of sustainability is especially needed in rural communities where weak governance, low per capita resources, and high per capita costs of obtaining water access combine to present a substantial barrier to water service delivery. In recent years there has been recognition in the development sector that in order to improve sustainability, water providers should shift from a paradigm that relies on external support yet operates independently from other WASH actors, to one that combines grants and a strong enough revenue base to recover operational and maintenance costs in collaboration with WASH actors. Water providers must achieve a difficult balance that increases impact (increasing the amount of impoverished communities using safe water) with a model that will continue to perform.
A broad, systematic review of WASH programs was conducted to develop a comprehensive summary of considerations for rural communities in developing regions to proactively develop their own water provision. The primary recommendations for community authorities seeking water service delivery are applied to a case study on the island of Île-à-Vache, Haiti.
FACULTY ADVISORS
LCDR Ethan Lust
Mechanical Engineering Department
Professor Patrick Caton
Mechanical Engineering Department
Professor Kurtis Swope
Economics Department
