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Articles 12091 - 12120 of 12690
Full-Text Articles in Physical Sciences and Mathematics
Interactions Between Local Magnetic Moments And Itinerant Charge Carriers In Fe-Based Systems, Yan Wu
Interactions Between Local Magnetic Moments And Itinerant Charge Carriers In Fe-Based Systems, Yan Wu
LSU Doctoral Dissertations
The interactions between magnetic moments and electrons are essential in creating many of the unique properties of magnetic systems. In this thesis, I focused on two Fe-based systems employing multiple experimental techniques to investigate the coupling between localized magnetic moments and conducting charge carriers in two systems with tendencies to order into itinerant magnetic phases.\\ With systematic investigations of Fe$_{1-y}$Co$_y$Si, we discovered a field depended non-Fermi-Liquid (non-FL) behavior near its insulator-metal-transition (IMT) that appears to share the same mechanism as previously discovered in Mn doped FeSi - the underscreened Kondo effect.\\ A similar interaction of the charge carrier moments screening …
Chesapeake Coastal Community Flood Vulnerability--Prediction And Verification, Alexander D. Renaud
Chesapeake Coastal Community Flood Vulnerability--Prediction And Verification, Alexander D. Renaud
Dissertations, Theses, and Masters Projects
Fast moving hurricanes and stationary nor’easters have resulted in significant flood damage in Chesapeake tidewater communities. The Chesapeake Bay region is one of A m erica’s most vulnerable regions with respect to sea-level rise, which will only increase storm surge impacts over upcoming decades. While the general trends are well documented, there is limited information relevant to specific communities’ relative flood risk and response. The dearth o f data is especially troublesome given the lengthy period o f time generally needed for communities to plan and implement adaptive action. This study contributes to the regional understanding of flood and sea-level …
Probabilistic And Deep Learning Algorithms For The Analysis Of Imagery Data, Saikat Basu
Probabilistic And Deep Learning Algorithms For The Analysis Of Imagery Data, Saikat Basu
LSU Doctoral Dissertations
Accurate object classification is a challenging problem for various low to high resolution imagery data. This applies to both natural as well as synthetic image datasets. However, each object recognition dataset poses its own distinct set of domain-specific problems. In order to address these issues, we need to devise intelligent learning algorithms which require a deep understanding and careful analysis of the feature space. In this thesis, we introduce three new learning frameworks for the analysis of both airborne images (NAIP dataset) and handwritten digit datasets without and with noise (MNIST and n-MNIST respectively). First, we propose a probabilistic framework …
Effect Of 5-Hydroxymethylcytosine Modifications On Stability Of Vegf I-Motifs, Bethany Summerford
Effect Of 5-Hydroxymethylcytosine Modifications On Stability Of Vegf I-Motifs, Bethany Summerford
Honors Theses
DNA i-motifs are a secondary structure of DNA formed at low pH by internal folding of strands rich in cytosine. This study focuses on trying to determine if the DNA from the vascular endothelial growth factor (VEGF) promoter, which can form an i-motif, can be stabilized with the epigenetic modification to 5- hydroxymethylcytosine in four separate locations on the DNA strand, and to what extent the degree of stabilization depends on the location of the modification. Stability of the i-motif was determined by measuring pKa and melting point (Tm) of each VEGF modification using circular dichroism spectroscopy. The modified samples …
Statistical Analysis Of Arsenic Concentrations In Subsurface Soils At The University Of Mississippi Field Station, David Thomas Webb
Statistical Analysis Of Arsenic Concentrations In Subsurface Soils At The University Of Mississippi Field Station, David Thomas Webb
Honors Theses
The purpose of this investigation is to determine how arsenic concentration varies in soils with respect to soil structures, grain size, soil type, and depth. The investigation was conducted at the University of Mississippi Field Station (UMFS). The UMFS is located in Abbeville, MS and is roughly 700 acres in size. It includes ponds and former agricultural fields, and lies within an internally draining basin. Seven boreholes were drilled using a direct push geoprobe and sampled. The cores obtained from the borings were then cut at one foot intervals, producing a total of 90 soil samples. Each sample was observed …
A Study On The Characterization And Implementation Of Tools For Advanced Ligo, Hunter Gabbard
A Study On The Characterization And Implementation Of Tools For Advanced Ligo, Hunter Gabbard
Honors Theses
The Laser Interferometer Gravitational Wave Observatory (LIGO) is aimed at directly detecting gravitational waves, small perturbations or ripples in the fabric of space-time. Because of their extreme sensitivity, the LIGO detectors are affected by many sources of non-astrophysical noise. In the first part of this thesis we test a pipeline designed for the identification of short-duration noise transients, called Omicron. We first inject simulated noise waveforms in engineering run data from the LIGO detector in Livingston, Louisiana and then determine Omicron efficiency by attempting to recover these injections. In the second part of this thesis, we present a novel method …
Blue Cheese Cosmology: Lensing By Cosmic Strings, Jared Wofford
Blue Cheese Cosmology: Lensing By Cosmic Strings, Jared Wofford
Honors Theses
The light bending effects around cosmic strings in universes with varying rates of expansion are investigated. A relationship between the angular deflection and the expansion rate is found. This is made possible by the Blue Cheese model, which is a generalization to a cylindrical realm of the Swiss Cheese model
Study Of An Active-State Cb1 Receptor Model And Jwh Compound Interactions To Predict New Emerging Synthetic Cannabinoids, Kelsey Leigh Pettus
Study Of An Active-State Cb1 Receptor Model And Jwh Compound Interactions To Predict New Emerging Synthetic Cannabinoids, Kelsey Leigh Pettus
Honors Theses
In recent years, a new class of compounds, called synthetic cannabinoids, have made their appearance in the market as a substitute for illegal marijuana or its constituent natural cannabinoids. These compounds, which are active at the same G- protein coupled receptors (GPCRS) as cannabinoids, are continuing to gain popularity because of the same cannabinoid-like effects they create. Though two cannabinoid receptors have been identified in humans, known as CB1 and CB2, synthetic cannabinoid activity at the CB1 receptor has been the focus of much research regarding synthetic cannabinoid ligand binding. In this study, the structure of the CB1 receptor is …
Conformational Analysis Of A Furan, Thiophene Alternating Π System, Laura Cline
Conformational Analysis Of A Furan, Thiophene Alternating Π System, Laura Cline
Honors Theses
Organic materials with conjugated Ï€-electron networks are increasingly being studied as an alternative to inorganic semiconductors. In order to effectively transport charge as a semiconductor, the organic materials should maintain a planar conformation, exhibit Ï€ conjugation, and be rigid to rotational interconversion. Both furan and thiophene systems have been investigated as potential organic semiconductors but difficulties with solubility, synthesis, and effectiveness hampered these efforts. A novel furan-thiophene hybrid system that exhibits promising semiconducting properties is examined here. Full geometry optimizations and corresponding harmonic vibrational frequency computations were run on a diverse set of potential furan and thiophene oligomer structures using …
The Synthesis Of Substituted Pentadentate Ligand Scaffolds And Their Future Application In Ruthenium-Catalyzed Water Oxidation, Manpreet Singh
The Synthesis Of Substituted Pentadentate Ligand Scaffolds And Their Future Application In Ruthenium-Catalyzed Water Oxidation, Manpreet Singh
Honors Theses
Rising global energy demands coupled with depleting natural resources have led to a strong emphasis on finding new sources of energy that are renewable and which limit the negative impact on the environment. One of the strongest candidates is utilizing solar energy to drive water oxidation to produce hydrogen as a fuel source. In order to do this, a better understanding of the mechanism involved in this process must be revealed. Homogenous molecular catalysts allow mechanistic studies and can be also used in Photoelectrochemical Cells (PECs) and other systems to produce chemical fuels. In this work, the new syntheses of …
The Evolution Of The Sugarcoated American Food Market And The Paradox Of Artificial Sweeteners, Mary Moses Hitt
The Evolution Of The Sugarcoated American Food Market And The Paradox Of Artificial Sweeteners, Mary Moses Hitt
Honors Theses
Living in present-day America makes it hard to imagine an era when sugar was not as inexpensive and readily available as it is now. It is in little colorful packets on restaurant tables, filled to the brim in jars at coffee shops, or mixed into candy products located at the beginning of every cash register. Today, sugar is one of, if not, the most widely consumed food products in the world, but our love for sugar is nothing new. Humans have been experiencing the bliss triggered by sweet-tasting foods since their earliest diets, which included fruits and honey. Our diets …
Paleosol Development And Trace Fossils In The Upper Triassic Cooper Canyon Formation Of The Dockum Group In Andrews County, Texas, Michael Charles Gratzer
Paleosol Development And Trace Fossils In The Upper Triassic Cooper Canyon Formation Of The Dockum Group In Andrews County, Texas, Michael Charles Gratzer
Honors Theses
It is unknown whether a relationship exists between paleosol development and the number of burrows in a paleosol. It is also unknown whether a relationship exists between the number of burrows in a paleosol and the diameters of those burrows. This paper details the methods, results, and conclusions of an investigation of these relationships. I assess the development of several paleosols in a core sample of the Upper Triassic Cooper Canyon Formation of the Dockum Group from well B-133 in Andrews County, Texas, using development scales based on methods from Bown and Kraus (1993) and Abels et al. (2013). I …
Advanced Monte Carlo Methods For The Study Of Nucleation, Troy David Loeffler
Advanced Monte Carlo Methods For The Study Of Nucleation, Troy David Loeffler
LSU Doctoral Dissertations
The process of nucleation is an essential part of understanding and controlling phase changes in a wide array of systems. In the past theories such as Classical Nucleation Theory have been used as a tool to aid experimentalist in the study of phase mechanisms. However, recent studies have shown in detail that theories such as this are not reliable, given that it can mispredict nucleation rates by several orders of magnitude. As a result newer methodologies must be developed into order to improve upon these deficiencies. In this study we use atomistic simulations to examine the non-ideal deviations from classical …
Paleolithic Protection In A Western World: A Look Into Preagricultural Nutrition As A Remedy For The Diseases Of Civilization, Emilie R. Caron
Paleolithic Protection In A Western World: A Look Into Preagricultural Nutrition As A Remedy For The Diseases Of Civilization, Emilie R. Caron
Honors Theses
The aim of this investigation is to discover the associations of the Western diet to noncommunicable diseases and to determine if a reversion to a Paleolithic diet will provide treatment and prevention of these diseases. Noncommunicable diseases, otherwise known as Diseases of Civilization, are lifestyle influenced diseases and encompass obesity, diabetes mellitus, cardiovascular disease, and associated cancers. Incidences of these diseases have skyrocketed in the past century and show no signs of decline. Since 1900, the death rates due to heart disease and cancer have risen to account for 47% of total deaths in the United States in 2010. (Tippett, …
Multidimensional Motion Capture Using Doppler Ultrasound, Forrest Nolan Gamble
Multidimensional Motion Capture Using Doppler Ultrasound, Forrest Nolan Gamble
Honors Theses
Ultrasonic waves are used to measure the velocity of a target object by measuring the Doppler shift of the reflected waves. In this work, ultrasonic Doppler Sonar (UDS) was used to measure the velocity of objects, including a pendulum and a battery on a turntable. The investigation focused on developing a method to measure motion in two and three dimensions, for applications in gait analysis and sports motion capture. By using multiple ultrasonic transducers and novel data processing techniques, the UDS captured motion in two and three dimensions. In order to test the accuracy of the velocity and position measurements, …
Single Crystal Growth And Physical Property Investigations Of Ca-Feas-Based Superconductors, Jiayun Pan
Single Crystal Growth And Physical Property Investigations Of Ca-Feas-Based Superconductors, Jiayun Pan
LSU Doctoral Dissertations
The discovery of Fe-based superconductors marked the beginning of a new era in unconventional superconductors. To date, the underlying superconducting mechanism has not yet been fully understood. Among Fe-based superconductors, the relatively new members are Ca10PtnAs8(Fe2As2)5 (n = 3, 4) and CaFeAs2. They are unique because they contain special adjacent layers, i.e., metallic Pt4As8 in Ca10Pt4As8(Fe2As2)5, semiconducting Pt3As8 in Ca10Pt3As8(Fe2As2)5, and As chains in CaFeAs2. The focus of this research is to understand the electrical and magnetic properties of Ca10PtnAs8(Fe2As2)5 (n = 3, 4) and CaFeAs2 in both the normal and superconducting state. Single crystals Ca10Pt4As8(Fe2As2)5 and Ca10Pt3As8(Fe2As2)5 with different …
Thermoelectric Properties Of Novel Layered Transition-Metal Compounds, Zhenyu Diao
Thermoelectric Properties Of Novel Layered Transition-Metal Compounds, Zhenyu Diao
LSU Doctoral Dissertations
This dissertation is designed to search for new good thermoelectric materials. Considering that both the low dimensionality and high spin entropy are in favor of thermoelectric performance, we focused on several layered transition-metal compounds including Bi2Sr2Co2O9-δ, Sr3(Ru1-xMnx)2O7, BaMn2Sb2 and Ba2Mn3Sb2O2. By investigating their structural, electrical and thermal transport, and magnetic properties, we discuss the relationship between structure, thermoelectric, and magnetic properties in these materials. For Bi2Sr2Co2O9-δ, both single crystal and thin film forms were studied. Among all films, the film grown 675 ℃ has the best power factor (S2/ρ, where S is Seebeck coefficient and ρ is electrical resistivity), which …
Hepatitis C Virus In Mexican Americans: A Population-Based Study Reveals Relatively High Prevalence And Negative Association With Diabetes, Gordon P. Watt, Kristina Vatcheva, Laura Beretta, Jen-Jung Pan, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch
Hepatitis C Virus In Mexican Americans: A Population-Based Study Reveals Relatively High Prevalence And Negative Association With Diabetes, Gordon P. Watt, Kristina Vatcheva, Laura Beretta, Jen-Jung Pan, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
This study aimed to estimate the prevalence and risk factors for hepatitis C virus (HCV) infection in Mexican Americans living in South Texas. We tested plasma for the presence of HCV antibody from the Cameron County Hispanic Cohort (CCHC), a randomized, population-based cohort in an economically disadvantaged Mexican American community on the United States/Mexico border with high rates of chronic disease. A weighted prevalence of HCV antibody of 2·3% [n = 1131, 95% confidence interval (CI) 1·2-3·4] was found. Participants with diabetes had low rates of HCV antibody (0·4%, 95% CI 0·0-0·9) and logistic regression revealed a statistically significant negative …
Regular Symmetry Patterns, Anthony W. Lin, Truong Khanh Nguyen, Philipp Rümmer, Jun Sun
Regular Symmetry Patterns, Anthony W. Lin, Truong Khanh Nguyen, Philipp Rümmer, Jun Sun
Research Collection School Of Computing and Information Systems
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework for capturing symmetry patterns in parameterised systems (i.e. an infinite family of finite-state systems): two regular word transducers to represent, respectively, parameterised systems and symmetry patterns. The framework subsumes various types of “symmetry relations” ranging from weaker notions (e.g. simulation preorders) to the strongest notion (i.e. isomorphisms). Our framework enjoys two algorithmic properties: (1) symmetry verification: given a transducer, we can automatically check whether it is a symmetry pattern of …
Data From: How Uncertainty In The Neutral Wind Limits The Accuracy Of Ionospheric Modeling And Forecasting, Michael David, Jan Sojka, Robert W. Schunk
Data From: How Uncertainty In The Neutral Wind Limits The Accuracy Of Ionospheric Modeling And Forecasting, Michael David, Jan Sojka, Robert W. Schunk
Browse all Datasets
Output files from runs of the TDIM ionospheric model used for the figures and calculations in the article in JGR Space Physics.
Novel Approaches To Investigate The Oxidation Rate Of Fe(Ii) And The Role Of Fe(Ii)/Fe(Iii) Cycling On The Maintenance Of Reactive Oxygen Species In Aquatic Systems, Justin Maurice Copeland
Novel Approaches To Investigate The Oxidation Rate Of Fe(Ii) And The Role Of Fe(Ii)/Fe(Iii) Cycling On The Maintenance Of Reactive Oxygen Species In Aquatic Systems, Justin Maurice Copeland
Theses and Dissertations
The biogeochemical cycling of iron, oxygen, and organic carbon are inextricably linked through the intermediacy of Reactive Oxygen Species (ROS) brought about by the autoxidation of ferrous iron (Fe(II)). This dissertation presents laboratory and field-based studies to investigate the kinetics of Fe(II) oxidation and its role in the production of ROS at oxic/anoxic interfaces. The net oxidation of Fe(II) in natural waters is a complex process consisting of alternating cycles of Fe(II) oxidation and Fe(III) reduction processes that are ultimately terminated via precipitation as insoluble Fe(III) (oxy)hydroxides. This complicates kinetic measurements of individual reaction steps in the process.
A critical …
Issues And Opportunities In Exotic Hadrons, R.A. Briceño, T. D. Cohen, S. Coito, J. J. Dudek, E. Eichten, R. E. Mitchell
Issues And Opportunities In Exotic Hadrons, R.A. Briceño, T. D. Cohen, S. Coito, J. J. Dudek, E. Eichten, R. E. Mitchell
Physics Faculty Publications
The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and …
Measurements Of Dⁿ² And Aⁿ¹: Probing The Neutron Spin Structure, D. Flay, M. Posik, D. S. Parno, K. Allada, M. Canan, C. Hyde, Jefferson Lab Hall A Collaboration
Measurements Of Dⁿ² And Aⁿ¹: Probing The Neutron Spin Structure, D. Flay, M. Posik, D. S. Parno, K. Allada, M. Canan, C. Hyde, Jefferson Lab Hall A Collaboration
Physics Faculty Publications
We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix element d2 of the neutron dⁿ2 was conducted. The quantity dⁿ2 represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the 3He spin structure functions, g1 and g2, after nuclear corrections had been applied to these …
Photoproduction Of Λ And Σº Hyperons Using Linearly Polarized Photons, C. A. Paterson, D. G. Ireland, K. Livingston, B. Mckinnon, D. Adikaram, M. Amaryan, Y. Prok, B. Torayev
Photoproduction Of Λ And Σº Hyperons Using Linearly Polarized Photons, C. A. Paterson, D. G. Ireland, K. Livingston, B. Mckinnon, D. Adikaram, M. Amaryan, Y. Prok, B. Torayev
Physics Faculty Publications
Background: Measurements of polarization observables for the reactions →ᵧp→K+ Λ and →ᵧp→ K+Σ0 have been performed. This is part of a program of measurements designed to study the spectrum of baryon resonances in particular, and nonperturbative QCD in general.
Purpose: The accurate measurement of several polarization observables provides tight constraints for phenomenological fits, which allow the study of strangeness in nucleon and nuclear systems. Beam-recoil observables for the →ᵧp→ K+Σ0 reaction have not been reported before now.
Method: Themeasurements were carried out using linearly polarized photon beams incident on a liquid hydrogen target, and the …
Trade-Offs Between Three Forest Ecosystem Services Across The State Of New Hampshire, Usa: Timber, Carbon, And Albedo, David A. Lutz, Elizabeth A. Burakowski, Mackenzie B. Murphy, Mark E. Borsuk
Trade-Offs Between Three Forest Ecosystem Services Across The State Of New Hampshire, Usa: Timber, Carbon, And Albedo, David A. Lutz, Elizabeth A. Burakowski, Mackenzie B. Murphy, Mark E. Borsuk
Dartmouth Scholarship
Forests are more frequently being managed to store and sequester carbon for the purposes of climate change mitigation. Generally, this practice involves long-term conservation of intact mature forests and/or reductions in the frequency and intensity of timber harvests. However, incorporating the influence of forest surface albedo often suggests that long rotation lengths may not always be optimal in mitigating climate change in forests characterized by frequent snowfall. To address this, we investigated trade-offs between three ecosystem services: carbon storage, albedo-related radiative forcing, and timber provisioning. We calculated optimal rotation length at 498 diverse Forest Inventory and Analysis forest sites in …
The Pathology Of Command And Control: A Formal Synthesis, Michael Cox
The Pathology Of Command And Control: A Formal Synthesis, Michael Cox
Dartmouth Scholarship
One of the most important theories in the study of environmental governance and policy is the pathology of command and control, which describes the negative consequences of top-down, technocratic governance of social and ecological systems. However, to date, this theory has been expressed somewhat inconsistently and informally in the literature, even by the seminal works that have established its importance and popularized it. This presents a problem for the sustainability science community if it cannot be sure of the precise details of one of its most important theories. Without such precision, applications and tests of various elements of the theory …
Anatomy, Implant Selection And Placement Influence Spine Mechanics Associated With Total Disc Replacement, Justin F.M. Hollenbeck
Anatomy, Implant Selection And Placement Influence Spine Mechanics Associated With Total Disc Replacement, Justin F.M. Hollenbeck
Electronic Theses and Dissertations
Through aging and injury, the intervertebral disc of the lumbar spine can undergo degeneration, leading to collapse of the vertebrae and low back pain, a symptom that affects half the adult population in any given year. In an effort to reduce low back pain, total disc replacement treatment removes the degenerated disc, restores natural height and lordosis of the segment, and preserves motion at the joint. Patient anatomy, implant selection, and implant placement play significant roles in a patient's outcomes after total disc replacement surgery. Thus, the objective of the work presented in this thesis was to develop a suite …
Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo
Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo
Mathematics & Statistics Faculty Publications
We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter a, and investigate the behaviors of the minimizers when the field strength is of order O (ε-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and …
The Martian Surface Radiation Environment- A Comparison Of Models And Msl/Rad Measurements, Daniel Matthiä, Bent Ehresmann, Henning Lohf, Jan Köhler, Cary Zeitlin, Jan Appel, John W. Wilson
The Martian Surface Radiation Environment- A Comparison Of Models And Msl/Rad Measurements, Daniel Matthiä, Bent Ehresmann, Henning Lohf, Jan Köhler, Cary Zeitlin, Jan Appel, John W. Wilson
Mathematics & Statistics Faculty Publications
Context: The Radiation Assessment Detector (RAD) on the Mars Science Laboratory (MSL) has been measuring the radiation environment on the surface of Mars since August 6th 2012. MSL-RAD is the first instrument to provide detailed information about charged and neutral particle spectra and dose rates on the Martian surface, and one of the primary objectives of the RAD investigation is to help improve and validate current radiation transport models.
Aims: Applying different numerical transport models with boundary conditions derived from the MSL-RAD environment the goal of this work was to both provide predictions for the particle spectra and the radiation …
Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak
Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak
Mathematics & Statistics Faculty Publications
A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated …