Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Discipline
Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 137251 - 137280 of 304041

Full-Text Articles in Physical Sciences and Mathematics

Personas: A Strategy For More Inclusive And Usable Reproductive Health Tracking Technologies, Anna R. Paul Jan 2016

Personas: A Strategy For More Inclusive And Usable Reproductive Health Tracking Technologies, Anna R. Paul

Dissertations, Master's Theses and Master's Reports

In this report, I argue for the inclusion of personas in the development process of technologies that are designed to allow users to collect and track their health information. Personas provide a profile of a user and their needs, goals, and contexts. This tool can help designers to better understand their users, in order to create better, more usable end products. I examine one particular self-tracking technology, smartphone applications that allow users to record information about their menstrual cycles. Many of the most popular period tracking applications available today only meet the needs of a narrow user group, resulting in …


Influence Of The Weathered Layer On Retrieving Body Wave Using Passive Siesmic Interferometry, Boming Wu Jan 2016

Influence Of The Weathered Layer On Retrieving Body Wave Using Passive Siesmic Interferometry, Boming Wu

Dissertations, Master's Theses and Master's Reports

Passive seismic interferometry (SI) is an increasingly popular seismic method due to its cost-efficient advantage because it does not need an active source. Techniques in using SI to retrieve surface waves are relatively well established, but using SI to retrieve body waves is still under development by many authors. These geophysicists have proved that many factors, such as average duration of the natural sources, the number of natural sources that occurred during recording time, source distribution, etc., influence the quality of body waves retrieved. In this research, I focus on how to make use of the attenuation property of weathered …


Laboratory Measurements Of Contact Nucleation By Mineral Dusts, Bacteria, And Soluble Salts, Joseph Niehaus Jan 2016

Laboratory Measurements Of Contact Nucleation By Mineral Dusts, Bacteria, And Soluble Salts, Joseph Niehaus

Dissertations, Master's Theses and Master's Reports

We present results from experiments that emulate atmospheric ice nucleation by aerosols. We have refined experimental techniques to improve measurements of ice forming nuclei in the contact mode. Our results show that atmospherically relevant dusts such as kaolinite, feldspar, rhyolitic ash, and Arizona Test Dust have efficiencies in the contact mode that are higher than the immersion mode. Experiments with bacteria show that biological material has the potential to contribute significantly to ice concentrations, but has large variability. By choosing a soluble compound as an ice nucleus, we are able to place bounds on the timescale for contact freezing and …


The Effect Of Using Wlans On Data Breaches: The Examination Of The Moderating Role Of Meaningful-Use Attestation, Dheyaaldin Alsalman, Insu Park Jan 2016

The Effect Of Using Wlans On Data Breaches: The Examination Of The Moderating Role Of Meaningful-Use Attestation, Dheyaaldin Alsalman, Insu Park

Research & Publications

Organizations have increasingly deployed wireless local area networks (WLANs) due to the benefits they can have such as mobility and flexibility. Unfortunately, the usage of wireless networks has raised many security concerns due to its capability of mobility. For instance, wireless networks are susceptible to many attacks such as eavesdropping, traffic analysis, data tampering and denial of service (DoS). Our study aims to identify a variable that moderates the effect of the usage of wireless local area networks (WLANs) on the occurrence of data breaches. Therefore, we propose a model that provides a basis for identifying the impact of meaningful-use …


Mystery Of The Moon's Origin, Abubakr Hassan Jan 2016

Mystery Of The Moon's Origin, Abubakr Hassan

UNF Undergraduate Capstone Projects and Honors Theses

The dominant theory of the moon’s origin is the Giant Impact Hypothesis, which states that the moon formed when a Mars-sized object - named Theia - impacted the proto-Earth early in the solar system’s formation, with the resulting material contributing to the formation of the Moon. Using models of planetary development and the solar system’s formation, we attempt to answer where the impactor - Theia - might have originated from. We conclude that the Asteroid belt is a likely location for Theia’s formation, and we find that the parameters associated with this point of origin may help advance other models …


Predicting The Impact Of Future Climate On Ecologically Important Macroalgae, Charlie Phelps Jan 2016

Predicting The Impact Of Future Climate On Ecologically Important Macroalgae, Charlie Phelps

Theses: Doctorates and Masters

Macroalgae play an important role in coastal reef systems and are often referred to as ecosystem engineers. They serve as primary producers, supporting a diverse range of organisms, and are a sink for atmospheric CO2. Water acidification and ocean warming caused by anthropogenic activities are affecting many marine flora and fauna, potentially impacting the physical and chemical performance of macroalgae and the consumption rates of associated herbivores. Many studies have focused on ocean acidification or ocean warming individually but there is an overall lack of research investigating the combined effects and the ensuing repercussions on consumer-prey relationships.

Three species of …


Influence Of Increased Sediment Exposure On Suspension-Feeder Assemblages In A Temperate Seagrass Meadow, Pierre Bouvais Jan 2016

Influence Of Increased Sediment Exposure On Suspension-Feeder Assemblages In A Temperate Seagrass Meadow, Pierre Bouvais

Theses: Doctorates and Masters

The impact of increased sediment exposure on coastal marine ecosystems is one of the most important contemporary environmental issues. Sediment exposure is defined as the concentrations of sediment particles suspended in the water column and the amount of sediment depositing on the seabed. In addition to natural events, such as land erosion, rainfall, and tidal currents, anthropogenic activities such as land use, road building, logging, mining, port maintenance and dredging, contribute to the discharge of a great amount of sediment in the water column. As sessile suspension-feeder assemblages play a critical role in marine ecosystems through their active transfers of …


Recoverable Resources Calculation Using Non-Linear Methods: A Comparative Study, Matthew Cobb Jan 2016

Recoverable Resources Calculation Using Non-Linear Methods: A Comparative Study, Matthew Cobb

Theses: Doctorates and Masters

The prediction of recoverable resources at an operating manganese mine is currently undertaken using univariate ordinary kriging of the target variable manganese, and 5 deleterious variables. Input data densities at the time of this calculation are considerably lower than at the time of final selection (grade control), and the potential for unnacceptable conditional bias to be introduced through the use of linear geostatistical methods when determining grade estimates over a small support has led to assessment of the potential benefit of employing the local change of support methods Localised Uniform Conditioning (LUC) and Conditional Simulation (CS). Allowances for the operating …


An Evaluation Of Exposures To Respirable Particulates, Environmental Pm2.5, Pahs And Metal Compounds In Western Australia, Desmond D. Menon Jan 2016

An Evaluation Of Exposures To Respirable Particulates, Environmental Pm2.5, Pahs And Metal Compounds In Western Australia, Desmond D. Menon

Theses: Doctorates and Masters

It has been well established that air pollution is associated with health impacts. This study investigated the relationship between exposure to air pollutants and potential biomarkers of health effects. The research project was conducted in 2 separate study locations and cohorts.

Study 1: An Evaluation of Children’s Exposures to Respirable Particulates, Environmental PM2.5, PAHs and Metal Compounds in The South West of Western Australia. A cross sectional study to evaluate the exposures of children (n=18), and controls (n=15) to respirable particulates PAHs and metal compounds in the South West of Australia during 2011. Ambient particulate matter (PM2.5) samples were found …


Gene Flow And Genetic Structure Of The Seagrass Thalassia Hemprichii In The Indo-Australian Archipelago, Udhi Eko Hernawan Jan 2016

Gene Flow And Genetic Structure Of The Seagrass Thalassia Hemprichii In The Indo-Australian Archipelago, Udhi Eko Hernawan

Theses: Doctorates and Masters

How genetic variation is distributed across space (genetic structure) and what factors influence the spatial genetic structuring is one of the primary questions in population genetics. The interaction between species biology (e.g. life-history traits) and physical processes operating in the seascape over time, including palaeo-historical events (e.g. sea level fluctuations) and contemporary processes (e.g. ocean currents), have been predicted to influence the extent of gene flow and the spatial genetic structuring in marine organisms. However, the relative contribution of each factor in governing the genetic pattern remains unclear. This study examined the pattern of genetic structure and the factors influencing …


Characterization Of Completely K-Magic Regular Graphs, Arnold A. Eniego, Ian June L. Garces Jan 2016

Characterization Of Completely K-Magic Regular Graphs, Arnold A. Eniego, Ian June L. Garces

Mathematics Faculty Publications

Let k ∈ N and c ∈ Zk. A graph G is said to be c-sum k-magic if there is a labeling ` : E(G) → Zk \ {0} such that P u∈N(v) `(uv) ≡ c (mod k) for every vertex v of G, where N(v) is the neighborhood of v in G. We say that G is completely k-magic whenever it is c-sum k-magic for every c ∈ Zk. In this paper, we characterize all completely k-magic regular graphs.


Risk And Safety Of Complex Network Systems, Xiao-Bing Hu, Adrian V. Gheorghe, Mark S. Leeson, Supeng Leng, Julien Bourgeois, Xiaobo Qu Jan 2016

Risk And Safety Of Complex Network Systems, Xiao-Bing Hu, Adrian V. Gheorghe, Mark S. Leeson, Supeng Leng, Julien Bourgeois, Xiaobo Qu

Engineering Management & Systems Engineering Faculty Publications

No abstract provided.


Heuristic And Exact Algorithms For The Two-Machine Just In Time Job Shop Scheduling Problem, Mohammed Al Salem, Leonardo Bedoya-Valencia, Ghaith Rabadi Jan 2016

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 …


Energy Sustainability Of Turkey In The Case Of Lng, Omer Ilker Poyraz, Omer Keskin, Resit Unal Jan 2016

Energy Sustainability Of Turkey In The Case Of Lng, Omer Ilker Poyraz, Omer Keskin, Resit Unal

Engineering Management & Systems Engineering Faculty Publications

Energy is both vital and strategic element for a nation to sustain its fundamental activities like security, logistics, heating, etc. Countries sustain their energy demands through internal or external sources. In the case of not being able to maintain energy demands from their internal sources, they would need to import their requirements. Whenever they need to buy raw materials, they have to build terminals to process the raw material into the required form. The dependency on the imports may cause the importing country to weaken its advantage in international conflicts, unemployment, and welfare. Therefore, countries aim to mitigate dependence to …


An Improved Smote Algorithm Based On Genetic Algorithm For Imbalanced Data Collection, Qiong Gu, Xian-Ming Wang, Zhao Wu, Bing Ning, Chun-Sheng Xin Jan 2016

An Improved Smote Algorithm Based On Genetic Algorithm For Imbalanced Data Collection, Qiong Gu, Xian-Ming Wang, Zhao Wu, Bing Ning, Chun-Sheng Xin

Electrical & Computer Engineering Faculty Publications

Classification of imbalanced data has been recognized as a crucial problem in machine learning and data mining. In an imbalanced dataset, minority class instances are likely to be misclassified. When the synthetic minority over-sampling technique (SMOTE) is applied in imbalanced dataset classification, the same sampling rate is set for all samples of the minority class in the process of synthesizing new samples, this scenario involves blindness. To overcome this problem, an improved SMOTE algorithm based on genetic algorithm (GA), namely, GASMOTE was proposed. First, GASMOTE set different sampling rates for different minority class samples. A combination of the sampling rates …


Microscopic Study Of Structure, Chemical Composition And Local Conductivity Of La2/3sr1/3mno3 Films, Lina Chen Jan 2016

Microscopic Study Of Structure, Chemical Composition And Local Conductivity Of La2/3sr1/3mno3 Films, Lina Chen

LSU Doctoral Dissertations

The colossal magnetoresistance (CMR) manganites have attracted intensive study due to their richness of underlying physics and potential technological applications. Of particular interest is half-metallic La2/3Sr1/3MnO3 (LSMO) because it possesses the highest known Curie temperature of the group ~ 370 K), which makes it a promising candidate for room temperature spintronic applications. On the other hand, LSMO ultrathin films exhibit a metal-insulator transition (MIT) when reducing film thickness. The origin of such a thickness-dependent MIT remains highly controversial, though understanding and controlling this kind of behavior is necessary for any possible device applications. An essential first step then, and the …


The Role Of Upper Ocean Heat Content And Sea Surface Temperature On Northeast Pacific Hurricane Evolution During Average And Active Years, Victoria Lauren Ford Jan 2016

The Role Of Upper Ocean Heat Content And Sea Surface Temperature On Northeast Pacific Hurricane Evolution During Average And Active Years, Victoria Lauren Ford

LSU Master's Theses

Upon comparison to typical neutral-ENSO conditions in the Northeast Pacific Ocean, the 2014 hurricane season has been identified as highly anomalous in both tropical cyclone frequency and intensity. This thesis seeks to investigate the influence of sea surface temperatures (SSTs) and upper ocean heat content (UOHC), defined as the excess of heat present above 26°C, upon the upper ocean thermal structure, mesoscale features, and anomalies that led to an active hurricane season in the Northeast Pacific. The 2012 Northeast Pacific hurricane season was selected as a ‘normal’ season to fully quantify the anomalous 2014 hurricane season. Data sets utilized in …


Investigating Species And Population Level Foraging Variation And Individual Specialization In Pygoscelis Penguins Using Stable Isotope Analysis, Rachael W. Herman Jan 2016

Investigating Species And Population Level Foraging Variation And Individual Specialization In Pygoscelis Penguins Using Stable Isotope Analysis, Rachael W. Herman

LSU Master's Theses

Gentoo Penguins (Pygoscelis papua) are known to be generalist foragers, while Adélie (P. adeliae) and Chinstrap (P. Antarctica) tend to specialize on krill within the Western Antarctic Peninsula and South Shetland Islands, particularly during the breeding season. However, little is known on temporal consistency in diet and foraging habitat of these species, particularly at the individual level. We used stable isotope analysis (SIA) of blood and feathers to evaluate seasonal and individual foraging consistency within Adélie, Chinstrap and Gentoo Penguins breeding in the South Shetland Islands, as well as among three Gentoo Penguins’ populations in the Western Antarctic Peninsula and …


Garbage Collection For General Graphs, Hari Krishnan Jan 2016

Garbage Collection For General Graphs, Hari Krishnan

LSU Doctoral Dissertations

Garbage collection is moving from being a utility to a requirement of every modern programming language. With multi-core and distributed systems, most programs written recently are heavily multi-threaded and distributed. Distributed and multi-threaded programs are called concurrent programs. Manual memory management is cumbersome and difficult in concurrent programs. Concurrent programming is characterized by multiple independent processes/threads, communication between processes/threads, and uncertainty in the order of concurrent operations. The uncertainty in the order of operations makes manual memory management of concurrent programs difficult. A popular alternative to garbage collection in concurrent programs is to use smart pointers. Smart pointers can collect …


Time-Lapse Polymerizations Triggered By Ph Clock Reactions, Elizabeth Jee Jan 2016

Time-Lapse Polymerizations Triggered By Ph Clock Reactions, Elizabeth Jee

LSU Doctoral Dissertations

The theme of this work is time-lapse polymerizations triggered by pH clock reactions. The first chapter is the introduction and gives a long overview of the different chemistries studied here. The second chapter focuses on the bromate-sulfite clock reaction. Based on some simplified and accepted reaction equations for the bromate-sulfite clock. We presumed it may be possible to increase the pH of the solution via ammonia addition and hinder or significantly reduce the reactivity of the clock reagents, thus creating a storage stable reaction. Adding a polymer system that would not crosslink until the solution became acidic would have created …


Derived Geometric Satake Equivalence, Springer Correspondence, And Small Representations, Jacob Paul Matherne Jan 2016

Derived Geometric Satake Equivalence, Springer Correspondence, And Small Representations, Jacob Paul Matherne

LSU Doctoral Dissertations

It is known that the geometric Satake equivalence is intimately related to the Springer correspondence when restricting to small representations of the Langlands dual group (see a paper by Achar and Henderson and one by Achar, Henderson, and Riche). This dissertation relates the derived geometric Satake equivalence of Bezrukavnikov and Finkelberg and the derived Springer correspondence of Rider when we restrict to small representations of the Langlands dual group under consideration. The main theorem of the before-mentioned paper of Achar, Henderson, and Riche sits inside this derived relationship as its degree zero piece.


Small-Scale Biogeographic Patterns Of Benthic Bacterial And Ciliate Communities In The Saline Ponds Of Lake Macleod, North-Western Australia, Christopher Kavazos Jan 2016

Small-Scale Biogeographic Patterns Of Benthic Bacterial And Ciliate Communities In The Saline Ponds Of Lake Macleod, North-Western Australia, Christopher Kavazos

Theses: Doctorates and Masters

This biogeographical thesis tests for the presence of taxa-area and distance-decay relationships, which are common among macrobionts, in prokaryotic (bacterial) and micro-eukaryotic (ciliate) communities. Microbial biogeographical patterns may be distinct because of the high abundances, diversity and dispersal capabilities of microbes, in comparison to macrobionts. The Northern Ponds of Lake MacLeod, north-western Australia, provide an ideal location to address this topic, because the ponds are effectively hydrogeomorphologically identical, other than in surface area, and biotic histories can be assumed to differ only according to distance of separation. This means that hypotheses concerning species-sorting and neutral processes on microbial assemblages can …


Impacts Of Artisanal And Large Scale Gold Mining On Tropical Rivers In West Africa: A Case Study From The Brong Ahafo Region Of Ghana, Karunia F. Macdonald Jan 2016

Impacts Of Artisanal And Large Scale Gold Mining On Tropical Rivers In West Africa: A Case Study From The Brong Ahafo Region Of Ghana, Karunia F. Macdonald

Theses: Doctorates and Masters

Mining communities in more than 70 developing countries, mostly in the tropical regions, still practise artisanal and small scale gold mining (ASGM). ASGM commonly operates along rivers and streams for easy access to process water and as receptacles for mine water discharges. A largely unregulated industry, ASGM employs rudimentary mining and processing methods including the use of mercury amalgamation, and is often found near to larger scale and modern mining (LSM) operations.

The substantial use of mercury by ASGM has drawn the attention of agencies and researchers but so has its persistent economic role in providing much needed rural employment. …


Measurement Of The Yb I 1S0-1P1 Transition Frequency At 399 Nm Using An Optical Frequency Comb, Michaela Kleinert, M. E. Gold Dahl, Scott D. Bergeson Jan 2016

Measurement Of The Yb I 1S0-1P1 Transition Frequency At 399 Nm Using An Optical Frequency Comb, Michaela Kleinert, M. E. Gold Dahl, Scott D. Bergeson

Faculty Publications

We determine the frequency of the Yb I 1S0-1P1 transition at 399 nm using an optical frequency comb. Although this transition was measured previously using an optical transfer cavity [D. Das et al., Phys, Rev. A 72, 032506 (2005)], recent work has uncovered significant errors in that method. We compare our result of 751 526 533.49 ± 0.33 MHz for the 174Yb isotope with those from the literature and discuss observed differences. We verify the correctness of our method by measuring the frequencies of well-known transitions in Rb and Cs, and by …


River Report. State Of The Lower St. Johns River Basin, Florida: Water Quality, Fisheries, Aquatic Life, Contaminants, 2016, Environmental Protection Board, City Of Jacksonville, University Of North Florida, Jacksonville University, Gerry Pinto, Nisse Goldberg, Radha Pyati, Peter Bacopoulos, Anthony Ouellette, Gretchen Bielmyer-Fraser, An-Phong Le, Ray Oldakowski Jan 2016

River Report. State Of The Lower St. Johns River Basin, Florida: Water Quality, Fisheries, Aquatic Life, Contaminants, 2016, Environmental Protection Board, City Of Jacksonville, University Of North Florida, Jacksonville University, Gerry Pinto, Nisse Goldberg, Radha Pyati, Peter Bacopoulos, Anthony Ouellette, Gretchen Bielmyer-Fraser, An-Phong Le, Ray Oldakowski

State of the River Report

No abstract provided.


Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak Jan 2016

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 …


Secondary Flow Of Liquid-Liquid Two-Phase Fluids In A Pipe Bend, M. Ayala, P. Santos, G. Hamester, O. Ayala Jan 2016

Secondary Flow Of Liquid-Liquid Two-Phase Fluids In A Pipe Bend, M. Ayala, P. Santos, G. Hamester, O. Ayala

Engineering Technology Faculty Publications

A simulated study of oil and water in 90 degree bend was carried on COMSOL 5.1 to characterize flow pattern and analyze the secondary flow. The Euler-Euler k-e Reynolds Averaged Navier-Stokes model was used to represent the fluid motion. Changes in the Reynolds number, curvature ratio and direction of gravity were made to evaluate the effects in the intensity of the secondary flow. In the end, it was possible to see that the bend direction does not affect the formation of secondary flow for Reynolds above 100,000. It appears that the fluid behavior on the pipe bend is strongly related …


Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu Jan 2016

Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu

Mathematics & Statistics Faculty Publications

We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 …


The Reconfigurable Machinery Efficient Workspace Analysis Based On The Twist Angles, Ana M. Djuric, Vukica Jovanovic, Mirjana Filipovic, Ljubinko Kevac Jan 2016

The Reconfigurable Machinery Efficient Workspace Analysis Based On The Twist Angles, Ana M. Djuric, Vukica Jovanovic, Mirjana Filipovic, Ljubinko Kevac

Engineering Technology Faculty Publications

A novel methodology for the calculation, visualisation and analysis of the Reconfigurable Machinery Efficient Workspace (RMEW), based on the twist angles, is presented in this paper. The machinery's kinematic parameters are used for calculating the workspace, while the efficient workspace is associated with the machinery's path and includes the end-effector position and orientation. To analyse and visualise many different machinery efficient workspaces at the same time, the calculation is based on the previously developed and validated complex reconfigurable machinery's kinematic structure named n-DOF Global Kinematic Model (n-GKM). An industrial robot is used as an example to demonstrate …


Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo Jan 2016

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 …