Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Daniel M. Oberlin, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (June 18, 2004). Includes bibliographical references.

Parametric equations are used to represent the pathway of an object in terms of time or another changing variable. This allows, for example, for equations that are written using two variables to be examined in terms of the passage of time. In this paper the author examines two traditional application problems whose solutions can be enriched through the use of parametric equations. In the first, the falling ladder problem, a ladder is leaned against a wall then pulled away with a constant velocity. Deriving parametric equations for this scenario permits the pathway of the ladder to be plotted. Parametric equations also make it possible for the horizontal and vertical velocities of the ladder to be examined separately. The second problem is that of maximizing the length of a ladder that can fit around a hallway corner. In this problem an envelope algorithm is first developed, then parametrized to further investigate this scenario. Using these two situations, this report ultimately shows how parametric equations can be used to give a more thorough approach to some of today’s most classic calculus problems. / text

Synthesis of polycrystalline, vs. single-crystalline porous materials, such as metal-organic frameworks (MOFs), is usually beneficial due to shorter synthetic time and higher yields. However, the structural characterization of these materials by X-ray powder diffraction can be complicated. Even more difficult, is to track structural changes of MOFs by in situ experiments. Hence, we designed several successful techniques for the structural investigation of porous MOFs. These methods utilize the Structure Envelope (SE) density maps. SEs are surfaces which describing the pore system with the framework. It was shown that these maps can be easily generated from the structure factors of a few (1 to 10) of the most intense low index reflections. Application of SE in Charge Flipping calculations shortens and simplifies structure determination of MOF materials. This method provides excellent MOF models which can be used as a good starting point for their refinement. However, the most interesting results have been found by using Difference Envelope Density (DED) analysis. DED plots are made by taking the difference between observed and calculated SE densities. This allows us to study guest related issues of MOFs such as, location of guest molecules in the pores, tracking activation of MOFs and gas loading, etc. We also have shown that, DED created from routine powder diffraction patterns might provide very important information about MOF structure itself. In fact DED can be used for study of interpenetration, substituents locations and effects conformational changes in the MOF ligands. Generation and analysis of SEs and DEDs are easy and straightforward. It provides the information needed to explain major deviations in structure-property relationship in MOFs. In our opinion, this method might become one of the important and routine techniques for MOFs structural analysis.

Face à la problématique énergétique du bâtiment et l’impact environnemental lié, il apparait que les enveloppes hygroscopiques sont une piste prometteuse en termes d’amélioration du confort thermique, de qualité de l’air intérieur, de consommation énergétique et de régulation de l'humidité intérieure. Aujourd'hui, on manque de valeurs de référence du comportement hygrothermique transitoire de ce type d’enveloppes. La physique des transferts hydriques dans les matériaux hygroscopiques, aptes à fixer l’humidité, est complexe et rend difficile la modélisation des transferts couplés de chaleur et de masse. Une approche expérimentale et numérique du comportement thermo hydrique des enveloppes hygroscopiques a donc été menée avec une caractérisation multi-échelle. Ainsi, le monitoring de quatre maisons habitées a été sujet de caractérisation au niveau de la première échelle. L’étude à l'échelle du matériau a permis de caractériser les propriétés liées aux transferts de chaleur et de masse. Le couplage thermo-hydrique a fait l'objet d'une étude spécifique à l'échelle de la paroi. Les implémentations différences finies et éléments finis ont abouti à une analyse fine des transferts à l'échelle de cellules-test avec un travail de réduction d'ordre nécessaire pour limiter les temps de calcul. L’accent est mis sur les effets de l’humidité apportés dans les ambiances intérieures afin de valider un outil numérique développé dans ce travail. Les enveloppes hygroscopiques choisies sont composées de matériaux biosourcés tels que le bois massif, le béton de bois, la terre et paille. Les enveloppes de travertin et de plaques de plâtre sont également étudiées. / In front of the building energy issues and environmental impact bound, it appears that the hygroscopic envelopes are a promising track in terms of improving of the thermal comfort, indoor air quality, energy consumption and indoor humidity regulation. Today, we lack reference values of the transient hygrothermal behavior of this envelope type. The physics of moisture transfer in hygroscopic materials (capable to fixing moisture) is complex and makes it difficult modeling of coupled heat and mass transfers. Experimental and numerical approaches of hygrothermal behavior in hygroscopic envelops was therefore conducted with a multi-scale visions. Thus, monitoring of four habited houses was the characterization focus at the first scale. The study on the material scale allowed to characterize the properties related to the heat and mass transfer. The hygrothermal coupling has been the subject of a specific study at a wall scale. Finite differences and finite elements implementations have resulted in a detailed analysis of transfers across cell-test with a reduction work of order required to limit the calculation time. Emphasis is placed on the effects of moisture brought in indoor environments in order to validate a digital tool developed in this work. The selected hygroscopic envelopes are composed of biosourced materials such as massive wood, wood concrete, earth and straw. Envelopes of travertine and plasterboard are also studied.

A major design issue in the implementation of a Subsurface Drip Irrigation (SDI) system for extensively crops such as alfalfa (i.e. crops that cover the entire surface as opposed to row crops), is the determination of the appropriate depth of placement of the drip line tubing. It is important to allow necessary farming operations with heavy equipment at harvesting times while still providing adequate water to meet the crop water requirements. It is also a need to ensure appropriate spacing between the dripline laterals to assure reasonable lateral irrigation uniformity for plant germination. In this study, the program HYDRUS-2D was used to determine the wetting pattern above and laterally from a subsurface drip emitter of an SDI system, for three soils typically found in Southern California and Arizona, a Sandy Clay Loam (SCL), a Clay Loam (CL) and a Loam (L). The design and management conditions from an experimental alfalfa field with an SDI system located at Holtville CA were used and analyzed. The first irrigation design was with a drip line depth of placement of 30 cm and the second design with an installation depth of 50 cm. The two different irrigation management schemes utilized by the farmers and producers in that area were: one with a running time of six hours and a frequency of every three days and the second one with an irrigation running time of twenty-four hours with a frequency of seven days or irrigation every week. After having carried out the analysis and studies of the irrigation designs and management schemes mentioned above, a new model with its corresponding management was proposed to meet the alfalfa water requirements under that particular field and weather conditions while we ensure a sufficiently dry soil surface at harvesting time for each soil case. This irrigation management includes twelve hours or irrigation every three days, for each of the three soils analyzed. It was found that the vertical rise of water above the emitters on the day of the cut, for our recommended SDI management was 26 cm, 29 cm, and 27 cm, with a moisture content at the soil surface of 14.9%, 24%, and 13% for the SCL, CL, and L soils respectively. Then, through the utilization of classical soil mechanics theory, an analysis to calculate the increase in stress on soils at any depth due to a load on the surface from a conventional tractor used during harvest operations was made for the proposed SDI system. The results from the increase in stress were then used together with soil strength properties such as shear strength as a function of soil moisture content to determine the minimum allowable depth of placement of the drip line tubing to ensure that soil failure does not occur. The load increase from a 3,300-kg four-wheel tractor was found to be 0.59 kg/cm2 under a rear tire at 10 cm below the surface and 0.07 kg/cm2 at 70 cm below the surface. To ensure that shearing failure does not occur, a stress analysis using Mohr’s circle indicated that the soil moisture content at 10 cm below the surface should be no greater than 26.8%, 32.7%, and 27% in the SCL, CL, and L soils respectively. The mimimum moisture content of 26.8% occur at 10 cm above the drip line for a SCL soil, which means that the minimum depth placement to avoid failure would be 40 cm below the surface. A similar analysis for the CL and L yielded minimum installation depths of 35 cm and 40 cm respectively. This type of analysis is useful in determining the depth of placement of SDI drip line tubing to ensure adequate trafficability of soil irrigated with subsurface drip irrigation systems. An additional outcome of the modeling study was the determination of the lateral extent of the wetted zone which can be used to determine the appropriate lateral spacing between drip line tubing. Thus, to ensure adequate spatial coverage by a subsurface drip system, the maximum horizontal spacing should be of 80 cm for SCL and L soils and 90 cm in CL soils.

We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study is radically different from that of domains in C by discussing some examples of special types of domains in Cn , n ≥2, such that every function holomorphic on them extends to strictly larger domains. Given a domain in Cn , n ≥ 2, we wish to construct the maximal domain of existence for the holomorphic functions defined on the given domain. This leads to Thullen’s construction of a domain (not necessarily in Cn)spread overCn, the so-called envelope of holomorphy, which fulfills our criteria. Unfortunately this turns out to beavery abstract space, far from giving us sense in general howa domain sitting in Cn can be constructed which is strictly larger than the given domain and such that all the holomorphic functions defined on the given domain extend to it. But with the help of this abstract approach we can give a characterization of the domains of holomorphyin Cn , n ≥ 2. The aforementioned characterization is as follows: adomain in Cn is a domain of holomorphy if and only if it is holomorphically convex. However, holomorphic convexity is a very difficult property to check. This calls for other (equivalent) criteria for a domain in Cn , n ≥ 2, to be a domain of holomorphy. We survey these criteria. The proof of the equivalence of several of these criteria are very technical – requiring methods coming from partial differential equations. We provide those proofs that rely on the first part of our survey: namely, on analytic continuation theorems. If a domain Ω Cn , n ≥ 2, is not a domain of holomorphy, we would still like to explicitly describe a domain strictly larger than Ω to which all functions holomorphic on Ω continue analytically. Aspects of Thullen’s approach are also useful in the quest to construct an explicit strictly larger domain in Cn with the property stated above. The tool used most often in such constructions s called “Kontinuitatssatz”. It has been invoked, without a clear statement, in many works on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We provide a precise statement of this folk Kontinuitatssatz and give a proof of it.

The brightness and proximity of many classical Be stars makes them perfect laboratories for studying the physics of astrophysical disks. They are also among the most popular targets for optical/IR interferometers, which are able to fully resolve their circumstellar disks, to which much of the recent progress in our understanding of these enigmatic objects is owed. The current consensus is that classical Be stars eject material from the stellar surface into Keplerian orbits, thus forming a disk, whose subsequent evolution is governed by turbulent viscosity, which is the basis of the so-called viscous decretion disk (VDD) model. Among the main results of the present work is arguably the best-constrained model of a particular Be star β CMi. The VDD predictions were confronted also with radio observations, which allowed for the first determination of the physical extent of a Be disk. This result subsequently led to the detection of a binary companion, which is truncating the disk by tidal forces. Extending the sample to include five more targets led to revealing a similar outer disk structure in all of them. The range of explanations includes the most plausible scenario, in which the truncation of Be disks by (unseen) companions is much more common than previously thought.

This paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks. Optically thin lines from Keplerian planar disks are considered. Model line profiles are calculated for simple field topologies of axial fields (i.e., vertical to the disk plane) and toroidal fields (i.e., purely azimuthal). A scheme for discerning field strengths and geometries in disks is developed based on Stokes Q − U diagrams for the run of polarization across line profiles that are Doppler-broadened by the disk rotation. A discussion of the Hanle effect for magnetized disks in which the magnetorotational instability (MRI) is operating is also presented. Given that the MRI has a tendency to mix the vector field orientation, it may be difficult to detect the disk fields with the longitudinal Zeeman effect, since the amplitude of the circularly polarized signal scales with the net magnetic flux in the direction of the observer. The Hanle effect does not suffer from this impediment, and so a multi-line analysis could be used to constrain field strengths in disks dominated by the MRI.

In recent years, it has been shown that microlensing is a powerful tool for examining the atmospheres of stars in the Galactic bulge and Magellanic Clouds. The high gradient of magnification across the source during both small impact parameter events and caustic crossings offers a unique opportunity for determining the surface brightness profile of the source. Furthermore, models indicate that these events can also provide an appreciable polarization signal: arising from differential magnification across the otherwise symmetric source. Earlier work has addressed the signal from a scattering photosphere for both point mass lenses and caustic crossings. In a previous paper, polarimetric variations from point lensing of a circumstellar envelope were considered, as would be suitable for an extended envelope around a red giant. In this work, we examine the polarization in the context of caustic crossing events, the scenario that represents the most easily accessible situation for actually observing a polarization signal in Galactic microlensing. Furthermore, we present an analysis of the effectiveness of using the polarimetric data to determine the envelope properties, illustrating the potential of employing polarimetry in addition to photometry and spectroscopy with microlensing follow-up campaigns.

This paper examines line profile evolution due to the linear expansion of circumstellar material obsverved during a microlensing event. This work extends our previous papers on emission line profile evolution from radial and azimuthal flow during point mass lens events and fold caustic crossings. Both “flavours” of microlensing were shown to provide effective diagnostics of bulk motion in circumstellar envelopes. In this work a different genre of flow is studied, namely linear homologous expansion, for both point mass lenses and fold caustic crossings. Linear expansion is of particular relevance to the effects of microlensing on supernovae at cosmological distances. We derive line profiles and equivalent widths for the illustrative cases of pure resonance and pure recombination lines, modelled under the Sobolev approximation. The efficacy of microlensing as a diagnostic probe of the stellar environs is demonstrated and discussed