Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

Genetically engineered sensors of cell signaling

Measuring electrical activity in large numbers of cells with high spatial and temporal resolution is a fundamental problem for the study of neural development and information processing. To address this problem, we have constructed FlaSh: a novel, genetically-encoded probe that can be used to measure trans-membrane voltage in single cells. We fused a modified green fluorescent protein (GFP) into a voltage-sensitive potassium channel so that voltage dependent rearrangements in the potassium channel induce changes in the fluorescence of GFP. A voltage sensor encoded into DNA has the advantage that it may be introduced into an organism non-invasively and targeted to specific developmental stages, brain regions, cell types, and sub-cellular compartments.

We also describe modifications to FlaSh that shift its color, kinetics, and dynamic range. We used multiple green fluorescent proteins to produce variants of the FlaSh sensor that generate ratiometric signal output via fluorescence resonance energy transfer (FRET). Finally, we describe initial work toward FlaSh variants that are sensitive to G-protein coupled receptor (GPCR) activation. These sensors can be used to design functional assays for receptor activation in living cells.

The strategic behavior of rational novices

There is a growing amount of experimental evidence that suggests people often deviate from the predictions of game theory. Some scholars attempt to explain the observations by introducing errors into behavioral models. However, most of these modifications are situation dependent and do not generalize. A new theory, called the rational novice model, is introduced as an attempt to provide a general theory that takes account of erroneous behavior. The rational novice model is based on two central principals. The first is that people systematically make inaccurate guesses when they are evaluating their options in a game-like situation. The second is that people treat their decisions similar to a portfolio problem. As a result, non optimal actions in a game theoretic sense may be included in the rational novice strategy profile with positive weights.

The rational novice model can be divided into two parts: the behavioral model and the equilibrium concept. In a theoretical chapter, the mathematics of the behavioral model and the equilibrium concept are introduced. The existence of the equilibrium is established. In addition, the Nash equilibrium is shown to be a special case of the rational novice equilibrium. In another chapter, the rational novice model is applied to a voluntary contribution game. Numerical methods were used to obtain the solution. The model is estimated with data obtained from the Palfrey and Prisbrey experimental study of the voluntary contribution game. It is found that the rational novice model explains the data better than the Nash model. Although a formal statistical test was not used, pseudo R^2 analysis indicates that the rational novice model is better than a Probit model similar to the one used in the Palfrey and Prisbrey study.

The rational novice model is also applied to a first price sealed bid auction. Again, computing techniques were used to obtain a numerical solution. The data obtained from the Chen and Plott study were used to estimate the model. The rational novice model outperforms the CRRAM, the primary Nash model studied in the Chen and Plott study. However, the rational novice model is not the best amongst all models. A sophisticated rule-of-thumb, called the SOPAM, offers the best explanation of the data.

Cytokine control of neuronal phenotype

Diffusible proteins regulate neural development at a variety of stages. Using a novel neuronal culture assay, I have identified several cytokines that regulate the expression of neurotransmitters and neuropeptides in sympathetic neurons. These cytokines fall into two families. The first group is termed the neuropoietic cytokines, while including CDF/LIF, CNTF, OSM and GPA, induces expression of the same set of neuropeptide mRNAs in cultured sympathetic neurons. These four factors not only exhibit similar biological activities; they also share a predicted secondary structure and bind to a signal-transducing receptor subunit in common with IL-6 and IL-11. The latter two cytokines display a weaker activity in this assay. In addition, I find that several members of the TGF-β superfamily, activin A, BMP-2, and BMP-6, have a selective overlap with the neuropoietic family in the spectrum of neuropeptides that these cytokines induce in sympathetic neurons. Different patterns of neuropeptides induced by the TGF-β family members, however, demonstrate that the activities of these cytokines are distinct from those of the neuropoietic family. Another 30 cytokines are without detectable effect in this neuronal assay.

Activin A induces a set of neurotransmitters and neuropeptides that is somewhat similar to the phenotype of sympathetic neurons innervating sweat glands in rat footpads. In situ hybridization and RNase protection were carried out to test whether activins were involved in the phenotypic transition when sympathetic neurons contact sweat glands. I find that activin mRNA is present in both cholinergic and noradrenergic targets. Moreover, homogenates of footpads do not contain activin-like activity in the neuronal assay in vitro. Taken together, these data do not support activins as the best candidates for the sweat gland factor.

Several novel factors that regulate neuropeptide expression exist in heart cell conditioned medium. I attempted to purify these factors in collaboration with Dr. Jane Talvenheimo. Our results suggest that these factors are sensitive to the storage conditions used. Several modifications of purification strategy are discussed.

Studies of Organic Molecule Recognition by Synthetic Cyclophane Receptors in Aqueous Media

The behaviors of six new cyclophane receptors for organic guest molecules in aqueous media are reported. These new hosts are modifications of more basic parent structures, and the main goal of their examination has been to determine how the modifications affect host selectivity for cationic guests. In particular, we have been interested in determining how additional non-covalent binding interactions can complement the cation-π interactions active in the parent systems. Three types of modifications were made to these systems. Firstly, neutral methoxy and bromine substituents were added to produce four of the six new macrocycles. Secondly, two additional aromatic rings (relative to the parent host) capable of making cation-π interactions with charged guest species were appended. Thirdly, a negatively charged carboxyl group was attached to produce a cavity in which electrostatic interactions should enhance cationic guest binding. ^1H-NMR and circular dichroic techniques were employed to determine the binding affinities of a wide variety of organic guests for the parent and modified structures in aqueous media.

Bromination of the parent host greatly enhances its binding in a general fashion, primarily as the result of hydrophobic interactions. The addition of methoxy groups does not enhance binding, apparently as a result of a collapse of the hosts into a conformation that is not suitable for binding. The appendage of extra aromatic rings enhances the binding of positively charged guests, most likely in response to more complete encapsulation of guest species. The addition of a negatively charged carboxylate enhances the binding to only selective groups of cationic guests. AM1 calculations of the electrostatic potentials of several guests molecules suggests that the enhancements seen with the modified receptor compared to the parent are most likely the result of close contact between regions of highest potential on the guest and the appended carboxylate.

One-dimensional models for organic magnetic materials

In the preparation of small organic paramagnets, these structures may conceptually be divided into spin-containing units (SCs) and ferromagnetic coupling units (FCs). The synthesis and direct observation of a series of hydrocarbon tetraradicals designed to test the ferromagnetic coupling ability of m-phenylene, 1,3-cyclobutane, 1,3- cyclopentane, and 2,4-adamantane (a chair 1,3-cyclohexane) using Berson TMMs and cyclobutanediyls as SCs are described. While 1,3-cyclobutane and m-phenylene are good ferromagnetic coupling units under these conditions, the ferromagnetic coupling ability of 1,3-cyclopentane is poor, and 1,3-cyclohexane is apparently an antiferromagnetic coupling unit. In addition, this is the first report of ferromagnetic coupling between the spins of localized biradical SCs.

The poor coupling of 1,3-cyclopentane has enabled a study of the variable temperature behavior of a 1,3-cyclopentane FC-based tetraradical in its triplet state. Through fitting the observed data to the usual Boltzman statistics, we have been able to determine the separation of the ground quintet and excited triplet states. From this data, we have inferred the singlet-triplet gap in 1,3-cyclopentanediyl to be 900 cal/mol, in remarkable agreement with theoretical predictions of this number.

The ability to simulate EPR spectra has been crucial to the assignments made here. A powder EPR simulation package is described that uses the Zeeman and dipolar terms to calculate powder EPR spectra for triplet and quintet states.

Methods for characterizing paramagnetic samples by SQUID magnetometry have been developed, including robust routines for data fitting and analysis. A precursor to a potentially magnetic polymer was prepared by ring-opening metathesis polymerization (ROMP), and doped samples of this polymer were studied by magnetometry. While the present results are not positive, calculations have suggested modifications in this structure which should lead to the desired behavior.

Source listings for all computer programs are given in the appendix.

Equilibrium in dynamic economic models

The main theme running through these three chapters is that economic agents are often forced to respond to events that are not a direct result of their actions or other agents actions. The optimal response to these shocks will necessarily depend on agents' understanding of how these shocks arise. The economic environment in the first two chapters is analogous to the classic chain store game. In this setting, the addition of unintended trembles by the agents creates an environment better suited to reputation building. The third chapter considers the competitive equilibrium price dynamics in an overlapping generations environment when there are supply and demand shocks.

The first chapter is a game theoretic investigation of a reputation building game. A sequential equilibrium model, called the "error prone agents" model, is developed. In this model, agents believe that all actions are potentially subjected to an error process. Inclusion of this belief into the equilibrium calculation provides for a richer class of reputation building possibilities than when perfect implementation is assumed.

In the second chapter, maximum likelihood estimation is employed to test the consistency of this new model and other models with data from experiments run by other researchers that served as the basis for prominent papers in this field. The alternate models considered are essentially modifications to the standard sequential equilibrium. While some models perform quite well in that the nature of the modification seems to explain deviations from the sequential equilibrium quite well, the degree to which these modifications must be applied shows no consistency across different experimental designs.

The third chapter is a study of price dynamics in an overlapping generations model. It establishes the existence of a unique perfect-foresight competitive equilibrium price path in a pure exchange economy with a finite time horizon when there are arbitrarily many shocks to supply or demand. One main reason for the interest in this equilibrium is that overlapping generations environments are very fruitful for the study of price dynamics, especially in experimental settings. The perfect foresight assumption is an important place to start when examining these environments because it will produce the ex post socially efficient allocation of goods. This characteristic makes this a natural baseline to which other models of price dynamics could be compared.

The electrical and magnetic properties of amorphous Pd-Cu-P alloys

The amorphous phases of the Pd-Cu-P system has been obtained using the technique of rapidly quenching from the liquid state. Broad maxima in the diffraction pattern were obtained in the X-ray diffraction studies which are indicative of a glass-like structure. The composition range over which the amorphous solid phase is retained for the Pd-Cu-P system is (Pd_100-xCu_x)₈₀P₂₀ with 10 ≤ x ≤ 50 and (Pd₆₅Cu₃₅)_100-yP_y with 15 ≤ y ≤ 24 and (Pd₆₀Cu₄₀)_100-yP_y with 15 ≤ y ≤ 24.

The electrical resistivity for the Pd-Cu-P alloys decreases with temperature as T² at low temperatures and as T at high temperatures up to the crystallization temperature. The structural scattering model of the resistivity proposed by Sinha and the spin-fluctuation resistivity model proposed by Hasegawa are re-examined in the light of the similarity of this result to the Pt-Ni-P and Pd-Ni-P systems. Objections are raised to these interpretations of the resistivity results and an alternate model is proposed consistent with the new results on Pd-Cu-P and the observation of similar effects in crystalline transition metal alloys. The observed negative temperature coefficients of resistivity in these amorphous alloys are thus interpreted as being due to the modification of the density of states with temperature through the electron-phonon interaction. The weak Pauli paramagnetism of the Pd-Cu-P, Pt-Ni-P and Pd-Ni-P alloys is interpreted as being modifications of the transition d-states as a result of the formation of strong transition metal-metalloid bonds rather than a large transfer of electrons from the glass former atoms (P in this case) to the d-band of the transition metal in a rigid band picture.

The influence of freestream turbulence, freestream nuclei populations and a drag-reducing polymer on cavitation inception on two axisymmetric bodies

The influence upon the basic viscous flow about two axisymmetric bodies of (i) freestream turbulence level and (ii) the injection of small amounts of a drag-reducing polymer (Polyox WSR 301) into the test model boundary layer was investigated by the schlieren flow visualization technique. The changes in the type and occurrence of cavitation inception caused by the subsequent modifications in the viscous flow were studied. A nuclei counter using the holographic technique was built to monitor freestream nuclei populations and a few preliminary tests investigating the consequences of different populations on cavitation inception were carried out.

Both test models were observed to have a laminar separation over their respective test Reynolds number ranges. The separation on one test model was found to be insensitive to freestream turbulence levels of up to 3.75 percent. The second model was found to be very susceptible having its critical velocity reduced from 30 feet per second at a 0.04 percent turbulence level to 10 feet per second at a 3.75 percent turbulence level. Cavitation tests on both models at the lowest turbulence level showed the value of the incipient cavitation number and the type of cavitation were controlled by the presence of the laminar separation. Cavitation tests on the second model at 0.65 percent turbulence level showed no change in the inception index, but the appearance of the developed cavitation was altered.

The presence of Polyox in the boundary layer resulted in a cavitation suppression comparable to that found by other investigators. The elimination of the normally occurring laminar separation on these bodies by a polymer-induced instability in the laminar boundary layer was found to be responsible for the suppression of inception.

Freestream nuclei populations at test conditions were measured and it was found that if there were many freestream gas bubbles the normally present laminar separation was elminated and travelling bubble type cavitation occurred - the value of the inception index then depended upon the nuclei population. In cases where the laminar separation was present it was found that the value of the inception index was insensitive to the free stream nuclei populations.

Study of Solid-Phase Reactions of metals on GaAs

To make stable and reproducible contacts to GaAs, metals which react with GaAs in the solid-phase should be favored. In this study, contacts formed employing Pd/TiN/Pd/Ag, Pd:Mg/TiN/Pd:Mg/Ag and Ru/TiN/Ru/Ag are studied. The TiN layer is included to investigate its application as diffusion barrier in these metallizations. Contacts to n-GaAs are rectifying and the value of barrier height is modified upon annealing. Contacts to p-GaAs are initially rectifying but exhibit ohmic behaviour after annealing. The modifications in the electrical properties are attributed to the solid-phase reaction of metal and GaAs. The integrity of the contacts relies critically on the success of TiN to prevent the intermixing of Ag overlayer and the underlying layers. At elevated annealing temperatures (450°C), TiN fails to function as a diffusion barrier. As a result, the properties of the contact deteriorates.

Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.

Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.

It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.

A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.

Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.

Mechanisms of Transposable Element Repression by Piwi Proteins in the piRNA Pathway of Drosophila Germ Cells

The ability to reproduce is a defining characteristic of all living organisms. During reproduction, the integrity of genetic material transferred from one generation to the next is of utmost importance. Organisms have diverse strategies to ensure the fidelity of genomic information inherited between generations of individuals. In sexually reproducing animals, the piRNA pathway is an RNA-interference (RNAi) mechanism that protects the genomes of germ cells from the replication of ‘selfish’ genetic sequences called transposable elements (TE). When left unabated, the replication of TE sequences can cause gene disruption, double-stranded DNA breaks, and germ cell death that results in sterility of the organism. In Drosophila, the piRNA pathway is divided into a cytoplasmic and nuclear branch that involves the functions of three Piwi-clade Argonaute proteins—Piwi, Aubergine (Aub) and Argonaute-3 (Ago3)—which bind piwi-interacting RNA (piRNA) to form the effector complexes that represses deleterious TE sequences.

The work presented in this thesis examines the function and regulation of Piwi proteins in Drosophila germ cells. Chapter 1 presents an introduction to piRNA biogenesis and to the essential roles occupied by each Piwi protein in the repression of TE. We discuss the architecture and function of germ granules as the cellular compartments where much of the piRNA pathway operates. In Chapter 2, we present how Piwi in the nucleus co-transcriptionally targets genomic loci expressing TE sequences to direct the deposition of repressive chromatin marks. Chapter 3 examines the cytoplasmic function of the piRNA pathway, where we find that the protein Krimper coordinates Aub and Ago3 in the piRNA ping-pong pathway to adaptively target and destroy TE transcripts. Chapter 4 explores how interactions of Piwis with associated proteins are modulated by arginine methylation modifications. Lastly, in Chapter 5 I present evidence that the cytoplasmic branch of the piRNA pathway can potentially ‘cross-talk’ with the nuclear branch to transfer sequence information to better target and co-transcriptionally silence the genomic loci coding active TE sequences. Overall, the work presented in this thesis constitutes a part of the first steps in understanding the molecular mechanisms that protect germ cells from invasion by TE sequences.

Structural Characterization of Pro-inflammatory and Anti-inflammatory Immunoglobulin G Fc Proteins

Immunoglobulin G (IgG) is central in mediating host defense due to its ability to target and eliminate invading pathogens. The fragment antigen binding (Fab) regions are responsible for antigen recognition; however the effector responses are encoded on the Fc region of IgG. IgG Fc displays considerable glycan heterogeneity, accounting for its complex effector functions of inflammation, modulation and immune suppression. Intravenous immunoglobulin G (IVIG) is pooled serum IgG from multiple donors and is used to treat individuals with autoimmune and inflammatory disorders such as rheumatoid arthritis and Kawasaki’s disease, respectively. It contains all the subtypes of IgG (IgG1-4) and over 120 glycovariants due to variation of an Asparagine 297-linked glycan on the Fc. The species identified as the activating component of IVIG is sialylated IgG Fc. Comparisons of wild type Fc and sialylated Fc X-ray crystal structures suggests that sialylation causes an increase in conformational flexibility, which may be important for its anti-inflammatory properties.

Although glycan modifications can promote the anti-inflammatory properties of the Fc, there are amino acid substitutions that cause Fcs to initiate an enhanced immune response. Mutations in the Fc can cause up to a 100-fold increase in binding affinity to activating Fc gamma receptors located on immune cells, and have been shown to enhance antibody dependent cell-mediated cytotoxicity. This is important in developing therapeutic antibodies against cancer and infectious diseases. Structural studies of mutant Fcs in complex with activating receptors gave insight into new protein-protein interactions that lead to an enhanced binding affinity.

Together these studies show how dynamic and diverse the Fc region is and how both protein and carbohydrate modifications can alter structure, leading to IgG Fc’s switch from a pro-inflammatory to an anti-inflammatory protein.

Design of an oxygen flow meter for hospital application

A general description of the need for hospital flow meters is given along with an analysis of some common flow measurement methods.

The design criteria, establishment of the basic configuration of the instrument, and the evolution of the final design are presented in detail. The ability of the magnetic crossover mechanism to extract the square root of an input is explained, and design curves are presented. The action of the flow totalizer is described in relation to the rest of the instrument. A complete set of manufacturing drawings for the instrument and its tooling is included in the thesis.

In conclusion, an evaluation of the completed instrument is made, and improvements and modifications are indicated. Mention is made of the adaptability of the magnetic crossover mechanism to other instrumentation.

Theoretical investigation of turbulent boundary layer over a wavy surface

The important features of the two-dimensional incompressible turbulent flow over a wavy surface of wavelength comparable with the boundary layer thickness are analyzed.

A turbulent field method using model equation for turbulent shear stress similar to the scheme of Bradshaw, Ferriss and Atwell (1967) is employed with suitable modification to cover the viscous sublayer. The governing differential equations are linearized based on the small but finite amplitude to wavelength ratio. An orthogonal wavy coordinate system, accurate to the second order in the amplitude ratio, is adopted to avoid the severe restriction to the validity of linearization due to the large mean velocity gradient near the wall. Analytic solution up to the second order is obtained by using the method of matched-asymptotic-expansion based on the large Reynolds number and hence the small skin friction coefficient.

In the outer part of the layer, the perturbed flow is practically "inviscid." Solutions for the velocity, Reynolds stress and also the wall pressure distributions agree well with the experimental measurement. In the wall region where the perturbed Reynolds stress plays an important role in the process of momentum transport, only a qualitative agreement is obtained. The results also show that the nonlinear second-order effect is negligible for amplitude ratio of 0.03. The discrepancies in the detailed structure of the velocity, shear stress, and skin friction distributions near the wall suggest modifications to the model are required to describe the present problem.