Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 29).In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series defined using Gauss sums, in order to demonstrate the arithmetic content. In this paper we reexamine this connection in the particular case that was discussed in Metaplectic Forms. By looking through the scope of twisted multiplicativity, a property of L-series, the computation is simplified and more easily generalized.by Sawyer Tabony.S.M

Death, Death, I Know Thee Now!\u27 Mourning Jewelry in England and New Orleans in the Nineteenth Century

Descriptions of mourning adornments in England and New Orleans in the nineteenth century are used to argue that many of the customs of mourning in England -- the designs, themes, and materials -- also were present in New Orleans. This study draws from these observations and sources to suggest that mourning practices involving jewelry and costume became more functional and less formal in both England and New Orleans as the century progressed, while French customs retained and even grew in complexity. The high level of trade between Britain and New Orleans during the nineteenth century, reflected in the jewelry and costume of Louisiana, supports an argument that this new world city was influenced by, absorbed and incorporated social customs and activities that were useful to them, drawn from a wider range of cultures and peoples than perhaps are usually mentioned in historical accounts

Death, Death, I Know Thee Now!\u27 Mourning Jewelry in England and New Orleans in the Nineteenth Century

Descriptions of mourning adornments in England and New Orleans in the nineteenth century are used to argue that many of the customs of mourning in England -- the designs, themes, and materials -- also were present in New Orleans. This study draws from these observations and sources to suggest that mourning practices involving jewelry and costume became more functional and less formal in both England and New Orleans as the century progressed, while French customs retained and even grew in complexity. The high level of trade between Britain and New Orleans during the nineteenth century, reflected in the jewelry and costume of Louisiana, supports an argument that this new world city was influenced by, absorbed and incorporated social customs and activities that were useful to them, drawn from a wider range of cultures and peoples than perhaps are usually mentioned in historical accounts

Self-assembled aggregates in the gravitational field: growth and nematic order

The influence of the gravitational field on the reversible process of assembly and disassembly of linear aggregates is focus of this paper. Even the earth gravitational field can affect the equilibrium properties of heavy biological aggregates such as microtubules or actin filaments. The gravity gives rise to the concentration gradient which results in the distribution of aggregates of different lengths with height. Strong enough gravitational field induces the overall growth of the aggregates. The gravitational field facilitates the isotropic to nematic phase transition reflecting in a broader transition region. Coexisting phases have notedly different length distributions and the phase transition represent the interplay between the growth in the isotropic phase and the precipitation into nematic phase. The fields in an ultracentrifuge can only reinforce the effect of gravity, so the present description can be applied to a wider range of systems

Inhibitor analysis for a solar heating and cooling system

A study of potential corrosion inhibitors for the NASA solar heating and cooling system which uses aluminum solar panels is provided. Research consisted of testing using a dynamic corrosion system, along with an economic analysis of proposed corrosion inhibitors. Very good progress was made in finding a suitable inhibitor for the system

Microtubule self-organisation by reaction-diffusion processes causes collective transport and organisation of cellular particles

BACKGROUND: The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. RESULTS: Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. CONCLUSIONS: This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo

Collision induced spatial organization of microtubules

The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. First, microtubules self-organize locally in randomly oriented domains that grow and compete with each other. By imposing even a weak orientation bias, external forces like gravity or cellular boundaries may bias the domain distribution eventually leading to a macroscopic sample orientation.Comment: Submitted to Biophysical Journa

Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure