Collective Coordinate Action for Charged Sigma-Model Vortices in Finite Geometries

In this Letter the method of Lund is applied to formulate a variational principle for the motion of charged vortices in an effective non-linear Schr\"{o}dinger field theory describing finite size two-dimensional quantum Hall samples under the influence of an arbitrary perpendicular magnetic field. Freezing out variations in the modulus of the effective field yields a $U(1)$ sigma-model. A duality transformation on the sigma-model reduces the problem to finding the Green function for a related electrostatics problem. This duality illuminates the plasma analogy to the Laughlin wave function.Comment: 7 pp., Plain TeX (macros included), MAD/TH-92-0

On zeros of Martin-L\"of random Brownian motion

We investigate the sample path properties of Martin-L\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\"of random Brownian path, (2) that the effective dimension of zeroes of a Martin-L\"of random Brownian path must be at least 1/2, and conversely that every real with effective dimension greater than 1/2 must be a zero of some Martin-L\"of random Brownian path, and (3) we will demonstrate a new proof that the solution to the Dirichlet problem in the plane is computable

Charged Vortex Dynamics in Ginzburg-Landau Theory of the Fractional Quantum Hall Effect

We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.Comment: 28 pages + 1 Figure, new phyzzx macro (included), MAD/TH-92-0

Hydromechanics of low-Reynolds-number flow. Part 4. Translation of spheroids

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio at low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, R[sub]b = Ub/v, and the other on the semi-major axis a, R[sub]a = Ua/v (U being the free-stream velocity at infinity, which is perpendicular to the major axis of the spheroid, and v the kinematic viscosity of the fluid). A drag formula is obtained for small values of R[sub]b and arbitrary values of R[sub]a. When R[sub]a is also small, the present drag formula reduces to the Oberbeck (1876) result for Stokes flow past a spheroid, and it gives the Oseen (1910) drag for an infinitely long cylinder when R[sub]a tends to infinity. This result thus provides a clear physical picture and explanation of the 'Stokes paradox' known in viscous flow theory

Greedy quasigroups and combinatorial games

Greedy quasigroups arose out of a desire to better understand certain combinatorial games. In this paper, I will discuss some basis combinatorial game theory to provide motivation and quasigroup theory as background information. Greedy quasigroups have remarkable algebraic properties. In particular, I will answer the question of the existence of subquasigroups and isomorphism classes of greedy quasigroups

Synthesis of Deoxy-glucosamine as a Possible Antibacterial Agent

An antibacterial agent is a substance which destroys or suppresses bacterial growth or reproduction. The discovery of the antibacterial properties of the sulfonamides in 1935 by Gerhard Domagk began one of the brightest eras in modern anti-bacterial chemotherapy. These drugs have remained useful as antibacterial agents but the introduction of the antibiotics, particularly penicillin, has made the sulfonamides less popular. However, the sulfonamides are effective and are still used today. Antibacterial agents are not characterized by one chemical grouping or a particular mode of action. Phenols and alcohols, for example, act by denaturing protein. Others such as arsenic and the heavy metals exert their effect by reaction with the sulfhydryl grouping present as the active portion of certain enzymes. The sulfonamides interfere with the utilization of p-aminobenzoic acid in bacteria. The antibiotics including penicillin, cycloserine, vancomycin, and cephalothin inhibit the normal build-up of the cell wall in bacteria. The penicillin are of interest as the mechanism of action is directly related to the objective of this work. The proposed compound would theoretically interfere with the cell wall build-up since it does not have a binding site which is necessary for normal cell wall formation. However, the compound synthesized should be similar enough structurally to the normal precursors to be taken up by the same enzymes involved in the biosynthesis of the cell wall

Macronuclear persistence of sequences normally eliminated during development in Tetrahymena thermophila

During conjugation in the ciliated protozoan, Tetrahymena thermophila , a somatic MAC-ronucleus develops from the germinal MICronucleus. Ten to 20 percent of the MIC genome is eliminated during this process. Three repetitive families have been identified which have different levels of repetition in the MIC and are eliminated to different degrees in the MAC. Some members of two of these families persist in the MAC. In this study, we have looked at these persistent sequences in the MAC of cell lines from a variety of sources including several inbed strains, two sets of caryonides, caryonidal subclones, and vegetatively aged cell clones. The results suggest that the sequences that remain in the MAC have a genetic predisposition to persist. However, epigenetic variations occur as the MAC develops so that only some of the persistent sequences are actually observed in a particular MAC. Polymorphisms may be generated if alternative processing of a single MIC segment occurs. These polymorphisms can later be resolved by phenotypic assortment during vegetative growth. These facultatively persistent sequences appear to differ from sequences previously described in this organism.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50176/1/1020060205_ftp.pd

Teaching Doppler Ultrasound in an Introductory Laboratory for Pre-health Students

We present a novel activity to demonstrate the Doppler shift of a sound wave, incident at an angle, upon a moving reflector. This activity is intended for use in an introductory physics laboratory focused on preparing students for the health and medical fields. The activity is designed to simulate Doppler velocity measurements from ultrasound imaging. While there have been previous qualitative discussions of blood flow measurements in the physics education literature, they were without associated laboratory activities.1 The lab can be part of a life science physics curriculum that has been identified in need of reforms to meet the needs of students and the medical and biology community