2-d physics and 3-d topology

Invariants of three dimensional manifolds and of framed oriented labeled links in them are rigorously defined using any solution to the Moore-Seiberg axioms for a Rational Conformal field theory. These invariants are generalizations of Witten's Chern-Simons path integrals. Connections are explored with supersymmetry, four dimensional manifolds, and quantum gravity.     

Turnover of hydrogen isotopes in lake sturgeon blood: implications for tracking movements of wild populations

Naturally occurring deuterium (²H) in biota can be used to trace movement, migration and geographic origin of a range of organisms. However, to evaluate movements of animals using δ²H measurements of tissues, it is necessary to establish the turnover time of ²H in the tissues and the extent of isotopic discrimination from different environmental ²H sources to those tissues. We investigated the turnover of ²H in lake sturgeon (Acipenser fulvescens) blood by manipulating both environmental water δ²H and diet δ²H over a four-month period. The half-life of deuterium in lake sturgeon blood was 37.9 days after an increase in the environmental water δ²H of +714?‰. However, no clear turnover in blood ²H occurred over the same period in a separate trial following a change of ?63.8?‰ or +94.2?‰ in diet. These findings suggest that environmental water ²H exchanges much faster with blood than diets and that blood δ²H values can be used to trace movements of sturgeon and other fish moving among isotopically distinct waters.     

3D sensitivity encoded ellipsoidal MR spectroscopic imaging of gliomas at 3T

Purpose

The goal of this study was to implement time efficient data acquisition and reconstruction methods for 3D magnetic resonance spectroscopic imaging (MRSI) of gliomas at a field strength of 3T using parallel imaging techniques.

Methods

The point spread functions, signal to noise ratio (SNR), spatial resolution, metabolite intensity distributions and Cho:NAA ratio of 3D ellipsoidal, 3D sensitivity encoding (SENSE) and 3D combined ellipsoidal and SENSE (e-SENSE) k-space sampling schemes were compared with conventional k-space data acquisition methods.

Results

The 3D SENSE and e-SENSE methods resulted in similar spectral patterns as the conventional MRSI methods. The Cho:NAA ratios were highly correlated (P<.05 for SENSE and P<.001 for e-SENSE) with the ellipsoidal method and all methods exhibited significantly different spectral patterns in tumor regions compared to normal appearing white matter. The geometry factors ranged between 1.2 and 1.3 for both the SENSE and e-SENSE spectra. When corrected for these factors and for differences in data acquisition times, the empirical SNRs were similar to values expected based upon theoretical grounds. The effective spatial resolution of the SENSE spectra was estimated to be same as the corresponding fully sampled k-space data, while the spectra acquired with ellipsoidal and e-SENSE k-space samplings were estimated to have a 2.36–2.47-fold loss in spatial resolution due to the differences in their point spread functions.

Conclusion

The 3D SENSE method retained the same spatial resolution as full k-space sampling but with a 4-fold reduction in scan time and an acquisition time of 9.28 min. The 3D e-SENSE method had a similar spatial resolution as the corresponding ellipsoidal sampling with a scan time of 4:36 min. Both parallel imaging methods provided clinically interpretable spectra with volumetric coverage and adequate SNR for evaluating Cho, Cr and NAA.     

Both systemic and local application of Granulocyte-colony stimulating factor (G-CSF) is neuroprotective after retinal ganglion cell axotomy

Background  

The hematopoietic Granulocyte-Colony Stimulating Factor (G-CSF) plays a crucial role in controlling the number of neutrophil progenitor cells. Its function is mediated via the G-CSF receptor, which was recently found to be expressed also in the central nervous system. In addition, G-CSF provided neuroprotection in models of neuronal cell death. Here we used the retinal ganglion cell (RGC) axotomy model to compare effects of local and systemic application of neuroprotective molecules.     

Bilayer structures in cholesteric, cyclic-siloxane liquid crystals

X-ray diffraction has been used to investigate a series of commercially available liquid crystals based on a cyclic penta(methylsiloxane) with combinations of cholesteryl-4'-allyloxybenzoate and biphenyl-4'-allyloxybenzoate mesogens pendant on the siloxane ring. A lamellar, (smectic-like) structure is indicated in the mesophase and quenched glassy solid state. Extended molecular dimensions of the mesogens generally account for the observed d spacings. The mesogens may interdigitate within lamellae but the packing and extent of interdigitation is dependent on the ratio of cholesteryl to biphenyl mesogens. There is probably also a structural contribution from the nano-aggregated (nano-phase separated), immiscible, siloxane-rich layer delineating the lamellae interfaces as this mesophase shows unusually good definition; diffraction patterns exhibit high order reflections (up to 6th order). The lamellae have a macroscopic helicoidal twist about an axis lying in the plane of the lamellae, a cholesteric supramolecular structure, which derives from the chiral, steroid mesogenic component. Surprisingly, this mesophase composed of low molar mass cyclic siloxanes may be drawn into fibres tens of metres in length, to give a morphology having the lamellae normal to the fibre axis.     

Super Riemann surfaces: Uniformization and Teichmüller theory

Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmüller space is a complex super-orbifold whose body is the ordinary Teichmüller space of the associated Riemann surfaces with spin structure. For genusg>1 it has 3g-3 complex even and 2g-2 complex odd dimensions. The super modular group which reduces super Teichmüller space to super moduli space is the ordinary modular group; there are no new discrete modular transformations in the odd directions. The boundary of super Teichmüller space contains not only super Riemann surfaces with pinched bodies, but Rogers supermanifolds having nontrivial topology in the odd dimensions as well. We also prove the uniformization theorem for super Riemann surfaces and discuss their representation by discrete supergroups of Fuchsian and Schottky type and by Beltrami differentials. Finally we present partial results for the more difficult problem of classifying super Riemann surfaces of arbitrary topology.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073).     

Numerical studies of laminar flow in ducts and pipes

In part I a method is introduced for the numerical solution of swirling axisymmetric laminar flow situations. Consideration is given to finite difference formulation, boundary condition implementation, iterative solution strategies and pressure calculation. Part II is devoted to the application of the method to non-swirling flow problems. Some of these problems are well covered in the literature whilst others are new. Swirling flows are considered in Part III. In particular, details of separation and vortex breakdown induced by swirl are discussed. All results are supplemented by a selection of contour plots to indicate the nature of the flows predicted.     

Exploring structural effects of ketone catalysts on asymmetric epoxidation of olefins

Several ketone catalysts containing spiro ethers and lactones have been investigated for the asymmetric epoxidation of olefins. The results showed that substituents on the spiro ring of the ketone catalysts have profound effects on enantioselectivity. Results also suggested that the high enantioselectivities previously observed for conjugated cis-olefins with oxazolidinone containing ketones could be partially due to attractive interactions between the R_π group of the olefin and the carbonyl group of the oxazolidinone. In addition, nonbonding interactions such as van der Waals forces and/or hydrophobic interactions between the olefin substituents and the nitrogen substituents of the oxazolidinone may also be involved in stereodifferentiation. The information gained provides additional understanding of factors important for ketone catalyzed epoxidations.     

Phase behavior of cyclic siloxane-based liquid crystalline compounds

A series of 24 cyclic siloxane-based liquid crystalline compounds was synthesized using conventional hydrosilation chemistry. Variables examined included ring size, spacer group length, and type and composition of pendant mesogeric groups. Both pentamethylhydro- and tetramethylhydrosiloxane rings were reacted with mesogens based on cholesterol, biphenyl, or equimolar mixtures of both. Four different length spacer groups containing terminal vinyl groups were used to attach the mesogens to the cyclic siloxane core. The thermotropic liquid crystalline phase behavior was studied using differential scanning calorimetry (DSC) and polarized optical microscopy (POM). A lengthening of spacer groups resulted in lower crystallization temperatures for the biphenyl-based compounds and lower glass transition temperatures for the cholesterol- and mixed mesogen-based compounds. The tetramethyl ring derivatives exhibited higher glass transition or crystallization temperatures than their pentamethyl counterparts. Biphenyl-based compounds exhibited low temperature crystalline phases while the cholesterol-based compounds exhibited low temperature glassy phases. © 1994 John Wiley & Sons, Inc.