Apparent thermalization due to plasma instabilities in the quark-gluon plasma

Hydrodynamical modeling of heavy-ion collisions at RHIC suggests that the quark-gluon plasma (QGP) "thermalizes" in a remarkably short time scale, about 0.6 fm/c. We argue that this should be viewed as indicating fast isotropization, but not necessarily complete thermalization, of the nonequilibrium QGP. Non-Abelian plasma instabilities can drive local isotropization of an anisotropic QGP on a time scale which is faster than ordinary perturbative scattering processes. As a result, we argue that theoretical expectations based on weak-coupling analysis are not necessarily in conflict with hydrodynamic modeling of the early part of RHIC collisions, provided one recognizes the key role of non-Abelian plasma instabilities.     

Mid-infrared electric field characterization using a visible charge-coupled-device-based spectrometer

We characterize ultrashort mid-infrared pulses through upconversion by using the stretched pulses obtained from the uncompressed output of a chirped-pulse amplifier. The power spectrum thus translated into the visible region can be readily measured with a standard silicon CCD camera-based spectrometer. The spectral phase is also characterized by a variant of zero-added-phase spectral phase interferometry for direct electric field reconstruction. This is a general method that provides a multiplex advantage over conventional infrared detector array-based methods.     

Efficient chemoenzymatic synthesis of ADP-D-glycero-beta-D-manno-heptose and a mechanistic study of ADP-L-glycero-D-manno-heptose 6-epimerase

[reaction: see text] A chemoenzymatic synthesis of ADP-D-glycero-beta-D-manno-heptose (ADP-D,D-Hep) is described in which D,D-Hep 7-phosphate is converted to ADP-D,D-Hep by two biosynthetic enzymes. This strategy allows access to the 6'-deuterated analogue, which upon incubation with the epimerase showed complete retention of the isotopic label at the 6'-position. This provides evidence for a direct oxidation mechanism in which the hydride initially transferred to the NADP+ cofactor is subsequently returned to the same carbon in a nonstereospecific manner.     

Melvin Models and Diophantine Approximation

Melvin models with irrational twist parameter provide an interesting example of conformal field theories with non-compact target space, and localized states which are arbitrarily close to being delocalized. We study the torus partition sum of these models, focusing on the properties of the regularized dimension of the space of localized states. We show that its behavior is related to interesting arithmetic properties of the twist parameter , such as the Lyapunov exponent. Moreover, for in a set of measure one the regularized dimension is in fact not a well-defined number but must be considered as a random variable in a probability distribution.     

Synthesis and characterization of monodendrons based on 9-phenylcarbazole

A series of 9-phenylcarbazole ethynylene monodenrons have been prepared by palladium-catalyzed coupling reactions creating well-organized arrays of redox centers. The tert-butyl groups attached to the 3,6-positions of peripheral 9-phenylcarbazole monomers provide adequate solubility to a limited degree. Trimer and 7-mer monodendrons were prepared using a monomer with 3, 3-diethyltriazene at its focal point. To facilitate purification, the synthesis of 15-mer monodendron, however, required a monomer bearing a 3-hydroxy-3-methyl-but-1-ynyl group at its focal point as a masking group for the terminal acetylene functionality. Although the solubility was limited, high generation monodendrons were found to be readily soluble in carbon disulfide, a solvent of high polarizability. Spectroscopic studies showed that there is limited through-bond conjugation over the monodendrons, but fluorescence studies suggested the presence of long-range through-space interactions in the higher members of the series.     

Decomposition of 2-(1-hydroxybenzyl)thiamin. Ruling out stepwise cationic fragmentation

[reaction: see text] The rapid fragmentation of 2-(1-hydroxybenzyl)thiamin (1) is initiated by transfer of a proton from C2alpha to give an enamine. The subsequent irreversible process can be written as a concerted (or stepwise) rearrangement involving migration of the hydroxyl hydrogen to the methylene bridge. An attractive alternative is internal addition of C2alpha to the pyrimidine, generating a carbocation. However, addition of azide to the reaction solution, which could trap the carbocation, has no effect on the rate or products of reaction.     

Synthesis of cryptophycin 52 using the sharpless asymmetric dihydroxylation: diol to epoxide transformation optimized for a base-sensitive substrate

A synthesis of cryptophycin 52 (2) is reported using a Sharpless asymmetric dihydroxylation (AD) strategy to install the epoxide moiety. The high stereoselectivity of the AD reaction that allows for an efficient means of preparing the epoxide is in contrast to the standard direct epoxidation of cryptophycin substrates, which proceeds with poor diastereoselectivity. Methodology for conversion of the diol AD product to the requisite epoxide is disclosed. The transformation has been optimized to proceed in high yield in the presence of base sensitive functionality.     

Linear equations in subspaces of operators

Given a subspace of operators on a Hilbert space, and given two operators and (not necessarily in ), when can we be certain that there is an operator in such that ? If there is one, can we find some bound for its norm? These questions are the subject of a number of papers, some by the present authors, and mostly restricted to the case where is a reflexive algebra. In this paper, we relate the broader question involving operator subspaces to the question about reflexive algebras, and we examine a new method of forming counterexamples, which simplifies certain constructions and answers an unresolved question. In particular, there is a simple set of conditions that are necessary for the existence of a solution in the reflexive algebra case; we show that -- even in the case where the co-rank of is one-these conditions are not in general sufficient.