A dynamic renormalization group study of active nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally irrelevant. We discover a special limit of parameters in which the equation of motion for the angle field bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts.

Disease burden due to Streptococcus dysgalactiae subsp equisimilis (group G and C streptococcus) is higher than that due to Streptococcus pyogenes among Mumbai school children

Streptococcus pyogenes [group A streptococcus (GAS)], a human pathogen, and Streptococcus dysgalactiae subsp. equisimilis [human group G and C streptococcus (GGS/GCS)] are evolutionarily related, share the same tissue niche in humans, exchange genetic material, share up to half of their virulence-associated genes and cause a similar spectrum of diseases. Yet, GGS/GCS is often considered as a commensal bacterium and its role in streptococcal disease burden is under-recognized. While reports of the recovery of GGS/GCS from normally sterile sites are increasing, studies describing GGS/GCS throat colonization rates relative to GAS in the same population are very few. This study was carried out in India where the burden of streptococcal diseases, including rheumatic fever and rheumatic heart disease, is high. As part of a surveillance study, throat swabs were taken from 1504 children attending 7 municipal schools in Mumbai, India, during 2006-2008. GAS and GGS/GCS were identified on the basis of beta-haemolytic activity, carbohydrate group and PYR test, and were subsequently typed. The GGS/GCS carriage rate (1166/1504, 11%) was eightfold higher than the GAS carriage (22/1504, 1.5%) rate in this population. The 166 GGS/GCS isolates collected represented 21 different emm types (molecular types), and the 22 GAS isolates represented 15 different emm types. Although the rate of pharyngitis associated with GGS/GCS is marginally lower than with GAS, high rates of throat colonization by GGS/GCS underscore its importance in the pathogenesis of pharyngitis.

Investigation of dye functional group on the photocatalytic degradation of dyes by nano-TiO2

The photocatalytic degradation of five anionic, eight cationic and three solvent dyes using combustion-synthesized nano-TiO2 (CSTiO2) and commercial Degussa P-25 TiO2 (DP-25) were evaluated to determine the effect of the functional group in the dye. The degradation of the dyes was quantified using the initial rate of decolorization and mineralization. The decolorization of the anionic dyes with CSTiO2 followed the order: indigo carmine > eosin Y > amido black 10B > alizarin cyanine green > orange G. The decolorization of the cationic dyes with DP-25 followed the order: malachite green > pyronin Y > rhodamine 6G > azure B > nile blue sulfate > auramine O approximate to acriflavine P approximate to safranin O. CSTiO2 showed higher rates of decolorization and mineralization for all the anionic dyes compared to DP-25, while DP-25 was better in terms of decolorization for most of the cationic dyes. The solvent dyes exhibited adsorption dependent decolorization. The order of decolorization and mineralization of the anionic and cationic dyes (a) with CS TiO2 and DP-25 was different and correlated with the surface properties of these catalysts (b) were rationalized with the molecular structure of the dye and the degradation pathway of the dye. (C) 2009 Elsevier B.V. All rights reserved.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Four group decodable differential scaled unitary linear space-time codes

Differential Unitary Space-Time Block codes (STBCs) offer a means to communicate on the Multiple Input Multiple Output (MIMO) channel without the need for channel knowledge at both the transmitter and the receiver. Recently Yuen-Guan-Tjhung have proposed Single-Symbol-Decodable Differential Space-Time Modulation based on Quasi-Orthogonal Designs (QODs) by replacing the original unitary criterion by a scaled unitary criterion. These codes were also shown to perform better than differential unitary STBCs from Orthogonal Designs (ODs). However the rate (as measured in complex symbols per channel use) of the codes of Yuen-Guan-Tjhung decay as the number of transmit antennas increase. In this paper, a new class of differential scaled unitary STBCs for all even number of transmit antennas is proposed. These codes have a rate of 1 complex symbols per channel use, achieve full diversity and moreover they are four-group decodable, i.e., the set of real symbols can be partitioned into four groups and decoding can be done for the symbols in each group separately. Explicit construction of multidimensional signal sets that yield full diversity for this new class of codes is also given.

Propargyloxycarbonyl as a protecting group for the side chains of serine, threonine and tyrosine

Propargyloxycarbonyl group is used as a protecting group for the hydroxyl groups of serine, threonine and tyrosine. The propargyloxycarbonyl derivatives of these hydroxy amino acids are stable to acidic and basic reagents commonly employed in peptide synthesis. The deprotection of the O-Poc derivatives using tetrathiomolybdate does not affect commonly used protecting groups such as N-Boc, N-Cbz, N-Fmoc, methyl and benzyl esters. The di-and tripeptides synthesized using O-Poc derivatives of serine, threonine and tyrosine are stable, isolable compounds and give the hydroxy peptides in good yields when treated with tetrathiomolybdate.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.