Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Systematic Construction of Linear Transform Based Full-Diversity, Rate-One Space-Time Frequency Codes

In this paper, we generalize the existing rate-one space frequency (SF) and space-time frequency (STF) code constructions. The objective of this exercise is to provide a systematic design of full-diversity STF codes with high coding gain. Under this generalization, STF codes are formulated as linear transformations of data. Conditions on these linear transforms are then derived so that the resulting STF codes achieve full diversity and high coding gain with a moderate decoding complexity. Many of these conditions involve channel parameters like delay profile (DP) and temporal correlation. When these quantities are not available at the transmitter, design of codes that exploit full diversity on channels with arbitrary DIP and temporal correlation is considered. Complete characterization of a class of such robust codes is provided and their bit error rate (BER) performance is evaluated. On the other hand, when channel DIP and temporal correlation are available at the transmitter, linear transforms are optimized to maximize the coding gain of full-diversity STF codes. BER performance of such optimized codes is shown to be better than those of existing codes.

Theoretical investigations of the two-bond proton-carbon-13 coupling constants. Angular variations of the couplings involving carboxyl carbon

A formulation has been developed using perturbation theory to evaluate the π-contribution to the nuclear spin coupling constants involving nuclei at least one of which is an unsaturated center. This fromulation accounts for the π-contribution in terms of the core polarization and one-center exchange at the π-center. The formulation developed together with the Dirac vector model and Penney-Dirac bond-order formalisms was employed to calculate the geminal (two-bond) proton coupling constants of carboxyl carbons in α-disubstituted acetic acids. The calculated coupling constants were found to have an orientational dependence. The results of the calculation are in good agreement with the experimental values.

Investigations Of Glasses In The System Pbo-Pbf2

Glass formation in the system PbO–PbF2 has been investigated. The structure of these glasses has been studied using X-ray diffraction. Densities, heat capacities, glass-transition and crystallization temperatures and Vicker's microhardnesses have been measured. D.c. conductivities of these glasses have also been measured as a function of temperature. A structural model has been developed which suggests the existence of [PbO2F4]-type units over the entire composition range. It is suggested that covalent linkages of the type—O—Pb—O— play a crucial role in determining the composition limits to glass formation. The structural model has been shown to be consistent with other physical properties of the glasses.

Investigations towards the synthesis of a CD-steroid intermediate

The development of a new synthesis of 2,6,7,7a-tetrahydro-lβ-hydroxy-4-formyl-7a-methylindene was undertaken involving the preparation of 2,6,7,7a-tetra-hydro-1β-hydroxy-4-methoxymethyl-7a-methylindene because of the erratic yield in the last oxidation step of the reported synthesis of the former compound. Although various attempts to prepare the latter were not successful, interesting rearrangement products, the dienone, 5,6,7,7a-tetrahydro-4,7a-dimethyl-5H-indene-1,5-dione and the tricyclic keto alcohol, 2,6-diketo-3-methyltricyclo(5,2,1,0)decan-8-ol, were obtained, the structures of which have been proved by spectral data. Mechanisms for the formation of these products have been proposed.

Systematic variation in bond lengths of peptides

The lengths of the carbonyl as well as of the adjacent C-N and C-C bonds in peptides are shown to vary systematically with the central C-N bond length. Results of ab initio calculations on N-methylacetamide and its Li+, Na+ and Mg2+ complexes are also discussed.

Proton NMR and infrared investigations of secondary dithiocarbamate ester: molecular conformation and vibrational assignment of S-methyl N-methyl dithiocarbamate

Rotational isomerism of S-methyl N-methyl dithiocarbamate (MMDTC) has been investigated by means of variable temperature proton NMR and i.r. spectroscopy. The i.r. spectra of MMDTC as neat, solution and at sub-ambient temperatures have been examined. Normal vibrational analysis of all the fundamentals of MMDTC has been carried out, the vibrational assignment has been compared with those of related secondary thioamides to note the consistency in the assignments and to obtain the pattern characteristic of the secondary thioamide vibrations.

Investigations of separated flow over backward facing steps in IISc hypersonic shock tunnel

Two backward facing step (2 mm and 3 mm step height) models are selected for surface heat transfer measurements. The platinum thin film gauges are deposited on the Macor inserts using both hand paint and vacuum sputtering technique. Using the Eckert reference temperature method the heating rates has been theoretically calculated along the flat plate portion of the model and the theoretical estimates are compared with experimentally determined surface heat transfer rate. Theoretical analysis of heat flux distribution down stream of the backward facing step model has been carried out using Gai’s non-dimensional analysis. Based on the measured surface heating rates on the backward facing step, the reattachment distance is estimated for 2 and 3 mm step height at nominal Mach number of 7.6. It has been found from the present study that for 2 and 3 mm step height, it approximately takes about 10 and 8 step heights downstream of the model respectively for the flow to re-attach.

Systematic search for optical Barker codes with minimum length

A method that yields optical Barker codes of smallest known lengths for given discrimination is described.

Mechanistic investigations into the photochemical oxidation of thioketones

Singlet-oxygen reaction with dialkyl, aryl alkyl, and diaryl thioketones is found to give the corresponding sulphines and ketones in proportions depending on the nature of the thioketone.

Investigations on the preparation, oxidation and reduction reactions of thiophosphoryl fluoride

Pure thiophosphoryl fluoride has been prepared by the fluorination of thiophosphoryl chloride by sodium fluoride in acetonitrile medium. Oxidation of this phosphoryl fluoride by acidified chloramine-T ruptures the phosphorus-sulphur bond and oxidises the sulphur present to the hexavalent state. Anhydrous hydrogen iodide reduces the sulphur to hydrogen sulphide and phosphorus to the trivalent state.

Mean Flow Measurements in Turbulent Boundary Layers along Mildly Curved Surfaces

An experimental investigation of the mean flow characteristics of two-dimensional turbulent boundary layers over surfaces of mild longitudinal curvature is reported. The study covered both convex and concave walls of \d/Rw I « 0.013 (d being the boundary-layer thickness and Rw being the wall radius). It was found that, whereas the region close to the wall was not affected significantly by wall curvature, the outer region was very sensitive to even mild wall curvature. A detailed study of the wake region using present and other available data suggests a systematic effect of b/Rw on the wake structure. The paper also discusses in detail the effect of mild wall curvature on the boundary-layer development with particular emphasis on the difference in behavior of the boundary layer at short and long distances from the leading edge of the curved wall, an aspect which has not received sufficient attention in previous experimental investigations. An attempt has been made to explain this behavior from a consideration of the structure of turbulence in boundary layers over curved surfaces taken into account.