Magnetic susceptibility studies on ternary oxides of copper(II)

The magnetic susceptibilities of a large number of ternary oxides of copper having structural features common to the presently identified phases of high-temperature superconductors have been studied in the temperature range 14-300 K. The systems studied are Ln2CuOP( Ln = La, Pr, Nd, etc.), Sr2CuO2CI2,B i2Cu0,, Ca2Cu03,S r2Cu03,S rCu02, MgCu203,B a2Cu3O4CI2Y, 2Cu205,Y2BaCu0,, BaCu02, Li2Cu02, etc. Cu2+ ions take different coordinations, like isolated square planar, square pyramidal or distorted-tetrahedral and octahedral, in these compounds. These compounds also exhibit different varieties of possible magnetic superexchange interactions like 180' or 90' Cu-0-Cu or Cu-0-0-Cu types as well as direct Cu-Cu interactions. Compounds in which there are extended 180' Cu-0-Cu interactions show a low, nearly temperature-independent susceptibility (100 X lod emu/mol). The estimated value of J for the Cu-0-Cu interaction is between 800 and 1500 K in these compounds. Isolated Cu2+ ions in which there are no 180' or close to 180" Cu-0-Cu interactions show Curie-Weiss susceptibility behavior. Compounds with only Cu-0-0-Cu interaction show evidence for the onset of antiferromagnetic coupling between 30 and 50 K. The superexchange rules are useful for explaining the qualitative features of the results. The possibility of disproportionation of Cu2+ ion when there are short Cu-Cu distances as in Bi2Cu04 is discussed. The extended geometry of the copper-oxygen framework seems to be more important than the local geometry around the Cu2+ ion in determining the magnetic properties.

On BCH codes over arbitrary integer rings

Bose-C-Hocquenghem (BCH) atdes with symbols from an arbitrary fhite integer ring are derived in terms of their generator polynomials. The derivation is based on the factohation of x to the power (n) - 1 over the unit ring of an appropriate extension of the fiite integer ring. lke eomtruetion is thus shown to be similar to that for BCH codes over fink flelda.

Regenerating Codes for Distributed Storage Networks

In a storage system where individual storage nodes are prone to failure, the redundant storage of data in a distributed manner across multiple nodes is a must to ensure reliability. Reed-Solomon codes possess the reconstruction property under which the stored data can be recovered by connecting to any k of the n nodes in the network across which data is dispersed. This property can be shown to lead to vastly improved network reliability over simple replication schemes. Also of interest in such storage systems is the minimization of the repair bandwidth, i.e., the amount of data needed to be downloaded from the network in order to repair a single failed node. Reed-Solomon codes perform poorly here as they require the entire data to be downloaded. Regenerating codes are a new class of codes which minimize the repair bandwidth while retaining the reconstruction property. This paper provides an overview of regenerating codes including a discussion on the explicit construction of optimum codes.

Electron paramagnetic resonance studies of some ternary oxides of copper (II)

The electron paramagnetic resonance (EPR) of ternary oxides of Cu(II) has been studied between 4.2 and 300 K. The systems include those with 180 degrees Cu-O-Cu interactions (such as Ln2CuO4, Sr2CuO2Cl2, Sr2CuO3 and Ca2CuO3) or 90 degrees Cu-O-Cu interactions (such as Y2Cu2O5 or BaCuO2) as well as those in which the Cu2+ ions are isolated (such as Y2BaCuO5, La1.8Ba1.2Cu0.9O4.8 and Bi2CuO4). The change in the EPR susceptibility as a function of temperature is compared with that of the DC magnetic susceptibility. Compounds with extended 180 degrees Cu-O-Cu interactions which have a low susceptibility also do not give EPR signals below room temperature. For compounds such as Ca2CuO3 with one-dimensional 180 degrees Cu-O-Cu interactions a weak EPR signal is found the temperature dependence of which is very different from that of the DC susceptibility. For Y2BaCuO5 as well as for La1.8Ba1.2Cu0.9O4.8 the EPR susceptibility as well as its temperature variation are comparable with those of the static susceptibility near room temperature but very different at low temperatures. Bi2CuO4 also shows a similar behaviour. In contrast, for Y2Cu2O5, in which the copper ions have a very distorted nonsquare-planar configuration, the EPR and the static susceptibility show very similar temperature dependences. In general, compounds in which the copper ions have a square-planar geometry give no EPR signal in the ground state (0 K) while those with a distortion from square-planar geometry do give a signal. The results are analysed in the light of recent MS Xalpha calculations on CuO46- square-planar clusters with various Cu-O distances as well as distortions. It is suggested that in square-planar geometry the ground state has an unpaired electron in anionic orbitals which is EPR inactive. Competing interactions from other cations, an increase in Cu-O distance or distortions from square-planar geometry stabilise another state which has considerably more Cu 3d character. These states are EPR active. Both these states, however, are magnetic. For isolated CuO46- clusters the magnetic interactions seem to involve only the states which have mainly anionic character.

Thermal and electrical switching studies on Ge20Se80-xBix (1 <= x <= 13) ternary chalcogenide glassy system

Alternating Differential Scanning Calorimetric (ADSC) and electrical switching studies have been undertaken on Ge20Se80-xBix glasses (1 <= x <= 13), to understand the effect of topological thresholds on thermal properties and electrical switching behavior. It is found that the compositional dependence of glass transition temperature (Tg), crystallization temperature (T-c1) and thermal stability (AT) of Ge20Se80-xBix glasses show anomalies at a composition x= 5, the rigidity percolation/stiffness threshold of the system. Further, unusual variations are also observed in different thermal properties, such as T-g, T-c1, Delta T, Delta C-p and Delta H-NR, at the composition x= 10, which indicates the occurrence of chemical threshold in these glasses at this composition. Electrical switching studies indicate that Ge20Se8o_RBig glasses with 5 11 exhibit threshold switching behavior and those with x = 12 and 13 show memory switching. A sharp decrease has been noticed in the switching voltages with bismuth concentration, which is due to the more metallic nature of bismuth and the presence of Bi+ ions. Further, a saturation is seen in the decrease in V-T around x = 6, which is related to bismuth phase percolation at higher concentrations of Bi. (C) 2010 Elsevier B.V. All rights reserved.

Microstructural changes induced by ternary additions in a hypo-eutectic titanium-silicon alloy

Hypo-eutectic Ti-6.5 wt % Si alloy modified by separate additions of misch metal and low surface tension elements (Na, Sr, Se and Bi) has been examined by microscopic study and thermal analysis. Addition of third element led to modification of microstructure with apparently no significant enhancement of tensile ductility, with the exception of bismuth. Bismuth enhanced the ductility of the alloy by a factor of two and elastic-plastic fracture toughness to 9 MPa m–1/2 from a value of almost zero. The improved ductility of bismuth modified alloy is attributed to the reduced interconnectivity of the eutectic suicide, absence of significant suicide precipitation in the eutectic region and increase in the volume fraction of uniformly distributed dendrites. These changes are accompanied by a decrease in the temperature of eutectic solidification.

Quasicrystals and their crystalline homologues in the Al-Mn-Cu ternary alloys

Electron diffraction and high-resolution electron microscopy have been employed to differentiate among icosahedral, decagonal and crystalline particles that occur in as-cast and rapidly solidified Al-Mn-Cu alloys. The resemblance between decagonal quasicrystals and crystals in their electron diffraction patterns is striking. The crystalline structure is based on the orthorhombic 'Al3Mn' structure, but also a new monoclinic phase called 'X' has been discovered and described here. The present observations are also closely related to the orthorhombic structures in Al60Mn11Ni4. The occurrence of fine-scale twinning and fragmentation into domains explains the complex diffraction effects.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

Explicit and Optimal Exact-Regenerating Codes for the Minimum-Bandwidth Point in Distributed Storage

In the distributed storage setting that we consider, data is stored across n nodes in the network such that the data can be recovered by connecting to any subset of k nodes. Additionally, one can repair a failed node by connecting to any d nodes while downloading beta units of data from each. Dimakis et al. show that the repair bandwidth d beta can be considerably reduced if each node stores slightly more than the minimum required and characterize the tradeoff between the amount of storage per node and the repair bandwidth. In the exact regeneration variation, unlike the functional regeneration, the replacement for a failed node is required to store data identical to that in the failed node. This greatly reduces the complexity of system maintenance. The main result of this paper is an explicit construction of codes for all values of the system parameters at one of the two most important and extreme points of the tradeoff - the Minimum Bandwidth Regenerating point, which performs optimal exact regeneration of any failed node. A second result is a non-existence proof showing that with one possible exception, no other point on the tradeoff can be achieved for exact regeneration.

A Flexible Class of Regenerating Codes for Distributed Storage

In the distributed storage setting introduced by Dimakis et al., B units of data are stored across n nodes in the network in such a way that the data can be recovered by connecting to any k nodes. Additionally one can repair a failed node by connecting to any d nodes while downloading at most beta units of data from each node. In this paper, we introduce a flexible framework in which the data can be recovered by connecting to any number of nodes as long as the total amount of data downloaded is at least B. Similarly, regeneration of a failed node is possible if the new node connects to the network using links whose individual capacity is bounded above by beta(max) and whose sum capacity equals or exceeds a predetermined parameter gamma. In this flexible setting, we obtain the cut-set lower bound on the repair bandwidth along with a constructive proof for the existence of codes meeting this bound for all values of the parameters. An explicit code construction is provided which is optimal in certain parameter regimes.

On Network-Error Correcting Convolutional Codes under the BSC Edge Error Model

Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the performance of CNECCs under the error model of the network where the edges are assumed to be statistically independent binary symmetric channels, each with the same probability of error pe(0 <= p(e) < 0.5). We obtain bounds on the performance of such CNECCs based on a modified generating function (the transfer function) of the CNECCs. For a given network, we derive a mathematical condition on how small p(e) should be so that only single edge network-errors need to be accounted for, thus reducing the complexity of evaluating the probability of error of any CNECC. Simulations indicate that convolutional codes are required to possess different properties to achieve good performance in low p(e) and high p(e) regimes. For the low p(e) regime, convolutional codes with good distance properties show good performance. For the high p(e) regime, convolutional codes that have a good slope ( the minimum normalized cycle weight) are seen to be good. We derive a lower bound on the slope of any rate b/c convolutional code with a certain degree.

Queued Cooperative Wireless Networks With Rateless Codes

Cooperative communication using rateless codes, in which the source transmits an infinite number of parity bits to the destination until the receipt of an acknowledgment, has recently attracted considerable interest. It provides a natural and efficient mechanism for accumulating mutual information from multiple transmitting relays. We develop an analysis of queued cooperative relay systems that combines the communication-theoretic transmission aspects of cooperative communication using rateless codes over Rayleigh fading channels with the queuing-theoretic aspects associated with buffering messages at the relays. Relay cooperation combined with queuing reduces the message transmission times and also helps distribute the traffic load in the network, which improves throughput significantly.