Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d >= 2k - 2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n = d + 1, k, d >= 2k - 1].

Insulating State and Breakdown of Fermi Liquid Description in Molecular-Scale Single-Crystalline Wires of Gold

Electrical transport measurements on ultrathin single-crystalline Au nanowires, synthesized via a wet chemical route, show an unexpected insulating behavior. The linear response electrical resistance exhibits a power-law dependence on temperature. In addition, the variation of current over a wide range of temperature and voltage obeys a universal scaling relation that provides compelling evidence for a non-Fermi liquid behavior. Our results demonstrate that the quantum ground state In ultrathin nanowires of simple metallic systems can be radically different from their bulk counterparts and can be described In terms of a Tomonaga-Luttinger liquid (TLL), in the presence of remarkably strong electron-electron interactions.

Atomic Scale Fluctuations Govern Brittle Fracture and Cavitation Behavior in Metallic Glasses

We perform atomistic simulations on the fracture behavior of two typical metallic glasses, one brittle (FeP) and the other ductile (CuZr), and show that brittle fracture in the FeP glass is governed by an intrinsic cavitation mechanism near crack tips in contrast to extensive shear banding in the ductile CuZr glass. We show that a high degree of atomic scale spatial fluctuations in the local properties is the main reason for the observed cavitation behavior in the brittle metallic glass. Our study corroborates with recent experimental observations of nanoscale cavity nucleation found on the brittle fracture surfaces of metallic glasses and provides important insights into the root cause of the ductile versus brittle behavior in such materials.

On the athermal nature of the beta to omega transformation

One characteristic feature of the athermal beta -> omega transformation is the short time scale of the transformation. So far, no clear understanding of this issue exists. Here we construct a model that includes contributions from a Landau sixth-order free energy density, kinetic energy due to displacement, and the Rayleigh dissipation function to account for the dissipation arising from the rapid movement of the parent product interface during rapid nucleation. We also include the contribution from omega-like fluctuations to local stress. The model shows that the transformation is complete on a time scale comparable to the velocity of sound. The estimated nucleation rate is several orders higher than that for diffusion-controlled transformations. The model predicts that the athermal omega phase is limited to a certain range of alloying composition. The estimated nucleation rate and the size of ``isothermal'' particles beyond 17% Nb are also consistent with experimental results. The model provides an explanation for the reprecipitation process of the omega particles in the ``cleared'' channels formed during deformation of omega-forming alloys. The model also predicts that acoustic emission should be detectable during the formation of the athermal phase. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory

This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier's method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

Multi-scale interactions and predictability of the Indian summer monsoon

Following the seminal work of Charney and Shukla (198 1), the tropical climate is recognised to be more predictable than extra tropical climate as it is largely forced by 'external' slowly varying forcing and less sensitive to initial conditions. However, the Indian summer monsoon is an exception within the tropics where 'internal' low frequency (LF) oscillations seem to make significant contribution to its interannual variability (IAV) and makes it sensitive to initial conditions. Quantitative estimate of contribution of 'internal' dynamics to IAV of Indian monsoon is made using long experiments with an atmospheric general circulation model (AGCM) and through analysis of long daily observations. Both AGCM experiments and observations indicate that more than 50% of IAV of the monsoon is contributed by 'internal' dynamics making the predictable signal (external component) burried in unpredictable noise (internal component) of comparable amplitude. Better understanding of the nature of the 'internal' LF variability is crucial for any improvement in predicition of seasonal mean monsoon. Nature of 'internal' LF variability of the monsoon and mechanism responsible for it are investigated and shown that vigorous monsoon intraseasonal oscillations (ISO's) with time scale between 10-70 days are primarily responsible for generating the 'internal' IAV. The monsoon ISO's do this through scale interactions with synoptic disturbances (1-7 day time scale) on one hand and the annual cycle on the other. The spatial structure of the monsoon ISO's is similar to that of the seasonal mean. It is shown that frequency of occurance of strong (weak) phases of the ISO is different in different seasons giving rise to stronger (weaker) than normal monsoon. Change in the large scale circulation during strong (weak) phases of the ISO make it favourable (inhibiting) for cyclogenesis and gives rise to space time clustering of synoptic activity. This process leads to enhanced (reduced) rainfall in seasons of higher frequency of occurence strong (weak) phases of monsoon ISO.

On the role of cloud adjustment time scale in simulating precipitation with Relaxed Arakawa-Schubert convection scheme

The precipitation by Relaxed Arakawa-Schubert cumulus parameterization in a General Circulation Model (GCM) is sensitive to the choice of relaxation parameter or specified cloud adjustment time scale. In the present study, we examine sensitivity of simulated precipitation to the choice of cloud adjustment time scale (tau(adj)) over different parts of the tropics using National Center for Environmental Prediction (NCEP) Seasonal Forecast Model (SFM) during June-September. The results show that a single specified value of tau(adj) performs best only over a particular region and different values are preferred over different parts of the world. To find a relation between tau(adj) and cloud depth (convective activity) we choose six regions over the tropics. Based on the observed relation between outgoing long-wave radiation and tau(adj), we propose a linear cloud-type dependent relaxation parameter to be used in the model. The simulations over most parts of the tropics show improved results due to this newly formulated cloud-type dependent relaxation parameter.

Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale

We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If the sphere diameter is larger than a threshold value, the settling velocity shows repeated short oscillatory bursts separated by long periods of relative quiescence. We propose a model incorporating the interplay of settling-induced flow, viscoelastic stress and, as in M. E. Cates, D. A. Head and A. Ajdari, Phys. Rev. E, 2002, 66, 025202(R) and A. Aradian and M. E. Cates, Phys. Rev. E, 2006, 73, 041508, a slow structural variable for which our experiments offer independent evidence.