On t-designs and bounds relating query complexity to error resilience in locally correctable codes

An n-length block code C is said to be r-query locally correctable, if for any codeword x ∈ C, one can probabilistically recover any one of the n coordinates of the codeword x by querying at most r coordinates of a possibly corrupted version of x. It is known that linear codes whose duals contain 2-designs are locally correctable. In this article, we consider linear codes whose duals contain t-designs for larger t. It is shown here that for such codes, for a given number of queries r, under linear decoding, one can, in general, handle a larger number of corrupted bits. We exhibit to our knowledge, for the first time, a finite length code, whose dual contains 4-designs, which can tolerate a fraction of up to 0.567/r corrupted symbols as against a maximum of 0.5/r in prior constructions. We also present an upper bound that shows that 0.567 is the best possible for this code length and query complexity over this symbol alphabet thereby establishing optimality of this code in this respect. A second result in the article is a finite-length bound which relates the number of queries r and the fraction of errors that can be tolerated, for a locally correctable code that employs a randomized algorithm in which each instance of the algorithm involves t-error correction.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.

Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

A Doubly curved Quadrilateral finite-element for the analysis of laminated anisotropic thin shells of revoution

The details of development of the stiffness matrix for a doubly curved quadrilateral element suited for static and dynamic analysis of laminated anisotropic thin shells of revolution are reported. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first order Hermite polynomials, it is possible to ensure that the displacement state for the assembled set of such elements, is geometrically admissible. Monotonic convergence of total potential energy is therefore possible as the modelling is successively refined. Systematic evaluation of performance of the element is conducted, considering various examples for which analytical or other solutions are available.

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.

Fast Public Key Cryptosystem Based On Matrix Rings

A public key cryptosystem is proposed, which is based on the assumption that finding the square root of an element in a large finite ring is computationally infeasible in the absence of a knowledge of the ring structure. The encryption and decryption operations are very fast, and the data expansion is 1:2.

Incompressible boundary layer for longitudinal flow over a cylinder with an applied magnetic field

The flow, heat and mass transfer problem for a steady laminar incompressible boundary layer flow in an electrically conducting fluid over a longitudinal cylinder with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The results are found to be strongly dependent on the magnetic field and dissipation parameter. The effect of the mass transfer is more pronounced on the skin friction than on the heat transfer. The results have been compared with those of the series solution, the asymptotic solution, the Glauert and Lighthill's solution, local similarity, local nonsimilarity and difference-differential methods. Good agreement is found with all of them, except with the results of the local similarity and series solution methods.

Tree-ring based hydroclimate reconstruction over northern Vietnam from Fokienia hodginsii: eighteenth century mega-drought and tropical Pacific influence

We present here the first statistically calibrated and verified tree-ring reconstruction of climate from continental Southeast Asia.The reconstructed variable is March-May (MAM) Palmer Drought Severity Index (PDSI) based on ring widths from 22 trees (42 radial cores) of rare and long-lived conifer, Fokienia hodginsii (Po Mu as locally called) from northern Vietnam. This is the first published tree ring chronology from Vietnam as well as the first for this species. Spanning 535 years, this is the longest cross-dated tree-ring series yet produced from continental Southeast Asia. Response analysis revealed that the annual growth of Fokienia at this site was mostly governed by soil moisture in the pre-monsoon season. The reconstruction passed the calibration-verification tests commonly used in dendroclimatology, and revealed two prominent periods of drought in the mid-eighteenth and late-nineteenth enturies. The former lasted nearly 30 years and was concurrent with a similar drought over northwestern Thailand inferred from teak rings, suggesting a ``mega-drought'' extending across Indochina in the eighteenth century. Both of our reconstructed droughts are consistent with the periods of warm sea surface temperature (SST)anomalies in the tropical Pacific. Spatial correlation analyses with global SST indicated that ENSO-like anomalies might play a role in modulating droughts over the region, with El Nio (warm) phases resulting in reduced rainfall. However, significant correlation was also seen with SST over the Indian Ocean and the north Pacific,suggesting that ENSO is not the only factor affecting the climate of the area. Spectral analyses revealed significant peaks in the range of 53.9-78.8 years as well as in the ENSO-variability range of 2.0 to 3.2 years.

Convenient construction of tetrahedral finite elements for the quasi-harmonic equation

It is shown that in the finite-element formulation of the general quasi-harmonic equation using tetrahedral elements, for every member of the element family there exists just one numerical universal matrix indpendent of the size, shape and material properties of the element. Thus the element matrix is conveniently constructed by manipulating this single matrix along with a set of reverse sequence codes at the same time accounting for the size, shape and material properties in a simple manner.

Unsteady laminar compressible stagnation-point boundary-layer flow over a three-dimensional body: Higher order effects

The unsteady laminar compressible three-dimensional stagnation-point boundary-layer flow with variable properties has been studied when the velocity of the incident stream, mass transfer and wall temperature vary arbitrarily with time. The second-order unsteady boundary-layer equations for all the effects have been derived by using the method of matched asymptotic expansions. Both nodal and saddle point flows as well as cold and hot wall cases have been considered. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for an accelerating stream, a decelerating stream and a fluctuating stream. The results indicate that the unsteady free stream velocity distributions, the nature of the stagnation point, the mass transfer, the wall temperature and the variation of the density-viscosity product across the boundary significantly affect the skin friction and heat transfer. The variation of the wall temperature with time strongly affects the heat transfer whereas its effect is comparatively less on skin friction. Suction increases the skin friction and heat transfer but injection does the opposite. The skin friction in the x direction due to the combined effects of first- and second-order boundary layers is less than the skin-friction in the x direction due to the first-order boundary layers for all the parameters. The overall skin friction in the z direction and heat transfer are more or less than the first-order boundary layers depending upon the values of the various parameters.

A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Mass transfer effects on the generalised vortex flow over a stationary surface with or without magnetic field

The effect of injection and suction on the generalised vortex flow of a steady laminar incompressible fluid over a stationary infinite disc with or without magnetic field under boundary-layer approximations has been studied. The coupled nonlinear ordinary differential equations governing the self-similar flow have been numerically solved using the finite-difference scheme. The results indicate that the injection produces a deeper inflow layer and de-stabilises the motion while suction or magnetic field suppresses the inflow layer and produces stability. The effect of decreasingn, the parameter characterising the nature of vortex flow, is similar to that of increasing the injection rate.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter λ which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when λ is small, whereas the effect of the dissipation parameter is more pronounced when λ is comparatively large.