An optimal asymptotic-numerical method for convection dominated systems having exponential boundary layers

The convection dominated diffusion problems are studied. Higher order accurate numerical methods are presented for problems in one and two dimensions. The underlying technique utilizes a superposition of given problem into two independent problems. The first one is the reduced problem that refers to the outer or smooth solution. Stretching transformation is used to obtain the second problem for inner layer solution. The method considered for outer or degenerate problems are based on higher order Runge–Kutta methods and upwind finite differences. However, inner problem is solved analytically or asymptotically. The schemes presented are proved to be consistent and stable. Possible extensions to delay differential equations and to nonlinear problems are outlined. Numerical results for several test examples are illustrated and a comparative analysis is presented. It is observed that the method presented is highly accurate and easy to implement. Moreover, the numerical results obtained are not only comparable with the exact solution but also in agreement with the theoretical estimates.     

Failed disk recovery in double erasure RAID arrays

Reliability is a major concern in the design of large disk arrays. In this paper, we examine the effect of encountering more failures than that for which the RAID array was initially designed. Erasure codes are incorporated to enable system recovery from a specified number of disk erasures, and strive beyond that threshold to recover the system as frequently, and as thoroughly, as is possible. Erasure codes for tolerating two disk failures are examined. For these double erasure codes, we establish a correspondence between system operation and acyclicity of its graph model. For the most compact double erasure code, the full 2-code, this underlies an efficient algorithm for the computation of system operation probability (all disks operating or recoverable).When the system has failed, some disks are nonetheless recoverable. We extend the graph model to determine the probability that d disks have failed, a of which are recoverable by solving one linear equation, b of which are further recoverable by solving systems of linear equations, and d−a−b of which cannot be recovered. These statistics are efficiently calculated for the full 2-code by developing a three variable ordinary generating function whose coefficients give the specified values. Finally, examples are given to illustrate the probability that an individual disk can be recovered, even when the system is in a failed state.     

Empirical process approach to some two-sample problems based on ranked set samples

We study the asymptotic properties of both the horizontal and vertical shift functions based on independent ranked set samples drawn from continuous distributions. Several tests derived from these shift processes are developed. We show that by using balanced ranked set samples with bigger set sizes, one can decrease the width of the confidence band and hence increase the power of these tests. These theoretical findings are validated through small-scale simulation studies. An application of the proposed techniques to a cancer mortality data set is also provided. Part of the research was conducted while Kaushik Ghosh was visiting Statistical Research and Applications Branch of the National Cancer Institute on an Intergovernmental Personnel Assignment.     

Redefining the transparency order

In this paper, we consider the multi-bit Differential Power Analysis (DPA) in the Hamming weight model. In this regard, we revisit the definition of Transparency Order (\(\mathsf {TO}\)) from the work of Prouff (FSE 2005) and find that the definition has certain limitations. Although this work has been quite well referred in the literature, surprisingly, these limitations remained unexplored for almost a decade. We analyse the definition from scratch, modify it and finally provide a definition with better insight that can theoretically capture DPA in Hamming weight model for hardware implementation with precharge logic. At the end, we confront the notion of (revised) transparency order with attack simulations in order to study to what extent the low transparency order of an s-box impacts the efficiency of a side channel attack against its processing. To the best of our knowledge, this is the first time that such a critical analysis is conducted (even considering the original notion of Prouff). It practically confirms that the transparency order is indeed related to the resistance of the s-box against side-channel attacks, but it also shows that it is not sufficient alone to directly achieve a satisfying level of security. Regarding this point, our conclusion is that the (revised) transparency order is a valuable criterion to consider when designing a cryptographic algorithm, and even if it does not preclude to also use classical countermeasures like masking or shuffling, it enables to improve their effectiveness.     

A parameter uniform difference scheme for parabolic partial differential equation with a retarded argument

The paper deals with the analysis of a non-stationary parabolic partial differential equation with a time delay. The highest order derivative term is affected by the small parameter. This is precisely the case when the magnitude of the convective term becomes much larger compare to that of diffusion term. The solution of problem exhibits steep gradients in the narrow intervals of space and short interval of times. In these cases a dissipative loss turned out to be more complex. Even for the one spatial dimension and one temporal variable, not all difference scheme can capture these steep variation. Although the analysis is restricted to the model in one space dimension, the technique and comparison principles developed should prove useful in assessing the merits of numerical solution of other nonlinear model equations too.     

Anomalous variation of the Lamb-M?ssbauer factor at the magnetic transition temperature in magnetoelectric?GaFeO(3)

Temperature-dependent (57)Fe M?ssbauer spectroscopy (5-723?K) and neutron diffraction (2-290?K) measurements are carried out on polycrystalline magnetoelectric GaFeO(3). From the neutron diffraction data, evidence for the magnetostriction and increased disorder at Fe sites close to the ferrimagnetic Curie transition temperature (T(C)) is observed. From the M?ssbauer data, it is observed that the Lamb-M?ssbauer factor as a function of temperature f(T), which is related to the integral over the first Brillouin zone of the phonon spectrum, shows a unequivocal variation at the T(C). The observations are discussed in terms of spin-phonon coupling. The observed average hyperfine fields from (57)Fe M?ssbauer spectra match with the bulk magnetization data. A critical exponent (β) of 0.38?±?0.02 and a Debye temperature (θ(D)) of ～350?K is estimated from the (57)Fe M?ssbauer data.     

A facile strategy for the fabrication of uniform CdS nanowires with high yield and its controlled morphological growth with the assistance of PEG in hydrothermal route

A series of novel wurtzite cadmium sulphide (CdS) nanowires with uniform diameter were synthesized by using a rapid and simple solvothermal route. CdS nano structures with certain morphology could be selectively produced by only varying the concentration of poly ethylene glycol (PEG) as a surfactant in the reaction system with cadmium acetate, sulphur powder and ethelynediamine (EDA). We extensively studied UV-vis absorption spectra, photoluminescence spectra after confirming CdS nanowires with diameter 24-25 nm and length ranging up to several nano meters by field emission scanning electron microscopy (FE-SEM). Therefore we may definitely propose a new formation mechanism of CdS nanowires assisted by PEG with its illustrating optical properties.     

Ground-state properties of neutron magic nuclei

A systematic study of the ground-state properties of the entire chains of even–even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82, and 126 has been carried out using relativistic mean-field plus Bardeen–Cooper–Schrieffer approach. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach (Skyrme–Hartree–Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip-lines, the (Z, N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.