On relativistic models of strange stars

The superdense stars with mass-to-size ratio exceeding 0.3 are expected to be made of strange matter. Assuming that the 3-space of the interior space-time of a strange star is that of a three-paraboloid immersed in a four-dimensional Euclidean space, we obtain a two-parameter family of their physically viable relativistic models. This ansatz determines density distribution of the interior self-gravitating matter up to one unknown parameter. The Einstein’s field equations determine the fluid pressure and the remaining geometrical variables. The information about mass-to-size ratio together with the conventional boundary conditions lead to the determination of total mass, radius and other parameters of the stellar configuration.      

On the inadmissibility of preliminary-test estimators when the loss involves a complexity cost

Summary Estimation-preceded-by-testing is studied in the context of estimating the mean vector of a multivariate normal distribution under squared error loss together with a complexity cost. It is shown that although the preliminary test estimator is admissible for the univariate problem (cf Meeden and Arnold (1979),J. Amer. Statist. Assoc.,74, 872–874), for dimensionp≧3, the estimator is inadmissible. A new preliminary test estimator is obtained, which depends on the cost for each component and dominates the usual preliminary test estimator. Research partially supported by the NSF Grant Number DMS-82-18091 and partially by the DSR Research Development Award, University of Florida.     

The FFTRR-based fast direct algorithms for complex inhomogeneous biharmonic problems with applications to incompressible flows

We develop analysis-based fast and accurate direct algorithms for several biharmonic problems in a unit disk derived directly from the Green’s functions of these problems and compare the numerical results with the “decomposition” algorithms (see Ghosh and Daripa, IMA J. Numer. Anal. 36(2), 824–850 [17]) in which the biharmonic problems are first decomposed into lower order problems, most often either into two Poisson problems or into two Poisson problems and a homogeneous biharmonic problem. One of the steps in the “decomposition algorithm” as discussed in Ghosh and Daripa (IMA J. Numer. Anal. 36(2), 824–850 [17]) for solving certain biharmonic problems uses the “direct algorithm” without which the problem can not be solved. Using classical Green’s function approach for these biharmonic problems, solutions of these problems are represented in terms of singular integrals in the complex z?plane (the physical plane) involving explicitly the boundary conditions. Analysis of these singular integrals using FFT and recursive relations (RR) in Fourier space leads to the development of these fast algorithms which are called FFTRR based algorithms. These algorithms do not need to do anything special to overcome coordinate singularity at the origin as often the case when solving these problems using finite difference methods in polar coordinates. These algorithms have some other desirable properties such as the ease of implementation and parallel in nature by construction. Moreover, these algorithms have O(logN) complexity per grid point where N ² is the total number of grid points and have very low constant behind this order estimate of the complexity. Performance of these algorithms is shown on several test problems. These algorithms are applied to solving viscous flow problems at low and moderate Reynolds numbers and numerical results are presented.     

Longitudinal Structure Function F L of Proton from Regge Like Behaviour of Structure Function at Small-x

The evolutions of longitudinal structure function F _L from quantum chromodynamics (QCD) evolution equation in next-to-leading order at small-x is presented using the Regge like behaviour of the structure function. The proposed simple analytical expression for F _L structure function provides the t- and x-evolution equations to study the behaviour of F _L structure function at small-x. The calculated results are compared with the data of H1, ZEUS collaborations and results of Block model, Donnachie–Landshoff model. Our calculated results can be described within the framework of perturbative QCD.     

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.     

Contact instability in adhesion and debonding of thin elastic films

Based on experiments and 3D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths, and cavities, all of which have the same lateral pattern length scale, lambda close to lambda/H approximately 3 for thick films, H > 1 microm . The linear stability analysis and experiments show a new thin film regime where lambda/H approximately equal to 3 + 2pi(lambda/3 muH)1/4 (gamma is surface tension, mu is shear modulus) because of a significant surface energy penalty (for example, lambda/H approximately equal to 6 for H = 200 nm; mu = 1 MPa).     

Cylindrically symmetric inhomogeneous cosmological models with viscous fluid and varying Λ

Cylindrically symmetric non-static cosmological models representing a bulk viscous fluid distribution have been obtained which are inhomogeneous and anisotropic. Without assuming anyadhoc law, we obtain a cosmological constant as a decreasing function of time. Various physical and geometrical features of the models are also discussed.     

Longitudinal Dust Lattice Shock Wave in a Strongly Coupled Complex Dusty Plasma

The effect of hydrodynamical damping that arises due to the irreversible processes within the system have been studied on 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. Analytical investigation shows that the nonlinear wave is governed by Korteweg‐de Vries Burgers' equation. This hydrodynamical damping induced dissipative effect is responsible for the Burgers' term that causes the generation of shock wave in dusty plasma crystal. Numerical investigation on the basis of the glow‐discharge plasma parameters reveal that LDLW exhibits both oscillatory and monotonic shock. The shock is compressive in nature and its strength decreases (increases) with the increase of the shielding parameter κ (characteristic length L). The effects of dust‐neutral collision are also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preferential mode of cyclization of tetrahydrofuran amino acids containing peptides: some theoretical insights

Theoretical insights have been provided for the observed preference of cyclodimerization over intramolecular cyclization reactions in linear tripeptides containing “2,5‐cis” (2S,5R)‐tetrahydrofuran amino acid as well as in those containing “2,5‐trans” (2S,5S)‐tetrahydrofuran amino acid, using quantum chemical methods. The geometries of species involved as well as the feasibility of cyclization reactions are studied at the B3LYP/6‐31G(d,p) level of theory in gas phase as well as in solvent phase. Thermodynamic data from Hessian calculations favor the intermolecular cyclization. Analysis of optimized geometries reveals the existence of additional stabilizing hydrogen bonding interactions in intermolecularly cyclized products. The existence of these second‐order interactions is substantiated by topological (atoms in molecules (AIM)) and natural bond orbital (NBO) analyses. Such interactions are absent in the intramolecular cyclization products. Further justification for the presence of stabilizing interactions in intermolecularly cyclized products comes from the molecular electrostatic potentials and electron density surfaces. Kinetic control favoring the intermolecularly cyclized products due to additional entropy of activation in the intramolecular case is surmised. Copyright © 2009 John Wiley & Sons, Ltd.     

Structural, electronic and magnetic properties of Cr-doped Cd12S12 clusters: A density functional investigation

We have carried out first-principles density functional investigation of Cd₁₂S₁₂ cluster doped with one (monodoped) and two (bidoped) Cr-atoms, to explore the manifestation of novel magnetism in this family of stable II-VI semiconducting clusters. Different types of possible configurations of the dopant e.g. substitutional, exohedral, endohedral and substitutional-exohedral have been considered. Both for monodoped and bidoped clusters, substitutional doping corresponds to the ground state. In case of bidoped clusters, the coupling is found to be short-ranged, that depends on the Cr-Cr separation and the local environment. The main competing factors stabilizing ferromagnetic (FM) state in this class of doped nanoclusters are: (a) the FM interaction between two Cr atoms via S atom due to strong p-d hybridization and (b) the short range Cr-Cr direct antiferromagnetic (AFM) interaction. When additional hole is introduced in the system by substituting S with P, in substitutional bidoped clusters, FM state is found to be the ground sate.