Solutions of Boundary Layer Equations Governing Free Convective and Magnetohydrodynamic Flows through Parametric Differentiation

In der vorliegenden Arbeit wird die Methode der parametrischen Differentiation angewendet, um ein System nichtlinearer Gleichungen zu lösen, das zwei- und dreidimensionale freie, konvektive Grenzschichströmungen bzw. eine zweidimensionale magnetohydrodynamische Grenzschichtströmung beherrscht. Der Hauptvorteil dieser Methode besteht darin, daß die nichlinearen Gleichungen auf lineare reduziert werden und die Nichtlinearität auf ein System von Gleichungen erster Ordnung beschränkt wird, das, verglichen mit den ursprünglichen Nichtlinearen Gleichungen, viel leichter gelöst werden kann. Ein anderer Vorzug der Methode ist, daß sie es ermöglicht, die Lösung von einer bekannten, zu einem bestimmten Parameterwert gehörigen Lösung aus durch schrittweises Vorgehen die Lösung für den gesamten Parameterbereich zu erhalten. Die mit dieser Methode gewonnenen Ergebnisse stimmen gut mit den entsprechenden, mit anderen numerischen Verfahren erzielten überein.

On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

A unit cube in k dimensions (k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k where R-i (for 1 <= i <= k) is a closed interval of the form [a(i), a(i) + 1] on the real line. A graph G on n nodes is said to be representable as the intersection of k-cubes (cube representation in k dimensions) if each vertex of C can be mapped to a k-cube such that two vertices are adjacent in G if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G denoted as cub(G) is the minimum k for which G can be represented as the intersection of k-cubes. An interesting aspect about cubicity is that many problems known to be NP-complete for general graphs have polynomial time deterministic algorithms or have good approximation ratios in graphs of low cubicity. In most of these algorithms, computing a low dimensional cube representation of the given graph is usually the first step. We give an O(bw . n) algorithm to compute the cube representation of a general graph G in bw + 1 dimensions given a bandwidth ordering of the vertices of G, where bw is the bandwidth of G. As a consequence, we get O(Delta) upper bounds on the cubicity of many well-known graph classes such as AT-free graphs, circular-arc graphs and cocomparability graphs which have O(Delta) bandwidth. Thus we have: 1. cub(G) <= 3 Delta - 1, if G is an AT-free graph. 2. cub(G) <= 2 Delta + 1, if G is a circular-arc graph. 3. cub(G) <= 2 Delta, if G is a cocomparability graph. Also for these graph classes, there axe constant factor approximation algorithms for bandwidth computation that generate orderings of vertices with O(Delta) width. We can thus generate the cube representation of such graphs in O(Delta) dimensions in polynomial time.

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler-Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence. (C) 2007 Elsevier Ltd. All rights reserved.

Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

Role of free valences and spin densities on the migrating atom in location of saddle points in radical-exchange reactions

The principle of the conservation of bond orders during radical-exchange reactions is examined using Mayer's definition of bond orders. This simple intuitive approximation is not valid in a quantitative sense. Ab initio results reveal that free valences (or spin densities) develop on the migrating atom during reactions. For several examples of hydrogen-transfer reactions, the sum of the reaction coordinate bond orders in the transition state was found to be 0.92 +/- 0.04 instead of the theoretical 1.00 because free valences (or spin densities) develop on the migrating atom during reactions. It is shown that free valence is almost equal to the square of the spin density on the migrating hydrogen atom and the maxima in the free valence (or spin density) profiles coincide (or nearly coincide) with the saddle points in the corresponding energy profiles.

Some results on the reconstruction problems. p-claw-free, chordal, and p4-reducible graphs

A claw is an induced subgraph isomorphic to K-1,K-3. The claw-point is the point of degree 3 in a claw. A graph is called p-claw-free when no p-cycle has a claw-point on it. It is proved that for p greater than or equal to 4, p-claw-free graphs containing at least one chordless p-cycle are edge reconstructible. It is also proved that chordal graphs are edge reconstructible. These two results together imply the edge reconstructibility of claw-free graphs. A simple proof of vertex reconstructibility of P-4-reducible graphs is also presented. (C) 1995 John Wiley and Sons, Inc.

Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

The relationship between classification of multi-domain proteins using an alignment-free approach and their functions: a case study with immunoglobulins

Establishing functional relationships between multi-domain protein sequences is a non-trivial task. Traditionally, delineating functional assignment and relationships of proteins requires domain assignments as a prerequisite. This process is sensitive to alignment quality and domain definitions. In multi-domain proteins due to multiple reasons, the quality of alignments is poor. We report the correspondence between the classification of proteins represented as full-length gene products and their functions. Our approach differs fundamentally from traditional methods in not performing the classification at the level of domains. Our method is based on an alignment free local matching scores (LMS) computation at the amino-acid sequence level followed by hierarchical clustering. As there are no gold standards for full-length protein sequence classification, we resorted to Gene Ontology and domain-architecture based similarity measures to assess our classification. The final clusters obtained using LMS show high functional and domain architectural similarities. Comparison of the current method with alignment based approaches at both domain and full-length protein showed superiority of the LMS scores. Using this method we have recreated objective relationships among different protein kinase sub-families and also classified immunoglobulin containing proteins where sub-family definitions do not exist currently. This method can be applied to any set of protein sequences and hence will be instrumental in analysis of large numbers of full-length protein sequences.

Free-to-bound and bound exciton transitions at isoelectronic impurities: GaP(Zn,O)

We show, for sufficiently high temperatures and sufficiently weak majority-carrier binding energies, that the dominant radiative transition at an isoelectronic acceptor (donor) in p-type (n-type) material consists of the recombination of singly trapped minority carriers (bound by central-cell forces) with free majority carriers attracted by a Coulomb interaction. There are two reasons why the radiative recombination rate of the free-to-bound process is greater than the bound exciton process, which dominates at lower temperatures: (i) The population of free majority-carrier states greatly exceeds that of exciton states at higher temperatures, and (ii) the oscillator strength of the free-to-bound transition is greatly enhanced by the Coulomb attraction between the free carrier and the charged isoelectronic impurity. This enhancement is important for isoelectronic centers and is easily calculable from existing exciton models. We show that the free carrier attracted by a Coulomb interaction can be viewed as a continuum excited state of the bound exciton. When we apply the results of our calculations to the GaP(Zn, O) system, we find that the major part of the room-temperature luminescence from nearest-neighbor isoelectronic Zn-O complexes results from free-to-bound recombination and not exciton recombination as has been thought previously. Recent experiments on impulse excitation of luminescence in GaP(Zn, O) are reevaluated in the light of our calculations and are shown to be consistent with a strong free-to-bound transition. For deep isoelectronic centers with weakly bound majority carriers, we predict an overwhelming dominance of the free-to-bound process at 300°K.

Homeostatic regulation of free retinol-binding protein and free thyroxine pools of plasma by their plasma carrier proteins in chicken

The mechanism underlying homeostatic regulation of the plasma levels of free retinol-binding protein and free thyroxine, the systemic distribution of which is of great importance, has been investigated. A simple method has been developed to determine the rate of dissociation of a ligand from the binding protein. Analysis of the dissociation process of retinol-binding protein from prealbumin-2 reveals that the free retinol-binding protein pool undergoes massive flux, and the prealbumin-2 participates in homeostatic regulation of the free retinol-binding protein pool. Studies on the dissociation process of thyroxine from its plasma carrier proteins show that the various plasma carrier proteins share two roles. Of the two types of protein, the thyroxine-binding globulin (the high affinity binding protein) contributes only 27% of the free thyroxine in a rapid transition process, despite its being the major binding protein. But prealbumin-2, which has lower affinity towards thyroxine, participates mainly in a rapid flux of the free thyroxine pool. Thus thyroxine-binding globulin acts predominantly as a plasma reservoir of thyroxine, and also probably in the �buffering� action on plasma free thyroxine level, in the long term, while prealbumin-2 participates mainly in the maintainance of constancy of free thyroxine levels even in the short term. The existence of these two types of binding protein facilitates compensation for the metabolic flux of the free ligand and maintenance of the thyroxine pool within a very narrow range.

Highly efficient dialkylphosphate-mediated syntheses of hydantoins and a bicyclohydantoin under solvent-free conditions

Diversely substituted hydantoins have been synthesized by new strategy from cyanamide based precursor, that is, methyl N-cyano-N-alkyl/arylaminoacetate. Dialkylphosphates were employed as the mild reagent to hydrolyze and cyclize the substrate in one step to give quantitative yields of the desired products. Syntheses of multivalent hydantoins viz bis-hydantoin, bicyclohydantoin have potentially widened the scope and applicability of the present method. Solvent-free conditions and very easy work-up procedure make the reaction convenient and eco-friendly. Single crystal structures of some of the representative compounds are also reported. (C) 2011 Elsevier Ltd. All rights reserved.

Novel and efficient protocol for the syntheses of N-1 substituted thiohydantoin and a bicyclothiohydantoin under solvent-free conditions

A novel approach for the synthesis of N-1 substituted thiohydantoin has been developed to give quantitative yields of the desired products. The efficient synthesis of bis-thiohydantoin derivative and bicyclothiohydantoin has extended scope and applicability of present method. Solvent-free conditions and very easy work-up procedure make the reaction convenient and eco-friendly. All the products were characterized by spectroscopic techniques and elemental analysis, and finally the structure of representative ;compound was also confirmed by X-ray crystallography. (C) 2012 Elsevier Ltd. All rights reserved.

Renyi entropies of free bosons on the torus and holography

We analytically evaluate the Renyi entropies for the two dimensional free boson CFT. The CFT is considered to be compactified on a circle and at finite temperature. The Renyi entropies S-n are evaluated for a single interval using the two point function of bosonic twist fields on a torus. For the case of the compact boson, the sum over the classical saddle points results in the Riemann-Siegel theta function associated with the A(n-1) lattice. We then study the Renyi entropies in the decompactification regime. We show that in the limit when the size of the interval becomes the size of the spatial circle, the entanglement entropy reduces to the thermal entropy of free bosons on a circle. We then set up a systematic high temperature expansion of the Renyi entropies and evaluate the finite size corrections for free bosons. Finally we compare these finite size corrections both for the free boson CFT and the free fermion CFT with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces as its boundary. One-loop corrections in these geometries are entirely determined by quantum numbers of the excitations present in the bulk. This implies that the leading finite size corrections contributions from one-loop determinants of the Chern-Simons gauge field and the Dirac field in the dual geometry should reproduce that of the free boson and the free fermion CFT respectively. By evaluating these corrections both in the bulk and in the CFT explicitly we show that this expectation is indeed true.