Non-Newtonian boundary layers on a moving cylinder

The analysis of steady laminar forced convection boundary layer of power-law non-Newtonian fluids on a continuously moving cylinder with the surface maintained at a uniform temperature or uniform heat flux is presented. Of interest were the effects of power-law viscosity index, transverse curvature, generalized Prandtl number and streamwise coordinate on the local Nusselt number as well as on the velocity and temperature profiles. The two thermal boundary conditions yield quite similar results. Comparison of the calculated results with available series expansion solutions for a Newtonian fluid shows a very good performance of the present numerical procedure.

Dynamics of activationless reactions in solution

Recent picosecond and subpicosecond laser spectroscopy experiments have revealed several chemically and biologically important reactions in solution in which the reaction potential surface does not present a barrier to the motion along the reaction coordinate.The dynamics of these reactions display diverse and interesting behavior. They include the dependence of relaxation rate on the solvent viscosity, the solvent polarity, the temperature, and the wavelength of the exciting light. In this article we review the recent developments in the theoretical description of activationless processes in solution and compare them with the available experimental results

Computer modelling studies of ribonuclease A-pyrimidine nucleotide complexes

Different modes of binding of pyrimidine monophosphates 2'-UMP, 3'-UMP, 2'-CMP and 3'-CMP to ribonuclease (RNase) A are studied by energy minimization in torsion angle and subsequently in Cartesian coordinate space. The results are analysed in the light of primary binding sites. The hydrogen bonding pattern brings out roles for amino acids such as Asn44 and Ser123 apart from the well known active site residues viz., His12,Lys41,Thr45 and His119. Amino acid segments 43-45 and 119-121 seem to be guiding the ligand binding by forming a pocket. Many of the active site charged residues display considerable movement upon nucleotide binding.

On Paley-Wiener Theorems for the Heisenberg Group

In this paper we prove two Paley-Wiener-type theorems for the Heisenberg group. One is for the group Fourier transform which is the analogue of the classical Paley-Wiener theorem. The other one is for the spectral projections associated to the sub-Laplacian

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow in the low-conductivity limit. Our treatment is non-perturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Re-m), but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Re-m. Our principal results are as follows: (i) the magnetic fluctuations are determined to the lowest order in Rem by explicit calculation of the resistive Green's function for the linear shear flow; (ii) the mean electromotive force is then calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the 'C' and 'D' terms, respectively, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the space-time integrals; (iii) the contribution of the D term is such that its contribution to the time evolution of the cross-shear components of the mean field does not depend on any other components except itself. Therefore, to the lowest order in Re-m, but to all orders in the shear strength, the D term cannot give rise to a shear-current-assisted dynamo effect; (iv) casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) the integral kernels are expressed in terms of the velocity-spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) the C term couples different components of the mean magnetic field, so they can, in principle, give rise to a shear-current-type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non-helical velocity dynamics at low fluid Reynolds number does not result in a shear-current-assisted dynamo effect.

Structure and conformation of the calcium complex of cyclo(Ala-Leu-Pro-Gly)2 in two crystal forms

Crystal structures of two different forms of the calcium perchlorate complex of cyclo(Ala-Leu-Pro-Gly)2 have been determined and refined using X-ray crystallographic techniques. Orthorhombic form: C32H52N8O8.Ca(ClO4)2.7H2O.2CH3OH, space group C222(1), a = 14.366, b = 18.653, c = 19.824 A, Z = 4, R = 0.068 for 2208 observed reflections. Monoclinic form: C32H52N8O8.Ca(ClO4)2.4H2O, space group C2, a = 21.096, b = 10.182, c = 11.256 A, beta = 103.33 degrees, Z = 2, R = 0.075 for 2165 observed reflections. The cyclic peptide molecule in both the structures has the form of a twofold symmetric, slightly elongated bowl. Type II' beta-turns, involving Gly and Ala at the corners, exist at the two ends of the molecule. The interior of the molecule is substantially hydrophilic, and the external surface of the bowl is largely hydrophobic. The calcium ion is located at the centre of the mouth of the bowl-like molecule. In both crystal forms, four peptide carbonyl oxygens from the cyclic peptide and two solvent oxygens coordinate to the metal ion. The mode of complexation may be described as incomplete encapsulation as, for example, in the case of metal complexes of antamanide. In the crystal structures the complex ions are held together by hydrogen bonds involving perchlorate ions and water molecules. The molecular structure observed in the crystals is entirely consistent with the results of solution studies, which also indicate the conformation of the cyclic peptide in the complex to be similar to that of the uncomplexed molecule.

Impact of climate change on Indian forests: a dynamic vegetation modeling approach

We make an assessment of the impact of projected climate change on forest ecosystems in India. This assessment is based on climate projections of the Regional Climate Model of the Hadley Centre (HadRM3) and the dynamic global vegetation model IBIS for A2 and B2 scenarios. According to the model projections, 39% of forest grids are likely to undergo vegetation type change under the A2 scenario and 34% under the B2 scenario by the end of this century. However, in many forest dominant states such as Chattisgarh, Karnataka and Andhra Pradesh up to 73%, 67% and 62% of forested grids are projected to undergo change. Net Primary Productivity (NPP) is projected to increase by 68.8% and 51.2% under the A2 and B2 scenarios, respectively, and soil organic carbon (SOC) by 37.5% for A2 and 30.2% for B2 scenario. Based on the dynamic global vegetation modeling, we present a forest vulnerability index for India which is based on the observed datasets of forest density, forest biodiversity as well as model predicted vegetation type shift estimates for forested grids. The vulnerability index suggests that upper Himalayas, northern and central parts of Western Ghats and parts of central India are most vulnerable to projected impacts of climate change, while Northeastern forests are more resilient. Thus our study points to the need for developing and implementing adaptation strategies to reduce vulnerability of forests to projected climate change.

Impact of climate change at species level: a case study of teak in India

In this study, we model the long-term effect of climate change on commercially important teak (Tectona grandis) and its productivity in India. This modelling assessment is based on climate projections of the regional climate model of the Hadley Center (HadRM3) and the dynamic vegetation model, IBIS. According to the model projections, 30% of teak grids in India are vulnerable to climate change under both A2 and B2 SRES scenarios because the future climate may not be optimal for teak at these grids. However, the net primary productivity and biomass are expected to increase because of elevated levels of CO2. Given these directions of likely impacts, it is crucial to further investigate the climate change impacts on teak and incorporate such findings into long-term teak plantation programs. This study also demonstrates the feasibility and limitations of assessing the impact of projected climate change at the species level in the tropics.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Average lattices and aperiodic structures

Statistically averaged lattices provide a common basis to understand the diffraction properties of structures displaying deviations from regular crystal structures. An average lattice is defined and examples are given in one and two dimensions along with their diffraction patterns. The absence of periodicity in reciprocal space corresponding to aperiodic structures is shown to arise out of different projected spacings that are irrationally related, when the grid points are projected along the chosen coordinate axes. It is shown that the projected length scales are important factors which determine the existence or absence of observable periodicity in the diffraction pattern more than the sequence of arrangement.

Binding of active site directed ligands to phospholipase A2: Implications on the molecular constraints and catalytic mechanism

Molecular constraints for the localization of active site directed ligands (competitive inhibitors and substrates) in the active site of phospholipase A2 (PLA2) are characterized. Structure activity relationships with known inhibitors suggest that the head : group interactions dominate the selectivity as well as a substantial part of the affinity. The ab initio fitting of the amide ligands in the active site was carried out to characterize the head group interactions. Based on a systematic coordinate space search, formamide is docked with known experimental constraints such as coordination of the carbonyl group to Ca2+ and hydrogen bond between amide nitrogen and ND1 of His48. An optimal position for a bound water molecule is identified and its significance for the catalytic mechanism is postulated. Unlike the traditional ''pseudo-triad'' mechanism, the ''Ca-coordinatedoxyanion'' mechanism proposed here invokes activation of the catalytic water to form the oxyanion in the coordination sphere of calcium. As it attacks the carbonyl carbon of the ester, a near-tetrahedral intermediate is formed. As the second proton of the catalytic water is abstracted by the ester oxygen, its reorientation and simultaneous cleavage form hydrogen bond with ND1 of His48. In this mechanism of esterolysis, a catalytic role for the water co-ordinated to Ca2+ is recognised.

Characterization of substrate UpA binding to RNase A--computer modelling and energetics approach.

In the past two decades RNase A has been the focus of diverse investigations in order to understand the nature of substrate binding and to know the mechanism of enzyme action. Although this system is reasonably well characterized from the view point of some of the binding sites, the details of interactions in the second base binding (B2) site is insufficient. Further, the nature of ligand-protein interaction is elucidated generally by studies on RNase A-substrate analog complexes (mainly with the help of X-ray crystallography). Hence, the details of interactions at atomic level arising due to substrates are inferred indirectly. In the present paper, the dinucleotide substrate UpA is fitted into the active site of RNase A Several possible substrate conformations are investigated and the binding modes have been selected based on Contact Criteria. Thus identified RNase A-UpA complexes are energy minimized in coordinate space and are analysed in terms of conformations, energetics and interactions. The best possible ligand conformations for binding to RNase A are identified by experimentally known interactions and by the energetics. Upon binding of UpA to RNase A the changes associated,with protein back bone, Side chains in general and at the binding sites in particular are described. Further, the detailed interactions between UpA and RNase A are characterized in terms of hydrogen bonds and energetics. An extensive study has helped in interpreting the diverse results obtained from a number of experiments and also in evaluating the extent of changes the protein and the substrate undergo in order to maximize their interactions.

Defects induced enhancement of Eu3+Emission in yttria (Y2O3:Eu3+)

Bixbyite type Y2O3:Eu3+ apart from being the efficient red phosphor extensively used in trichromatic fluorescent lamps, it is a typical system one can apply Jorgensen's refined electron spin pairing theory. This can be used to explain the enhancement in Eu3+ emission intensity observed with the aliovalent substitution in the yttria host matrix. Results based on these are explained qualitatively by considering a simple configurational coordinate model. Futhermore, an insight into the different types of defects induced with the aliovalent substitution in the yttria lattice has become possible with EPR probe.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Mixed convection heat transfer from the bottom tip of a cylinder spinning about a vertical axis in a saturated porous medium

The present work is a numerical study of heat transfer characteristics from the bottom tip of a cylinder spinning about a vertical axis in an infinitely saturated porous medium. The problem is axisymmetric. The non-dimensionalized governing equations are solved using the SIMPLER algorithm on a staggered grid. The influence of rotational Reynolds numbers and Darcy numbers on the heat transfer for a Grashof number of 104 and Prandtl number of 7.0 is studied. It is found that for very high Darcy numbers, over a wide range of rotational Reynolds numbers, the heat transfer takes place mainly due to conduction. The convective heat transfer takes place for lower Darcy numbers and for higher rotational Reynolds numbers. Moreover, there is a rapid increase in the overall Nusselt number below a certain Darcy number with increase in the rotational Reynolds numbers. The effect of the Darcy number and the rotational Reynolds number on the heat transfer and fluid flow in the porous medium is depicted in the form of streamline and isotherm plots. The variation of the overall Nusselt number with respect to the Darcy number for various rotational Reynolds numbers is plotted. The variation of the local Nusselt number with respect to the radial coordinate at the heated tip of the vertical cylinder is plotted for various Darcy and rotational Reynolds numbers.