Evolution of Transformation Texture in a Metastable B - Titanium Alloy

Texture evolution in h. c. p. (alpha) phase derived from aging of a differently processed metastable b.c.c. (beta) titanium alloy was investigated. The study was aimed at examining (i) the effect of different b. c. c. cold rolling textures and (ii) the effect of different defect structures on the h. c. p transformation texture. The alloy metastable beta alloy Ti-10V-4.5Fe-1.5Al was rolled at room temperature by unidirectional (UDR) and multi-step cross rolling (MSCR). A piece of the as-rolled materials were subjected to aging in order to derive the h. c. p. (alpha) phase. In the other route, the as-rolled materials were recrystallized and then aged. Textures were measured using X-ray as well as Electron Back Scatter Diffraction. Rolling texture of beta phase, as characterized by the presence of a strong gamma fibre, was found stronger in M S C R compared to UDR, although they were qualitatively similar. The stronger texture of MSCR sample could be attributed to the inhomogeneous deformation taking place in the sample that might contribute to weakening of texture. Upon recrystallization in beta phase field close to beta-transus. the textures qualitatively resembled the corresponding beta deformation textures; however, they got strengthed. The aging of differently beta rolled samples resulted in the product alpha-phase with different textures. The (UDR + Aged) sample had a stronger texture than (MSCR + Aged) sample, which could be due to continuation of defect accumulation in UDR sample, thus providing more potential sites for the nucleation of alpha phase. The trend was reversed in samples recrystallized prior to aging. The (MSCR + Recrystallized + Aged) sample showed stronger texture of alpha phase than the (UDR + Recrystallized + Aged) sample. This could be attributed to extensive defect annihilation in the UDR sample on recrystallization prior to aging. The (MSCR + Aged) sample exhibited more alpha variants when compared to (MSCR + Recrystallized + Aged) sample. This has been attributed to the availability of more potential sites for nucleation of alpha phase in the former. It could be concluded that alpha transformation texture depends mainly on the defect structure of the parent phase.

Study of Texture Evolution at High Strain Rates in FCC Materials

Evolution of crystallographic texture during high strain rate deformation in FCC materials with different stacking fault energy (Ni, Cu, and Cu-10Zn alloy) has been studied. The texture evolved in FCC materials at these strain rates show little dependence on the Stacking Fault Energy and the amount of deformation. Copper shows an anomalous behavior that is attributed to the ease of cross slip and continuous Dynamic Recrystallization that are operative under the experimental conditions.

Perturbative growth of cosmological clustering. I: Formalism

Here we rederive the hierarchy of equations for the evolution of distribution functions of various orders using a convenient parameterization. We use this to obtain equations for two- and three-point correlation functions in powers of a small parameter, viz., the initial density contrast. The correspondence of the lowest order solutions of these equations to the results from the linear theory of density perturbations is shown for an OMEGA = 1 universe. These equations are then used to calculate, to the lowest order, the induced three-point correlation function that arises from Gaussian initial conditions in an OMEGA = 1 universe. We obtain an expression which explicitly exhibits the spatial structure of the induced three-point correlation function. It is seen that the spatial structure of this quantity is independent of the value of OMEGA. We also calculate the triplet momentum. We find that the induced three-point correlation function does not have the ''hierarchical'' form often assumed. We discuss possibilities of using the induced three-point correlation to interpret observational data. The formalism developed here can also be used to test a validity of different schemes to close the

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

Kinetic evolution studies of silver nanoparticles in a bio-based green synthesis process

Silver nanoparticles are being extensively studied due to their widespread applications and unique properties. In the present study, the growth kinetics of silver nanoparticles as synthesized on reduction of silver nitrate solution by aqueous extract of Azadirachta indica leaves was investigated. The formation of silver nanoparticles was preliminarily monitored by measuring the absorption maxima at different time intervals after adding the reducing agent to the silver salt solution (0.5, 1, 1.5, 2, 2.5, 3, 3.5 and 4 h). At different time points characterization studies were conducted using X-ray diffraction studies, FT-IR techniques, zeta potential studies and transmission electron microscopy. The total available silver in the reaction medium was determined at different durations using ICP-OES. The changes in reduction potential in the medium were also monitored using potentiometric analysis. The results confirm a definite change in the medium pertaining to formation of the stable nanoparticles after 2 h, and a significant increase in the agglomeration tendency after 4 h of interaction. The growth kinetic data of the nanoparticles till 3.5 h was found to fit the LSW model confirming diffusion limited growth. (C) 2011 Elsevier B.V. All rights reserved.

Studies on molecular evolution and structural features of double-headed inhibitors of ?-amylase and trypsin in plants

Plant seeds usually have high concentrations of proteinase and amylase inhibitors. These inhibitors exhibit a wide range of specificity, stability and oligomeric structure. In this communication, we report analysis of sequences that show statistically significant similarity to the double-headed alpha-amylase/trypsin inhibitor of ragi (Eleusine coracana). Our aim is to understand their evolutionary and structural features. The 14 sequences of this family that are available in the SWISSPROT database form three evolutionarily distinct branches. The branches relate to enzyme specificities and also probably to the oligomeric state of the proteins and not to the botanical class of the plant from which the enzymes are derived. This suggests that the enzyme specificities of the inhibitors evolved before the divergence of commercially cultivated cereals. The inhibitor sequences have three regions that display periodicity in hydrophobicity. It is likely that this feature reflects extended secondary structure in these segments. One of the most variable regions of the polypeptide corresponds to a loop, which is most probably exposed in the native structure of the inhibitors and is responsible for the inhibitory property.

Analysis of texture evolution in pure magnesium and the magnesium alloy AM30 during rod and tube extrusion

The evolution of microstructure and texture during extrusion of pure magnesium and its single phase alloy AM30 has been studied experimentally as well as by crystal plasticity simulation. Microstructure and micro-texture were characterized by electron back scattered diffraction (EBSD), bulk-texture was measured using X-ray diffraction and deformation texture simulations were carried out using visco-plastic self consistent (VPSC) model. In spite of clear indications of the occurrence of dynamic recrystallization (DRX), simulations were able to reproduce the experimental textures successfully. This was attributed to the fact that the textures were c-type fibers with their axis of rotation parallel to the c-axis and DRX leads to simply rotate the texture around the c-axis. (C) 2011 Elsevier B.V. All rights reserved.

Social selection and the evolution of cooperative groups: The example of the cellular slime moulds

In social selection the phenotype of an individual depends on its own genotype as well as on the phenotypes, and so genotypes, of other individuals. This makes it impossible to associate an invariant phenotype with a genotype: the social context is crucial. Descriptions of metazoan development, which often is viewed as the acme of cooperative social behaviour, ignore or downplay this fact. The implicit justification for doing so is based on a group-selectionist point of view. Namely, embryos are clones, therefore all cells have the same evolutionary interest, and the visible differences between cells result from a common strategy. The reasoning is flawed, because phenotypic heterogeneity within groups can result from contingent choices made by cells from a flexible repertoire as in multicellular development. What makes that possible is phenotypic plasticity, namely the ability of a genotype to exhibit different phenotypes. However, co-operative social behaviour with division of labour requires that different phenotypes interact appropriately, not that they belong to the same genotype, or have overlapping genetic interests. We sketch a possible route to the evolution of social groups that involves many steps: (a) individuals that happen to be in spatial proximity benefit simply by virtue of their number; (b) traits that are already present act as preadaptations and improve the efficiency of the group; and (c) new adaptations evolve under selection in the social context-that is, via interactions between individuals-and further strengthen group behaviour. The Dictyostelid or cellular slime mould amoebae (CSMs) become multicellular in an unusual way, by the aggregation of free-living cells. In nature the resulting group can be genetically homogeneous (clonal) or heterogeneous (polyclonal); in either case its development, which displays strong cooperation between cells (to the extent of so-called altruism) is not affected. This makes the CSMs exemplars for the study of social behaviour.

Why the Definition of Eusociality Is Not Helpful to Understand Its Evolution and What Should We Do about It

The evolution of altruism is the central problem of the evolution of eusociality. The evolution of altruism is most likely to be understood by studying species that show altruism in spite of being capable of ''selfish'' individual reproduction. But the definition of eusociality groups together primitively eusocial species where workers retain the ability to reproduce on their own and highly eusocial species where workers have lost reproductive options. At the same time it separates the primitively eusocial species from semisocial species, species that lack life-time sterility and cooperatively breeding birds and mammals, in most of which, altruism and the associated social life are facultative. The definition of eusociality is also such that it is sometimes difficult to decide,what is eusocial and what is not. I therefore suggest that, (1) we expand the scope of eusociality to include semisocial species, primitively eusocial species, highly eusocial species as well as those cooperatively breeding birds and mammals where individuals give up substantial or all personal reproduction for aiding conspecifics, (2) there should be no requirement of overlap of generations or of life-time sterility and (3) the distinction between primitively and highly eusocial should continue, based on the presence or absence of morphological caste differentiation.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

A note on a class of singular integro-differential equations

A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions

Brownian dynamics simulation of dense binary colloidal mixtures. I. Structural evolution and dynamics

We have carried out Brownian dynamics simulations of binary mixtures of charged colloidal suspensions of two different diameter particles with varying volume fractions phi and charged impurity concentrations n(i). For a given phi, the effective temperature is lowered in many steps by reducing n(i) to see how structure and dynamics evolve. The structural quantities studied are the partial and total pair distribution functions g(tau), the static structure factors, the time average g(<(tau)over bar>), and the Wendt-Abraham parameter. The dynamic quantity is the temporal evolution of the total meansquared displacement (MSD). All these parameters show that by lowering the effective temperature at phi = 0.2, liquid freezes into a body-centered-cubic crystal whereas at phi = 0.3, a glassy state is formed. The MSD at intermediate times shows significant subdiffusive behavior whose time span increases with a reduction in the effective temperature. The mean-squared displacements for the supercooled liquid with phi = 0.3 show staircase behavior indicating a strongly cooperative jump motion of the particles.

Magnetic and spin evolution of pulsars

We explore the consequences of the model of spin-down-induced flux expulsion for the magnetic field evolution in solitary as well as in binary neutron stars. The spin evolution of pulsars, allowing for their field evolution according to this model, is shown to be consistent with the existing observational constraints in both low- and high-mass X-ray binary systems. The contribution from pulsars recycled in massive binaries to the observed excess in the number of low-field (10(11)-10(12) G) solitary pulsars is argued to be negligible in comparison with that of normal pulsars undergoing a 'restricted' field decay predicted by the adopted field decay model. Magnetic fields of neutron stars born in close binaries with intermediate- or high-mass main-sequence companions are predicted to decay down to values as low as similar to 10(6) G, which would leave them unobservable as pulsars during most of their lifetimes. The post-recycling evolution of some of these systems can, however, account for the observed binary pulsars having neutron star or massive white dwarf companions. Pulsars recycled in the disc population low-mass binaries are expected to have residual fields greater than or similar to 10(8) G, while for those processed in globular clusters larger residual fields are predicted because of the lower field strength of the neutron star at the epoch of binary formation. A value of tau similar to 1-2 x 10(7) yr for the mean value of the Ohmic decay time-scale in the crusts of neutron stars is suggested, based on the consistency of the model predictions with the observed distribution of periods and magnetic fields in the single and binary pulsars.

Perturbative growth of cosmological clustering .2. The two-point correlation

We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two-point correlation and the pair velocity for Gaussian initial conditions in a critical density matter-dominated cosmological model. We compare our results with the results obtained using the hydrodynamic equations that neglect pressure and find that the two match, indicating that there are no effects of multistreaming at this order of perturbation. We analytically study the effect of small scales on the large scales by calculating the nonlinear correction for a Dirac delta function initial two-point correlation. We find that the induced two-point correlation has a x(-6) behavior at large separations. We have considered a class of initial conditions where the initial power spectrum at small k has the form k(n) with 0 < n less than or equal to 3 and have numerically calculated the nonlinear correction to the two-point correlation, its average over a sphere and the pair velocity over a large dynamical range. We find that at small separations the effect of the nonlinear term is to enhance the clustering, whereas at intermediate scales it can act to either increase or decrease the clustering. At large scales we find a simple formula that gives a very good fit for the nonlinear correction in terms of the initial function. This formula explicitly exhibits the influence of small scales on large scales and because of this coupling the perturbative treatment breaks down at large scales much before one would expect it to if the nonlinearity were local in real space. We physically interpret this formula in terms of a simple diffusion process. We have also investigated the case n = 0, and we find that it differs from the other cases in certain respects. We investigate a recently proposed scaling property of gravitational clustering, and we find that the lowest order nonlinear terms cause deviations from the scaling relations that are strictly valid in the linear regime. The approximate validity of these relations in the nonlinear regime in l(T)-body simulations cannot be understood at this order of evolution.

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface-in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of the n-locus genetic system moves on the surface of the product space of n higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.