A formula for the solution of general Abel integral equation

A new formula for the solution of the general Abel Integral equation is derived, and an important special case is checked with the known result.

Structure evolution and phase change in Ag-5.1 at.% Bi alloy during mechanical alloying

In this paper we explore the enhancement of solubility in a mechanically driven immiscible system experimentally using a mixture of Ag and Bi powders corresponding to a composition of Ag-5.1 at.% Bi. Increase in solubility can be correlated with the combination of sizes of both Ag and Bi at the nanometric scale. It is shown that complete solid solution of Ag-5.1 at.% Bi forms when the respective sizes of :Bi and Ag exceed 13 and 8 nm respectively. We have carried out a thermodynamic analysis of the size- and strain-dependent free energy landscape and compared the results to the initial mixture of microsized particles to rationalize the evolution of Ag solid solution. The agreement indicates that the emerging driving force for the formation of solid solution is primarily due to size reduction rather than the enhanced kinetics of mass transport due to mechanical driving. (c) 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc.

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to 1/4 pi. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.

Exact N-Wave Solutions for the Non-Planar Burgers Equation

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).

Generalised one-dimensional burgers'equation in relativistic fluiddynamics

This work deals with the effects of weak nonlinearity and weak dissipation on a linear wave in relativistic gasdynamics. Using perturbation and asymptotic expansions, a relativistic analogue of generalised one-dimensional Burgers' equation of classical gasdynamics is derived to describe far-field description of the wave. Steady state solution is presented for strict one-dimensional case.

Texture Evolution in Boron Modified Ti-6Al-4V Alloy

Owing to their high strength-to-weight ratio, excellent mechanical properties and corrosion resistance, titanium (Ti) and its alloys, especially (alpha+beta) alloys like Ti-6Al-4V is the backbone materials for aerospace, energy, and chemical industries. Trace boron addition (similar to 0.1 wt. %) to the alloy Ti-6Al-4V produces a reduction in as-cast grain size by roughly an order of magnitude resulting in enhanced ductility, higher stiffness, strength and good fracture resistance. Boron addition could also affect the evolution of texture and microstructure in the material. The solidification microstructures of Boron free as well as Boron containing Ti-6Al-4V are found to be almost homogeneous from periphery towards the center of as-cast ingot in terms of both alpha-colony size and distribution. Boron addition substantially reduces alpha-colony size (similar to 50-80 mu m). A gradual change in alpha texture from periphery towards the center has been observed with orientations close to specific texture components suggesting the formation of texture zones. The mechanism of texture evolution can be visualized as a result of variant selection during solidification through (alpha+beta) phase field.

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.

On the solution of the equation ut+unux+H(x, t, u)=0

We consider the equation u(t) + u(n)u(x) + H(x, t, u) = 0 and derive a transformation relating it to u(t) + u(n)u(x) = 0. Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.

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.