Quasichemical equations for oxygen and sulphur in liquid binary alloys

An equation has been derived for predicting the activity coefficient of oxygen or sulphur in dilute solution in binary alloys, based on the quasichemical approach, where the metal atoms and the oxygen atoms are assigned different bond numbers. This equation is an advance on Alcock and Richardson's earlier treatment where all the three types of atoms were assigned the same coordination number. However, the activity coefficients predicted by this new equation appear to be very similar to those obtained through Alcock and Richardson's equation for a number of alloy systems, when the coordination number of oxygen in the new model is the same as the average coordination number used in the earlier equation. A second equation based on the formation of “molecular species” of the type XnO and YnO in solution is also derived, where X and Y atoms attached to oxygen are assumed not to make any other bonds. This equation does not fit experimental data in all the systems considered for a fixed value of n. Howover, if the strong oxygen-metal bonds are assumed to distort the electronic configuation around the metal atoms bonded to oxygen and thus reduce the strength of the bonds formed by these atoms with neighbouring metal atoms by approximately a factor of two, the resulting equation is found to predict the activity coefficients of oxygen that are in good agreement with experimental data in a number of binary alloys.

Galois Theory and Solvable Equations of Prime Degree

In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

Functional Analysis of DNA Replication Fork Reversal Catalyzed by Mycobacterium tuberculosis RuvAB Proteins

Initially discovered in Escherichia coli, RuvAB proteins are ubiquitous in bacteria and play a dual role as molecular motor proteins responsible for branch migration of the Holliday junction(s) and reversal of stalled replication forks. Despite mounting genetic evidence for a crucial role of RuvA and RuvB proteins in reversal of stalled replication forks, the mechanistic aspects of this process are still not fully understood. Here, we elucidate the ability of Mycobacterium tuberculosis RuvAB (MtRuvAB) complex to catalyze the reversal of replication forks using a range of DNA replication fork substrates. Our studies show that MtRuvAB, unlike E. coli RuvAB, is able to drive replication fork reversal via the formation of Holliday junction intermediates, suggesting that RuvAB-catalyzed fork reversal involves concerted unwinding and annealing of nascent leading and lagging strands. We also demonstrate the reversal of replication forks carrying hemi-replicated DNA, indicating that MtRuvAB complex-catalyzed fork reversal is independent of symmetry at the fork junction. The fork reversal reaction catalyzed by MtRuvAB is coupled to ATP hydrolysis, is processive, and culminates in the formation of an extended reverse DNA arm. Notably, we found that sequence heterology failed to impede the fork reversal activity of MtRuvAB. We discuss the implications of these results in the context of recognition and processing of varied types of replication fork structures by RuvAB proteins.

Functional regulation of PVBV Nuclear Inclusion protein-a protease activity upon interaction with Viral Protein genome-linked and phosphorylation

Regulation of NIa-Pro is crucial for polyprotein processing and hence, for successful infection of potyviruses. We have examined two novel mechanisms that could regulate NIa-Pro activity. Firstly, the influence of VPg domain on the proteolytic activity of NIa-Pro was investigated. It was shown that the turnover number of the protease increases when these two domains interact (as: two-fold; trans: seven-fold) with each other. Secondly, the protease activity of NIa-Pro could also be modulated by phosphorylation at Ser129. A mutation of this residue either to aspartate (phosphorylation-mimic) or alanine (phosphorylation-deficient) drastically reduces the protease activity. Based on these observations and molecular modeling studies, we propose that interaction with VPg as well as phosphorylation of Ser129 could relay a signal through Trp143 present at the protein surface to the active site pocket by subtle conformational changes, thus modulating protease activity of NIa-Pro. (C) 2011 Elsevier Inc. All rights reserved.

A computational procedure to generate difference equations from differential equations

In this paper we have developed methods to compute maps from differential equations. We take two examples. First is the case of the harmonic oscillator and the second is the case of Duffing's equation. First we convert these equations to a canonical form. This is slightly nontrivial for the Duffing's equation. Then we show a method to extend these differential equations. In the second case, symbolic algebra needs to be used. Once the extensions are accomplished, various maps are generated. The Poincare sections are seen as a special case of such generated maps. Other applications are also discussed.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

On the solution of bivariate population balance equations for aggregation: Pivotwise expansion of solution domain

The solution of a bivariate population balance equation (PBE) for aggregation of particles necessitates a large 2-d domain to be covered. A correspondingly large number of discretized equations for particle populations on pivots (representative sizes for bins) are solved, although at the end only a relatively small number of pivots are found to participate in the evolution process. In the present work, we initiate solution of the governing PBE on a small set of pivots that can represent the initial size distribution. New pivots are added to expand the computational domain in directions in which the evolving size distribution advances. A self-sufficient set of rules is developed to automate the addition of pivots, taken from an underlying X-grid formed by intersection of the lines of constant composition and constant particle mass. In order to test the robustness of the rule-set, simulations carried out with pivotwise expansion of X-grid are compared with those obtained using sufficiently large fixed X-grids for a number of composition independent and composition dependent aggregation kernels and initial conditions. The two techniques lead to identical predictions, with the former requiring only a fraction of the computational effort. The rule-set automatically reduces aggregation of particles of same composition to a 1-d problem. A midway change in the direction of expansion of domain, effected by the addition of particles of different mean composition, is captured correctly by the rule-set. The evolving shape of a computational domain carries with it the signature of the aggregation process, which can be insightful in complex and time dependent aggregation conditions. (c) 2012 Elsevier Ltd. All rights reserved.

Functional characterization of UvrD helicases from Haemophilus influenzae and Helicobacter pylori

Haemophilus influenzae and Helicobacter pylori are major bacterial pathogens that face high levels of genotoxic stress within their host. UvrD, a ubiquitous bacterial helicase that plays important roles in multiple DNA metabolic pathways, is essential for genome stability and might, therefore, be crucial in bacterial physiology and pathogenesis. In this study, the functional characterization of UvrD helicase from Haemophilus influenzae and Helicobacter pylori is reported. UvrD from Haemophilus influenzae (HiUvrD) and Helicobacter pylori (HpUvrD) exhibit strong single-stranded DNA-specific ATPase and 3'5' helicase activities. Mutation of highly conserved arginine (R288) in HiUvrD and glutamate (E206) in HpUvrD abrogated their activities. Both the proteins were able to bind and unwind a variety of DNA structures including duplexes with strand discontinuities and branches, three- and four-way junctions that underpin their role in DNA replication, repair and recombination. HiUvrD required a minimum of 12 nucleotides, whereas HpUvrD preferred 20 or more nucleotides of 3'-single-stranded DNA tail for efficient unwinding of duplex DNA. Interestingly, HpUvrD was able to hydrolyze and utilize GTP for its helicase activity although not as effectively as ATP, which has not been reported to date for UvrD characterized from other organisms. HiUvrD and HpUvrD were found to exist predominantly as monomers in solution together with multimeric forms. Noticeably, deletion of distal C-terminal 48 amino acid residues disrupted the oligomerization of HiUvrD, whereas deletion of 63 amino acids from C-terminus of HpUvrD had no effect on its oligomerization. This study presents the characteristic features and comparative analysis of Haemophilus influenzae and Helicobacter pylori UvrD, and constitutes the basis for understanding the role of UvrD in the biology and virulence of these pathogens.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

Dual functional performance of fiber Bragg gratings coated with metals using flash evaporation technique

Metallic and other type of coatings on fiber Bragg grating (FBG) sensors alter their sensitivity with thermal and mechanical stress while protecting the fragile optical fiber in harsh sensing surroundings. The behavior of the coated materials is unique in their response to thermal and mechanical stress depending on the thickness and the mode of coating. The thermal stress during the coating affects the temperature sensitivity of FBG sensors. We have explored the thermal response of FBGs coated with Al and Pb to an average thickness of 80 nm using flash evaporation technique where the FBG sensor is mounted in a region at room temperature in an evacuated chamber having a pressure of 10(6) Torr which will minimize any thermal stress during the coating process. The coating thickness is chosen in the nanometer region with the aim to study thermal behavior of nanocoatings and their effect on FBG sensitivity. The sensitivity of FBGs is evaluated from the wavelengths recorded using an optical sensing interrogator sm 130 (Micron Optics) from room temperature to 300 degrees C both during heating and cooling. It is observed that the sensitivity of the metal coated fibers is better than the reference FBG with no coating for the entire range of temperature. For a coating thickness of 80 nm, Al coated FBG is more sensitive than the one coated with Pb up to 170 degrees C and it reverses at higher temperatures. This point is identified as a reversible phase transition in Pb monolayers as the 2-dimensional aspects of the metal layers are dominant in the nanocoatings of Pb. On cooling, the phase transition reverses and the FBGs return to the original state and for repeated cycles of heating and cooling the same pattern is observed. Thus the FBG functions as a sensor of the phase transitions of the coatings also. (C) 2012 Elsevier Inc. All rights reserved.

SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Ito form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order gamma = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

Functional Analysis of the Genes Encoding Diaminopropionate Ammonia Lyase in Escherichia coli and Salmonella enterica Serovar Typhimurium

Diaminopropionate ammonia lyase (DAPAL) is a pyridoxal-5'phosphate (PLP)-dependent enzyme that catalyzes the conversion of diaminopropionate (DAP) to pyruvate and ammonia and plays an important role in cell metabolism. We have investigated the role of the ygeX gene of Escherichia coli K-12 and its ortholog, STM1002, in Salmonella enterica serovar Typhimurium LT2, presumed to encode DAPAL, in the growth kinetics of the bacteria. While Salmonella Typhimurium LT2 could grow on DL-DAP as a sole carbon source, the wild-type E. coli K-12 strain exhibited only marginal growth on DL-DAP, suggesting that DAPAL is functional in S. Typhimurium. The expression of ygeX in E. coli was low as detected by reverse transcriptase PCR (RT-PCR), consistent with the poor growth of E. coli on DL-DAP. Strains of S. Typhimurium and E. coli with STM1002 and ygeX, respectively, deleted showed loss of growth on DL-DAP, confirming that STM1002 (ygeX) is the locus encoding DAPAL. Interestingly, the presence of DL-DAP caused a growth inhibition of the wild-type E. coli strain as well as the knockout strains of S. Typhimurium and E. coli in minimal glucose/glycerol medium. Inhibition by DL-DAP was rescued by transforming the strains with plasmids containing the STM1002 (ygeX) gene encoding DAPAL or supplementing the medium with Casamino Acids. Growth restoration studies using media lacking specific amino acid supplements suggested that growth inhibition by DL-DAP in the absence of DAPAL is associated with auxotrophy related to the inhibition of the enzymes involved in the biosynthetic pathways of pyruvate and aspartate and the amino acids derived from them.