Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Preparation of cast aluminium alloy-mica particle composites

The optimum conditions for producing cast aluminium alloy-mica particle composites, by stirring mica particles (40 to 120 mgrm) in molten aluminium alloys (above their liquidus temperatures), followed by casting in permanent moulds, are described. Addition of magnesium either as pieces along with mica particles on the surface of the melts or as a previously added alloying element was found to be necessary to disperse appreciable quantities (1.5 to 2 wt.%) of mica particles in the melts and retain them as uniform dispersions in castings under the conditions of present investigation. These castings can be remelted and degassed with nitrogen at least once with the retention of about 80% mica particles in the castings. Electron probe micro-analysis of these cast composites showed that magnesium added to the surface of the melt along with mica has a tendency to segregate around the mica particles, apparently improving the dispersability for mica particles in liquid aluminium alloys. The mechanical properties of the aluminium alloy-mica particle composite decrease with an increase in mica content, however, even at 2.2% the composite has a tensile strength of 14.22 kg mm–2 with 1.1% elongation, a compression strength of 42.61 kg mm–2, and an impact strength of 0.30 kgm cm–2. The properties are adequate for certain bearing applications, and the aluminium-mica composite bearings were found to run under boundary lubrication, semi-dry and dry friction conditions whereas the matrix alloy (without mica) bearings seized or showed stick slip under the same conditions.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Specific polyadenylation and purification of total messenger RNA from Escherichia coli

Obtaining pure mRNA preparations from prokaryotes has been difficult, if not impossible, for want of a poly(A) tail on these messages, We have used poly(A) polymerase from yeast to effect specific polyadenylation of Escherichia coli polysomal mRNA in the presence of magnesium and manganese, The polyadenylated total mRNA, which could be subsequently purified by binding to and elution from oligo(dT) beads, had a size range of 0.4-4.0 kb. We have used hybridization to a specific plasmid-encoded gene to further confirm that the polyadenylated species represented mRNA, Withdrawal of Mg2+ from the polyadenylation reaction rRNA despite the presence of Mn2+, indicating the vital role of Mg2+ in maintaining the native structure of polysomes, Complete dissociation of polysomes into ribosomal subunits resulted in quantitative polyadenylation of both 16S and 23S rRNA species, Chromosomal lacZ gene-derived messages were quantitatively recovered in the oligo(dT)-bound fraction, as demonstrated by RT-PCR analysis, Potential advantages that accrue from the availability of pure total mRNA from prokaryotes is discussed.

DNA-condensing and chromatin-condensing properties of rat testes hla and hit compared to those of rat-liver hlbdec - hlt is a poor condenser of chromatin

Histones H1a and H1t are two major linker histone variants present at the pachytene interval of mammalian spermatogenesis. The DNA- and chromatin-condensing properties of these two variants isolated from rat testes were studied and compared with those from rat liver. For this purpose, the histone H1 subtypes were purified from the respective tissues using bath acid and salt extraction procedures, Circular dichroism studies revealed that acid exposure during isolation affects the alpha-helical structure of both the globular domain (in the presence of 1 M NaCl) and the C-terminal lambda-tail (in the presence of 60% trifluoroethanol). The condensation of rat oligonucleosomal DNA, as measured by circular dichroism spectroscopy, by the salt-extracted histone H1 was at least 10 times more efficient than condensation by the acid-extracted histone H1. A site size of 16-20 base pairs was calculated for the salt-extracted histone H1. Among the different histone H1 subtypes, somatic histone H1bdec had the highest DNA-condensing property, followed by histone H1a and histone H1t. All the salt-extracted histones condensed rat oligonucleosomal DNA more efficiently than linear pBR-322 DNA, Histones H1bdec and H1a condensed histone H1-depleted chromatin, prepared from rat liver nuclei, with relatively equal efficiency. On the other hand, there was no condensation of histone H1-depleted chromatin with the testes specific histone H1t. A comparison of the amino acid sequences of histone H1d (rat) and histone H1t (rat) revealed several interesting differences in the occurrence of DNA-binding motifs at the C-terminus. A striking observation is the presence of a direct repeat of an octapeptide motif K(A)T(S)PKKA(S)K(T)K(A) in histone H1d that is absent in histone H1t.

Co(II) and Cr(III) complexes of formate-formamide mixed ligands: synthesis, structures, single crystal-to-single crystal transformation and magnetic behaviour

Solvothermal treatment of an equimolar mixture of Co(NO3)(2)center dot 6H(2)O, HCONH2 and NaN3 in MeOH at 100 degrees C yielded a three-dimensional NaCl type network Co(HCOO)(2)(HCONH2)(2) center dot HCONH2 (1a) containing formamides in the pores of the structure. Solvated pink 1a undergoes single crystal-to-single crystal (SCSC) transformation at 215 degrees C to form the desolvated dark brown product Co(HCOO)(2)-( HCONH2)(2) (1b) with the retention of the original framework. Reversible single crystal-to-single crystal transformation of 1b (brown) to 1a (pink) in the presence of excess formamide was also established at room temperature. The coordination environment around Co(II) in both 1a and 1b is octahedral with a CoN2O4 coordination composition. A similar reaction replacing Co(II) by Cr(III) produced a heterometallic 3D extended network Na[Cr(HCOO)(4)(HCONH2)(2)]center dot 2H(2)O (2a) at 100 degrees C. An increase in reaction temperature to 150 degrees C produced a simple mononuclear complex Cr(HCOO)(3)(HCONH2)(3) center dot 3H(2)O (2b). Variable temperature magnetic studies revealed the presence of a canting phenomena in both 1a and 1b, and hysteresis loop in the field dependent magnetisation plot at 2 K whereas complex 2a is simply paramagnetic in nature.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

lac Repressor Is an Antivirulence Factor of Salmonella enterica: Its Role in the Evolution of Virulence in Salmonella

The genus Salmonella includes many pathogens of great medical and veterinary importance. Bacteria belonging to this genus are very closely related to those belonging to the genus Escherichia. lacZYA operon and lacI are present in Escherichia coli, but not in Salmonella enterica. It has been proposed that Salmonella has lost lacZYA operon and lacI during evolution. In this study, we have investigated the physiological and evolutionary significance of the absence of lacI in Salmonella enterica. Using murine model of typhoid fever, we show that the expression of Lacl causes a remarkable reduction in the virulence of Salmonella enterica. Lacl also suppresses the ability of Salmonella enterica to proliferate inside murine macrophages. Microarray analysis revealed that Lacl interferes with the expression of virulence genes of Salmonella pathogenicity island 2. This effect was confirmed by RT-PCR and Western blot analysis. Interestingly, we found that SBG0326 of Salmonella bongori is homologous to lacI of Escherichia coli. Salmonella bongori is the only other species of the genus Salmonella and it lacks the virulence genes of Salmonella pathogenicity island 2. Overall, our results demonstrate that Lacl is an antivirulence factor of Salmonella enterica and suggest that absence of lacI has facilitated the acquisition of virulence genes of Salmonella pathogenicity island 2 in Salmonella enterica making it a successful systemic pathogen.

Mechanics of Deformation under Traction and Friction of a Micrometric Monolithic MoS2 Particle in Comparison with those of an Agglomerate of Nanometric MoS2 Particles

Tribology of small inorganic nanoparticles in suspension in a liquid lubricant is often impaired because these particles agglomerate even when organic dispersants are used. In this paper we use lateral force microscopy to study the deformation mechanism and dissipation under traction of two extreme configurations (1) a large MoS2 particle (similar to 20 mu m width) of about 1 mu m height and (2) an agglomerate (similar to 20 mu m width), constituting 50 nm MoS2 crystallites, of about 1 mu m height. The agglomerate records a friction coefficient which is about 5-7 times that of monolithic particle. The paper examines the mechanisms of material removal for both the particles using continuum modeling and microscopy and infers that while the agglomerate response to traction can be accounted for by the bulk mechanical properties of the material, intralayer and interlayer basal planar slips determine the friction and wear of monolithic particles. The results provide a rationale for selection of layered particles, for suspension in liquid lubricants.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Mechanism of failure in a free-standing Pt-aluminide bond coat during tensile testing at room temperature

The room temperature (RT) tensile behaviour of a free-standing high activity Pt-aluminide bond coat has been evaluated by microtensile testing technique. The coating had a typical three-layer microstructure. The stress-strain plot for the free-standing coating was linear, indicating the coating to be brittle at RT. Different fracture features were observed across the coating layers, namely quasi-cleavage in the outer layer and inner interdiffusion zone, and cleavage in the intermediate layer. By employing interrupted tensile test and observing the cross-sectional microstructure of the tested specimens, it was determined that failure of the microtensile samples occurred by the initiation of a single crack in the intermediate layer of the coating and its subsequent inside-out propagation. Such a mechanism of failure has been explained in terms of the fracture features observed across the sample thickness. This mechanism of failure is consistent with fracture toughness values of the individual coating layers. (C) 2009 Elsevier B.V. All rights reserved.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Crystallite size effects in stacking faulted nickel hydroxide and its electrochemical behaviour

P-Nickel hydroxide comprises a long range periodic arrangement of atoms with a stacking sequence of AC AC AC-having an ideal composition Ni(OH)(2). Variation in the preparative conditions can lead to the changes in the stacking sequence (AC AC BA CB AC AC or AC AC AB AC AC) This type of variation in stacking sequence can result in the formation of stacking fault in nickel hydroxide. The stability of the stacking fault depends on the free energy content of the sample. Stacking faults in nickel hydroxide is essential for better electrochemical activity. Also there are reports correlating particle size to the better electrochemical activity. Here we present the effect of crystallite size on the stacking faulted nickel hydroxide samples. The electrochemical performance of stacking faulted nickel hydroxide with small crystallite size exchanges 0.8e/Ni, while the samples with larger crystallite size exchange 0.4e/Ni. Hence a right combination of crystallite size and stacking fault content has to be controlled for good electrochemical activity of nickel hydroxide. (C) 2008 Elsevier B.V. All rights reserved.

Transonic Properties of Accretion Disk Around Compact Objects

An accretion flow is necessarily transonic around a black hole. However, around a neutron star it may or may not be transonic, depending on the inner disk boundary conditions influenced by the neutron star. I will discuss various transonic behavior of the disk fluid in general relativistic (or pseudo general relativistic) framework. I will address that there are four types of sonic/critical point. possible to form in an accretion disk. It will be shown that how the fluid properties including location of sonic point's vary with angular momentum of the compact object which controls the overall disk dynamics and outflows.

Structural transformations in Mn2NiGa due to residual stress

Powder x-ray diffraction study of Mn2NiGa ferromagnetic shape memory alloy shows the existence of a 7M monoclinic modulated structure at room temperature (RT). The structure of Mn2NiGa is found to be highly dependent on residual stress. For higher stress, the structure is tetragonal at RT, and for intermediate stress it is 7M monoclinic. However, only when the stress is considerably relaxed, the structure is cubic, as is expected at RT since the martensitic transition temperature is 230 K.