Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Phenyl-Ring-Bearing Cationic Surfactants: Effect of Ring Location on the Micellar Structure

A series of isomeric cationic surfactants (S1-S5) bearing a long alkyl chain that carries a 1,4-phenylene unit and a trimethyl ammonium headgroup was synthesized; the location of the phenyl ring within the alkyl tail was varied in an effort to understand its influence on the amphiphilic properties of the surfactants. The cmc's of the surfactants were estimated using ionic conductivity measurements and isothermal calorimetric titrations (ITC); the values obtained by the two methods were found to be in excellent agreement. The ITC measurements provided additional insight into the various thermodynamic parameters associated with the micellization process. Although all five surfactants have exactly the same molecular formula, their micellar properties were seen to vary dramatically depending on the location of the phenyl ring; the cmc was seen to decrease by almost an order of magnitude when the phenyl ring was moved from the tail end (cmc of S1 is 23 mM) to the headgroup region (cmc of S5 is 3 mM). In all cases, the enthalpy of micellization was negative but the entropy of micellization was positive, suggesting that in all of these systems the formation of micelles is both enthalpically and entropically favored. As expected, the decrease in cmc values upon moving the phenyl ring from the tail end to he headgroup region is accompanied by an increase in the thermodynamic driving force (Delta G) for micellization. To understand further the differences in the micellar structure of these surfactants, small-angle neutron scattering (SANS) measurements were carried out; these measurements reveal that the aggregation number of the micelles increases as the cmc decreases. This increase in the aggregation number is also accompanied by an increase in the asphericity of the micellar aggregate and a decrease in the fractional charge. Geometric packing arguments are presented to account for these changes in aggregation behavior as a function of phenyl ring location.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Improved mechanical properties of polymer nanocomposites incorporating graphene-like BN: Dependence on the number of BN layers

The mechanical properties of composites of polymethylmethacrylate (PMMA) with two-dimensional graphene-like boron nitride (BN) have been investigated to explore the dependence of the properties on the number of BN layers. This study demonstrates that significantly improved mechanical properties are exhibited by the composite with the fewest number of BN layers. Thus, with incorporation of three BN layers, the hardness and elastic modulus of the composite showed an increase of 125% and 130%, respectively, relative to pure PMMA. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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.

Five-level inverter scheme for an open-end winding induction machine with less number of switches

Higher level of inversion is achieved with a less number of switches in the proposed scheme. The scheme proposes a five-level inverter for an open-end winding induction motor which uses only two DC-link rectifiers of voltage rating of Vdc/4, a neutral-point clamped (NPC) three-level inverter and a two-level inverter. Even though the two-level inverter is connected to the high-voltage side, it is always in square-wave operation. Since the two-level inverter is not switching in a pulse width modulated fashion and the magnitude of switching transient is only half compared to the convention three-level NPC inverter, the switching losses and electromagnetic interference is not so high. The scheme is experimentally verified on a 2.5 kW induction machine.

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024(3) collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr-M over a large range, namely 0.01 <= Pr-M <= 10. We obtain data for a wide variety of statistical measures, such as probability distribution functions (PDFs) of the moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterize intermittency, isosurfaces of quantities, such as the moduli of the vorticity and current density, and joint PDFs, such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from a larger intermittency in the magnetic field than in the velocity field, at large Pr-M, to a smaller intermittency in the magnetic field than in the velocity field, at low Pr-M. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr-M, multiscaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

ChemInform Abstract: Synthesis of Anion-Deficient Layered Perovskites, ACa2Nb3-xMxO10-x (A: Rb, Cs; M: Al, Fe), Exhibiting Ion-Exchange and Intercalation. Evidence for the Formation of Layered Brownmillerites, ACa2Nb2AlO9 (A: Cs, H)

Anion-deficient layered perovskite oxides of the formula, ACa2Nb3-xMxO10-x (A = Rb, Cs; M = Al, Fe) for 0 < x less-than-or-equal-to 1.0, possessing tetragonal structures similar to the parent ACa2Nb3O10, have been synthesized. The interlayer A cations in these materials are readily exchanged with protons in aqueous HNO3 to give the protonated derivatives, HCa2Nb3-xMxO10-x; the latter are solid Bronsted acids intercalating a number of organic amines including aniline (pK(a) = 4.63). The distribution of acid sites in the interlayer region of HCa2Nb2MO9 inferred from n-alkylamine intercalation suggests that oxygen vacancies and Nb/M atoms are disordered in the ACa2Nb2MO9 samples prepared at 1100-1200-degrees-C. Annealing a disordered sample of CsCa2Nb2AlO9 for a long time at lower temperatures tends to order the Nb/Al atoms and oxygen vacancies to produce octahedral (NbO6/2)-tetrahedral (AlO4/2)-octahedral (NbO6/2) layer sequence reminiscent of the brownmillerite structure.

Unsteady nonsimilar two-dimensional and axisymmetric water boundary layers with variable viscosity and prandtl number

The influence of temperature-dependent viscosity and Prandtl number on the unsteady laminar nonsimilar forced convection flow over two-dimensional and axisymmetric bodies has been examined where the unsteadiness and (or) nonsimilarity are (is) due to the free stream velocity, mass transfer, and transverse curvature. The partial differential equations governing the flow which involve three independent variables have been solved numerically using an implicit finite-difference scheme along with a quasilinearization technique. It is found that both the skin friction and heat transfer strongly respond to the unsteady free stream velocity distributions. The unsteadiness and injection cause the location of zero skin friction to move upstream. However, the effect of variable viscosity and Prandtl number is to move it downstream. The heat transfer is found to depend strongly on viscous dissipation, but the skin friction is little affected by it. In general, the results pertaining to variable fluid properties differ significantly, from those of constant fluid properties.

Differential influence of ions on the copy number of plasmids in Thiobacillus ferrooxidans

Thiobacillus ferrooxidans MAL4-1, an isolate from Malanjkhand copper mines, India, was adapted to grow in the presence of high concentration (30 gL(-1)) of Cu2+, resulting in a 15-fold increase in its tolerance to Cu2+. While wild-type T. ferrooxidans MAL4-1 contained multiple plasmids, cultures adapted to Cu2+ concentrations of 20 gL(-1) or more showed a drastic reduction in the copy number of the plasmids. The reduction for three of the plasmids was estimated to be over 50-fold. Examination of the plasmid profiles of the strains adapted to high concentration of SO42- anion (as Na2SO4 or ZnSO4) indicated that the reduction in plasmid copy number is not owing to SO42- anion, but is specific for Cu2+. The effect of mercury on the plasmids was similar to that of copper. Deadaptation of the Cu2+- Or Hg2+-adapted T. ferrooxidans resulted in restoration of the plasmids to the original level within the first passage. The fact that the plasmid copy number, in general, is drastically reduced in Cu2+-adapted T. ferrooxidans suggests that resistance to copper is chromosome mediated. This is the first report of a selective negative influence of copper ions on the copy number of plasmids in T. ferrooxidans.

Phosphate derivatives of 123 cuprates of the formula LnSr(2)Cu(3)O(7) (Ln=Gd, Dy, Ho)

Partial substitution of Cu in the chain by the phosphate ion stabilizes LnSr(2)Cu(3)O(7) (Ln = Gd, Dy or Ho) in the 123 structure. The LnSr(2)Cu(2.8)(PO4)(0.2)O-y derivatives exhibit incommensurately modulated structures. The holmium oxy-phosphate derivative has been rendered superconducting by the partial substitution of Ho by Ca.

Japanese encephalitis virus infection of mouse cell lines: ability to prime mice for generation of virus specific cytotoxic T lymphocytes and differences in CTL recognisable viral determinants

Ten different mouse cell lines were examined for Japanese encephalitis virus (JEV) infection in vitro and then tested for their ability to generate virus specific cytotoxic T lymphocytes (CTL). Among all cell lines examined, Neuro La (a neuroblastoma) was readily infected with JEV as examined by immunofluorescence and viral replication. Among other cells, P388D1, RAW 264.7 (Macrophage origin), Sp2/0 (B-cell Hybridoma), YAC-1 (T-cell lymphoma), and L929 (Fibroblast) were semipermissive to JEV infection. The cytopathic effects caused by progressive JEV infection varied from cell line to cell line. In the case of YAC-1 cells long-term viral antigen expression was observed without significant alterations in cell viability. Intermediate degrees of cytopathicity are seen in RAW 264.7 and L929 cells while infection of PS, Neuro 2a, P388D1 and Sp2/0 caused major viability losses. All infected cell lines were able to prime adult BALB/c (H-2(d)) mice for the generation of secondary JEV specific CTL. In contrast to YAC-1, the permissive neuroblastoma cell line Neuro 2a (H-2K(k)D(d)) was found to be least efficient in its ability to stimulate anti-viral CTL generation. Cold target competition studies demonstrated that both Neuro 2a and YAC-1 (H-2K(k)D(d)) cells expressed similar viral determinants that are recognised by CTL, suggesting that the reason for the lower ability of Neuro 2a to stimulate anti-viral CTL was not due to lack of viral CTL determinants. These findings demonstrate that a variety of mouse cell lines can be infected with Japanese encephalitis virus, and that these infected cells could be utilised to generate virus specific CTL in BALB/c mice.