Effect of random density irregularities on nonlinear evolution of Langmuir waves in interplanetary medium

The evolution of nonlinear Langmuir waves in the interplanetary medium is investigated by appropriately accounting for the random density irregularities of the medium. A pair of modified Zakharov equations, which describe these waves, is solved numerically as an initial value problem for large scale (≫ 10² km) initial pertubations. For an ion acoustic-Langmuir solitary wave, the random irregularities damp the Langmuir wave by way of scattering and let the ion density perturbation radiate away in a few days. However an initial solitary or shock-like Langmuir wave excites the ion density perturbations within a fraction of a second, and then itself gets damped. These effects will strongly decelerate the collapse of large scale Langmuir waves. The possibility of detecting these processes, by means of interplanetary scintillation, is discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Influence of power-law index on transitional Reynolds numbers for flow over a semi-circular cylinder

In this work, the governing partial differential equations (continuity and Cauchy’s momentum equations) describing the flow of power-law type non-Newtonian fluids across a semi-circular cylinder (oriented with its curved surface in the upstream direction) have been solved numerically. In particular, consideration has been given to the delineation of the critical Reynolds numbers denoting the onset of flow separation from the surface of the cylinder and the onset of the laminar vortex shedding regime. This information is germane to establish the scaling of the macroscopic characteristics like drag coefficient and Strouhal number on the governing parameters, namely, Reynolds number and power-law index. The present results clearly suggest that the transitional Reynolds numbers show a strong dependence on the type (shear-thinning and shear-thickening) of fluid behavior as well as on the severity of the shear-dependence of the viscosity. With reference to the behavior seen in Newtonian fluids, the flow remains not only attached to the surface up to higher Reynolds numbers, but shear-thinning behavior also delays the onset of the laminar vortex shedding regime. As expected, shear-thickening fluids, of course, display the opposite characteristics.     

Some results on λ‐designs with two block sizes

A λ‐design is a family ?? = {B₁, B₂, …, B_v} of subsets of X = {1, 2, …, v} such that |B_i∩B_j| = λ for all i≠jand not all B_i are of the same size. The only known example of λ‐designs (called type‐1 designs) are those obtained from symmetric designs by a certain complementation procedure. Ryser [J Algebra 10 (1968), 246–261] and Woodall [Proc London Math Soc 20 (1970), 669–687] independently conjectured that all λ‐designs are type‐1. Let g = gcd(r ? 1, r^* ? 1), where rand r^* are the two replication numbers. Ionin and Shrikhande [J Combin Comput 22 (1996), 135–142; J Combin Theory Ser A 74 (1996), 100–114] showed that λ‐designs with g = 1, 2, 3, 4 are type‐1 and that the Ryser–Woodall conjecture is true for λ‐designs on p + 1, 2p + 1, 3p + 1, 4p + 1 points, where pis a prime. Hein and Ionin [Codes and Designs—Proceedings of Conference honoring Prof. D. K. Ray‐Chaudhuri on the occasion of his 65th birthday, Ohio State University Mathematical Research Institute Publications, 10, Walter de Gruyter, Berlin, 2002, pp. 145–156] proved corresponding results for g = 5 and Fiala [Codes and Designs—Proceedings of Conference honoring Prof. D. K. Ray‐Chaudhuri on the occasion of his 65th birthday, Ohio State University Mathematical Research Institute Publications, 10, Walter de Gruyter, Berlin, 2002, pp. 109–124; Ars Combin 68 (2003), 17–32; Ars Combin, to appear] for g = 6, 7, and 8. In this article, we consider λ designs with exactly two block sizes. We show that in this case, the conjecture is true for g = 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, and for g = 10, 14, 18, 22 with v≠4λ ? 1. We also give two results on such λ‐designs on v = 9p + 1 and 12p + 1 points, where pis a prime. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:95‐110, 2011     

Physical properties of LiMn2O4 spinel prepared at moderate temperature

A moderate-temperature method of preparation of the spinel LiMn₂O₄ was developed around 500 °C. Physical features of the products were identified by X-ray photoelectron spectroscopy, X-ray diffractometry, Raman scattering and FTIR spectroscopy. The electronic conductivity of LiMn₂O₄ has been studied as a function of annealing temperature. The product LiMn₂O₄ is identified as a micron-sized powder and analysis of the local environment is in good accordance with the classical structural model of Fd3m space group. LiMn₂O₄ exhibits an electrical conductivity of 1.9×10⁻⁵ S/cm at room temperature with an activation energy of 0.16 eV which corresponds to an electron hopping mechanism between the two charge states of Mn³⁺ and Mn⁴⁺ ions. A first-order phase transition is observed at 292 K.     

Magnetic and Raman scattering studies of Co-doped ZnO thin films grown by pulsed laser deposition

Phase pure Zn_1?x Co _x O thin films grown by pulsed laser deposition have transmittance greater than 75 % in the visible region. Raman studies confirm the crystalline nature of Zn_1?x Co _x O thin films. Zn_0.95Co_0.05O thin films show room temperature ferromagnetism with saturation magnetization of 0.4μ _B /Co atom. The possible origin of paramagnetism at higher Co doping concentrations can be attributed to the increased nearest-neighbor antiferromagnetic interactions between Co²⁺ ions in ZnO matrix. XPS confirms the substitution of Co²⁺ ions into the ZnO host lattice.     

Embeddings of anisotropic Sobolev spaces on unbounded domains

Summary Integral representations of junctions in the anisotropic Sobolev spaces on unbounded domains are used in the study of the embeddings of these spaces into Lebesgue spaces. Estimates of entropy numbers of the embedding are obtained, where k, p and q satisfy certain conditions and where is a certain type of quasibounded domain,     

Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

The main object of this paper is to investigate several general families of hyper-geometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.     

Spectroscopy: the study of DNA cleavage by newly synthesized polydentate macrocyclic ligand and its copper(II) complexes

A novel hexadentate nitrogen donor [N6] macrocyclic ligand, i.e. 2,6,12,16,21,22-hexaaza-3,5,13,15-tetramethyl-4,14-diethyl-tricyclo-[15.3.1.1(7-11)]docosane-1(21),2,5,7(22),8,10,12,15,17,19-decaene (L), has been synthesized. Copper(II) complexes with this ligand have been prepared and subjected to elemental analyses, molar conductance measurements, magnetic susceptibility measurements, mass, 1H NMR (ligand), IR, electronic, and EPR spectral studies. On the basis of molar conductance the complexes may be formulated as [Cu(L)X2] [X = Cl(-), Br(-), NO3(-) and CH3COO(-)] due to their nonelectrolytic nature in N,N'-dimethylformamide (DMF). All the complexes are of the high spin type and are six coordinated. On the basis of IR, electronic and EPR spectral studies tetragonal geometry has been assigned to the Cu(II) complexes. The interaction of these complexes with calf thymus DNA has been explored by using absorption, emission, viscosity measurements, electrochemical studies and DNA cleavage. All the experimental results suggest that the complexes bind to DNA and also promote the cleavage plasmid pBR 322, in the presence of H2O2 and ascorbic acid.     

IR-UV double resonance spectroscopic investigation of phenylacetylene-alcohol complexes. Alkyl group induced hydrogen bond switching

The electronic transitions of phenylacetylene complexes with water and trifluoroethanol are shifted to the blue, while the corresponding transitions for methanol and ethanol complexes are shifted to the red relative to the phenylacetylene monomer. Fluorescence dip infrared (FDIR) spectra in the O-H stretching region indicate that, in all the cases, phenylacetylene is acting as a hydrogen bond acceptor to the alcohols. The FDIR spectrum in the acetylenic C-H stretching region shows Fermi resonance bands for the bare phenylacetylene, which act as a sensitive tool to probe the intermolecular structures. The FDIR spectra reveal that water and trifluoroethanol interact with the pi electron density of the acetylene C-C triple bond, while methanol and ethanol interact with the pi electron density of the benzene ring. It can be inferred that the hydrogen bonding acceptor site on phenylacetylene switches from the acetylene pi to the benzene pi with lowering in the partial charge on the hydrogen atom of the OH group. The most significant finding is that the intermolecular structures of water and methanol complexes are notably distinct, which, to the best of our knowledge, this is first such observation in the case of complexes of substituted benzenes.     

Dual activation in asymmetric allylsilane addition to chiral N-acylhydrazones: method development, mechanistic studies, and elaboration of homoallylic amine adducts

[reaction: see text] Chiral N-acylhydrazones derived from commercially available 4-benzyl-2-oxazolidinone provide a rigid, conformationally restricted template to impart facial selectivity in additions to C=N bonds. In the presence of indium(III) trifluoromethanesulfonate [In(OTf)3], N-acylhydrazones undergo highly diastereoselective fluoride-initiated additions of allylsilanes (aza-Sakurai reaction). Mechanistic studies including control experiments and comparisons with allyltributylstannane, allylmagnesium bromide, and allylindium species implicate a dual activation mechanism involving addition of an allylfluorosilicate species to a chelate formed from In(OTf)3 and the chiral N-acylhydrazone. The N-N bonds of the adducts are readily cleaved in a two-step protocol to provide synthetically useful homoallylic N-trifluoroacetamides. Further elaboration of the latter compounds through Wacker oxidation and olefin metathesis provides diversely functionalized building blocks and expands the potential applications of this C-C bond construction approach to asymmetric amine synthesis.