Specifications of dust-ion-acoustic shock waves affected by dust charge variation in four-component dissipative quantum plasma

ABSTRACT

Nonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (H_c) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices.     

Weak Density of Smooth Maps in W 1, 1(M,N) for Non-Abelian π1(N)

We prove that smooth maps are dense in the sense of biting convergence in W ^{1, 1}(M, N) when M and Nare compact Riemannian manifolds and N is closed.     

Morphological characterization of cells in concentrated suspensions using multispectral diffuse optical tomography

Based on a non-spherical model of particle scattering, we investigate the capabilities and limitations of a T-matrix based inverse algorithm to morphologically characterize cells in concentrated suspensions. Here the cells are modeled as randomly orientated spheroidal particles with homogenous dielectric properties and suspended in turbid media. The inverse algorithm retrieves the geometrical parameters and the concentration of cells simultaneously by inverting the reduced scattering coefficient spectra obtained from multispectral diffuse optical tomography (MS-DOT). Both round and spheroidal cells are tested and the role of multiple and higher order scattering of particles on the performance of the algorithm is evaluated using different concentrations of cells.     

Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II

In the previous article (Seyyedali, Duke Math. J. 153(3):573–605, 2010), we proved that slope stability of a holomorphic vector bundle E over a polarized manifold (X,L) implies Chow stability of $(\mathbb{P}E^{*},\mathcal{O}_{\mathbb{P}E^{*}}(1)\otimes\pi^{*} L^{k})$ for k?0 if the base manifold has no nontrivial holomorphic vector field and admits a constant scalar curvature metric in the class of 2πc ₁(L). In this article, using asymptotic expansions of the Bergman kernel on Sym ^d E, we generalize the main theorem of Seyyedali (Duke Math. J. 153(3):573–605, 2010) to polarizations $(\mathbb{P}E^{*},\mathcal {O}_{\mathbb{P}E^{*}}(d)\otimes\pi^{*} L^{k})$ for k?0, where d is a positive integer.     

Acceleration of alkenyltrimethylsilane fluorination under mild conditions using ultrasound

Alkenyltrimethylsilanes are selectively fluorodesilated to alkenyl fluoride very readily by reaction with 1-chloromethyl-4-fluoro-1,4-diazoniabicyclo[2,2,2]octane bis-tetrafluoroborate (Selectfluor) and N-fluorobenzensulfonimids at room temperature under ultrasound. In the presence of ultrasound irradiation in the case of one of the reactions, the yield was 85% after 25 min, but using the previously established thermal method the yield was only 32% after 20 h.     

The study of an infinite class of dendrimer nanostars by topological index approaches

A topological index for a molecular graph G is a numeric quantity invariant under automorphisms of G. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this article an infinite class of dendrimer nanostars is investigated under three topological indices containing PI, Szeged and edge Szeged.     

Computing topological indices of Sudoku graphs

In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi?, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. A topological index is actually designed by transforming a chemical structure into a numeric number. These topological indices correlate certain physico-chemical properties like boiling point, stability, strain energy etc. of chemical compounds. Graph theory has found a considerable use in this area of research. The topological indices of certain interconnection networks were studied recently by Imran et al. (Appl Math Comput 244:936–951, 2014). In this paper, we extend this study to \(n\times n\) Sudoku graphs and derive analytical closed results of general Randi? index \(R_{\alpha }(G)\) for different values of “\(\alpha \)” for Sudoku (SK). We also compute the general Randi?, first Zagreb, ABC, GA, \(ABC_{4}\) and \(GA_{5}\) indices and give closed formulae of these indices for Sudoku graphs.     

Novel isocyanide-based three-component one-pot synthesis of cyanophenylamino-acetamide derivatives

A one-pot multicomponent synthesis of a novel class of cyanophenylamino-acetamides through the conversion of primary amides to the corresponding nitriles, starting from simple and readily available inputs including 2-aminobenzamide, an aldehyde, and an isocyanide in the presence of p-toluenesulfonic acid as a catalyst, in excellent yields at room temperature in ethanol as a green reaction medium is described.     

Highly selective transport of silver ion through a supported liquid membrane using calix[4]pyrroles as suitable ion carriers

Facilitated transport of silver ion across a supported liquid membrane (SLM) by calix[4]pyrroles, as selective ion carriers, dissolved in kerosene has been investigated. The influences of fundamental parameters affecting the transport of silver ion including ion carrier concentration in the membrane phase, thiosulfate concentration in strip phase, picric acid concentration in the feed phase, stirring speed of aqueous phases, type of membrane solvent and time of transport have been studied. In the presence of thiosulfate as a suitable metal ion acceptor in the strip phase and picrate ion as ion pairing agent in the source phase, transport of silver occurs almost quantitatively after 75 min. The selectivity and efficiency of silver transport from aqueous solution containing Cu²⁺, Mg²⁺, Ni²⁺, Ca²⁺, Zn²⁺, Pb²⁺, Co²⁺, Al³⁺, Hg²⁺, Cd²⁺, Fe³⁺, Fe²⁺ and Cr³⁺ were investigated.     

Structural,theoretical and multinuclear NMR study of mercury(II) complexes of phosphorus ylides: Mono and binuclear complexes

Reaction of phosphorus ylide Ph₃PCHC(O)C₆H₄Cl (Y₁) with HgX₂ (X = Cl, Br and I) and ylide (p-tolyl)₃PCHC(O)CH₃ (Y₂) with HgI₂ in equimolar ratios using methanol as solvent leads to binuclear products. The bridge-splitting reaction of binuclear complex [(Y₁) · HgCl₂]₂ by DMSO yields a mononuclear complex containing DMSO as ligand. O-coordination of DMSO is revealed by single crystal X-ray analysis in mononuclear complex of [(Y₁) · HgCl₂ · DMSO]. C-coordination of ylides is confirmed by X-ray structure of binuclear complex [(Y₂) · HgI₂]₂. Characterization of the obtained compounds was also performed by elemental analysis, IR, ¹H, ³¹P, and ¹³C NMR. Theoretical studies on mercury(II) complexes of Y₁ show that formation of mononuclear complexes in DMSO solution in which DMSO acts as a ligand, energetically is more favorable than that of binuclear complexes.