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.     

Efficient model order reduction for dynamic systems with local nonlinearities

In the nonlinear structural analysis, the nonlinear effects are commonly localized and the rest of the structure behaves in a linear manner. Considering this fact, this research work proposes a harmonic balance solution in order to determine the nonlinear response of the structures. The solution is simplified by using an exact dynamic reduction along with the modal expansion technique. This novel approach, which is applicable to both discrete and continuous systems, converts the system equations of motion in each harmonic to a small set of nonlinear algebraic equations. The full set of system equations is reduced to a discrete system with a few generalized degrees of freedom (DOFs) confined to the localized nonlinear regions. The resultant reduced order model is shown to be accurate enough for determining the periodic response. To demonstrate the capability of the proposed method, numerical case studies for continuous and discrete systems, including systems with internal resonance, have been studied and the outcomes are validated with benchmark studies. In addition, the method is applied in the identification process of an experimental test setup with unknown frictional support parameters, and the results are presented and discussed.     

Voltammetric determination of hydroxylamine in water samples using a 1-benzyl-4-ferrocenyl-1H-[1,2,3]-triazole/carbon nanotube-modified glassy carbon electrode

A modified glassy carbon electrode has been constructed using a 1-benzyl-4-ferrocenyl-1H-[1,2,3]-triazole along with multiwalled carbon nanotubes. The electrochemical behaviour of modified electrode has been investigated by cyclic voltammetry. Electrocatalytic activity of the modified electrode was investigated for the oxidation of hydroxylamine in 0.1 M phosphate-buffered solution of pH 8. The modified electrode showed electrocatalytic response to the oxidation of hydroxylamine at the potential of 330 mV. The linear range and detection limit for the detection of hydroxylamine in the optimum condition were found to be 4.0?×?10^?7 to 6.75?×?10^?4 M and 28.0?±?1.0 nM, respectively. Finally, the method was employed for the determination of hydroxylamine in water samples.     

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.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

The clique numbers of regular graphs of matrix algebras are finite

Let F be a field, char(F)≠2, and SGL_n(F), where n is a positive integer. In this paper we show that if for every distinct elements x,yS, x+y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring.     

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.