Wavevector and frequency dependent dielectric function dynamic structure factor and the instability of plasma waves in two component hot rare quantum and classical plasmas

The full wavevector and frequency dependent complex dielectric function for two component classical and quantum rare hot plasmas have been derived. The real part of dielectric function is obtained in the form of a series. Difference between quantum and classical real and imaginary parts of dielectric function have been brought out by making explicit calculations. The quantum nature of the plasma brings about significant changes in both parts depending upon the magnitude of quantum parameter,R (= 8.93(λ_th)/λ). Expressions for the dynamic structure factors for both two component classical and quantum plasma have been evaluated for different values of the mass of the positive componentm ₊, temperature T₊ and wavevector k. It is found that the plasma exhibits well defined collective modes for certain values of |k| accompanied by varying disorder which depends upon the values of m₊ as well as on |k| and T₊. For the quantum case the collective modes are less well defined as compared to the corresponding classical case, thus proving that quantum nature introduces inherent disorder in the system. But for both the cases, increase in temperature destroys collective modes. Another feature is the appearance of a hump near Ω = 0 which becomes smaller and vanishes as the quantum parameter is decreased. Instability of plasma modes in the presence of constant electric field has also been worked out for the quantum case.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

Wide range humidity sensing of LiCl incorporated in mesoporous silica circular discs

Lithium chloride (LiCl) incorporated MCM-41 has been synthesised by sol-gel method using tetraethyl orthosilicate as a precursor in basic medium. 5, 10, 15, 20, 25, 30 and 35 wt% of LiCl were incorporated in mesoporous silica to investigate the humidity sensing. With increasing wt% of LiCl broadening of O–H peak is observed in the Fourier Transform Infrared spectra, indicating greater adsorption of hydroxyl groups on porous silica. The surface area of the MCM-41 circular discs was determined by Brunauer?Emmett?Teller (BET). Scanning electron microscopy images suggest that incorporation of LiCl leads to coalescence of grains in mesoporous silica. 25 wt% LiCl incorporated MCM-41 showed a wide range linear response of impedance change for 11%–90% RH exhibiting 3.5-order drop in impedance at a 1 kHz frequency. The Nyquist plots for all compositions showed increased ionic conduction with increasing relative humidity.     

A Phosphoramidite Analogue of Cyclotriphosphate Enables Iterative Polyphosphorylations

An iterative polyphosphorylation approach is described, which is based on a phosphoramidite (P‐amidite) derived reagent (c‐PyPA) obtained from the cyclization of pyrophosphate with a reactive diisopropylaminodichlorophosphine. This type of reagent is unprecedented as it represents a reactive P‐amidite without protecting groups. The reagent proved to be stable in solution over several weeks. Its utility is described in the context of iterative monodirectional and bidirectional polyphosphorylations. The ensuing functionalized cyclotriphosphate can be opened with a variety of nucleophiles providing ready access to diverse functionalized polyphosphate chains of defined length with several tags, including both P‐N and P‐O labels. Their interaction with exo‐ and endopolyphosphatases is described.     

A delayed ratio-dependent predator–prey model of interacting populations with Holling type III functional response

In this article, we study a ratio-dependent predator–prey model described by a Holling type III functional response with time delay incorporated into the resource limitation of the prey logistic equation. This investigation includes the influence of intra-species competition among the predator species. All the equilibria are characterized. Qualitative behavior of the complicated singular point (0,0) in the interior of the first quadrant is investigated by means of a blow-up transformation. Uniform persistence, stability, and Hopf bifurcation at the positive equilibrium point of the system are examined. Global asymptotic stability analyses of the positive equilibrium point by the Bendixon–Dulac criterion for non-delayed model and by constructing a suitable Lyapunov functional for the delayed model are carried out separately. We perform a numerical simulation to validate the applicability of the proposed mathematical model and our analytical findings.     

Apparent wall slip velocity measurements in free surface flow of concentrated suspensions

In this work we have experimentally measured the apparent wall slip velocity in open channel flow of neutrally buoyant suspension of non-colloidal particles. The free surface velocity profile was measured using the tool of particle imaging velocimetry (PIV) for two different channels made of plane and rough walls. The rough walled channel prevents wall slip, whereas the plane wall showed significant wall slip due to formation of slip layer. By comparing the velocity profiles from these two cases we were able to determine the apparent wall slip velocity. This method allows characterization of wall slip in suspension of large sized particles which cannot be performed in conventional rheometers. Experiments were carried out for concentrated suspensions of various particle volume concentrations and for two different sizes of particles. It was observed that wall slip velocity increases with particle size and concentration but decreases with increase in the viscosity of suspending fluid. The apparent wall slip velocity coefficients are in qualitative agreement with the earlier measurements. The effect of wall slip on free surface corrugation was also studied by analyzing the power spectral density (PSD) of the refracted light from the free surface. Our results indicate that free surface corrugation is a bulk flow response and it does not arise from boundary problem such as development of slip layer.     

Polarographic study of dioxo-uranium(VI)-8-hydroxyquinoline-succinate system and thermodynamic parameters

The dioxo-uranium(VI)-8-hydroxyquinoline-succinate system has been studied polarographically at constant ionic strength (μ = 0.6 M KCl) in aqueous alcohol (7 : 3) at different temperatures. The reduction of the simple and mixed complexes is reversible and diffusion controlled. The DeFord-Hume and Schaap-McMaster methods have been applied in the determination of composition and stability constants of the simple and mixed complexes respectively. The thermodynamic parameters ΔG, ΔH and ΔS have also been calculated.     

Hot atom chemistry in oxyanion targets. Part IV1: Recoil isochronal annealing in permanganates

Investigations on isochronal annealing behaviour of /n, / activated⁵⁶Mn recoils in crystalline potassium and ammonium permanganates have given different results indicating a varying degree of sensitivity of the samples to recoil annealing. The presence of ammonium ion in ammonium permanganate shows the reduction of recoil species during annealing. Vand-Primak model has been utilized to deduce the kinetic behaviour by which the energy of activation is found to be 1.1 and 1.2 eV for KMnO₄ and NH₄MnO₄, respectively. Furthermore, the present work reveals the role of defects in the transient reactions of the lattice stable precursors and hence the mechanism of the recoil reactions.     

Congruences for ℓ-regular overpartition for ℓ ∈ {5, 6, 8}

Let A? _?(n) denote the number of overpartitions of a non-negative integer n with no part divisible by ?, where ? is a positive integer. In this paper, we prove infinite family of congruences for A? ₅(n) modulo 4, A? ₆(n) modulo 3, and A? ₈(n) modulo 4. In the process, we also prove some other congruences.