A qualocation method for parabolic partial differential equations

In this paper a qualocation method is analysed for parabolicpartial differential equations in one space dimension. Thismethod may be described as a discrete H¹-Galerkin method inwhich the discretization is achieved by approximating the integralsby a composite Gauss quadrature rule. An O (h^4-i) rate of convergencein the W^i.p norm for i = 0, 1 and 1 p is derived for a semidiscretescheme without any quasi-uniformity assumption on the finiteelement mesh. Further, an optimal error estimate in the H² normis also proved. Finally, the linearized backward Euler methodand extrapolated Crank-Nicolson scheme are examined and analysed.     

Sensitive determination of hydrazine using poly(phenolphthalein), Au nanoparticles and multiwalled carbon nanotubes modified glassy carbon electrode

This study reports a detailed analysis of an electrode material containing poly(phenolphthalein), carbon nanotubes and gold nanoparticles which shows superior catalytic effect towards to hydrazine oxidation in Britton–Robinson buffer (pH 10.0). Glassy carbon electrode was modified by electropolymerization of phenolphthalein (PP) monomer (poly(PP)/GCE) and the multiwalled carbon nanotubes (MWCNTs) was dropped on the surface. This modified surface was electrodeposited with gold nanoparticles (AuNPs/CNT/poly(PP)/GCE). The fabricated electrode was analysed the determination of hydrazine using cyclic voltammetry, linear sweep voltammetry and amperometry. The peak potential of hydrazine oxidation on bare GCE, poly(PP)/GCE, CNT/GCE, CNT/poly(PP)/GCE, and AuNPs/CNT/poly(PP)/GCE were observed at 596 mV, 342 mV, 320 mV, 313 mV, and 27 mV, respectively. A shift in the overpotential to more negative direction and an enhancement in the peak current indicated that the AuNPs/CNT/poly(PP)/GC electrode presented an efficient electrocatalytic activity toward oxidation of hydrazine. Modified electrodes were characterized with High-resolution transmission electron microscopy (HRTEM), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and electrochemical impedance spectroscopy (EIS). Amperometric current responses in the low hydrazine concentration range of 0.25–13 µM at the AuNPs/CNT/poly(PP)/GCE. The limit of detection (LOD) value was obtained to be 0.083 µM. A modified electrode was applied to naturel samples for hydrazine determination.     

Photon transport in thin disordered slabs

We examine using Monte Carlo simulations, photon transport in optically ‘thin’ slabs whose thickness L is only a few times the transport mean free path l*, with particles of different scattering anisotropies. The confined geometry causes an auto-selection of only photons with looping paths to remain within the slab. The results of the Monte Carlo simulations are borne out by our analytical treatment that incorporates directional persistence by the use of the Ornstein-Uhlenbeck process, which interpolates between the short time ballistic and long time diffusive regimes.     

Ultra-low-frequency dust-electromagnetic modes in self-gravitating magnetized dusty plasmas

Obliquely propagating altra-low-frequency dust-electromagnetic waves in a self-gravitating, warm, magnetized, two fluid dusty plasma system have been investigated. Two special cases, namely, dust-Alfvén mode propagating parallel to the external magnetic field and dustmagnetosonic mode propagating perpendicular to the external magnetic field have also been considered. It has been shown that effects of self-gravitational field, dust fluid temperature, and obliqueness significantly modify the dispersion properties of these ultra-low-frequency dust-electromagnetic modes. It is also found that in parallel propagating dust-Alfvén mode these effects play no role, but in obliquely propagating dust-Alfvén mode or perpendicular propagating dust-magnetosonic mode the effect of self-gravitational field plays destabilizing role whereas the effect of dust/ion fluid temperature plays stabilizing role.     

Non-resonant microwave absorption studies of superconducting MgB2 and MgB2 + MgO

Non-resonant microwave absorption (NRMA) studies of superconducting MgB₂ and a sample containing ∼10% by weight of MgO in MgB₂ are reported. The NRMA results indicate near absence of intergranular weak links in the pure MgB₂ sample. A linear temperature dependence of the lower critical field H _c1 is observed indicating a non-s wave superconductivity. However, the phase reversal of the NRMA signal which could suggest d wave symmetry is also not observed. In the MgB₂ + MgO sample, much larger low field dependent absorption is observed indicating the presence of intergranular weak links. The hysteretic behavior of NRMA is compared and contrasted in the two samples. In the pure MgB₂ sample, a large hysteresis is observed between the forward and the reverse scans of the magnetic field indicating strong pinning of flux lines. This hysteresis saturates a few degrees below T _c while in the MgB₂ + MgO sample, a much slower increase of hysteresis with decreasing temperature is observed, a signature of weaker pinning.     

Gas phase ion chemistry of charged silver(I) adenine ions via multistage mass spectrometry experiments and DFT calculations

Electrospray ionization (ESI) of solutions containing adenine and AgNO(3) yields polymeric [Ad(x)+ Ag(y)-zH]((y-z)+) species. Density functional theory (DFT) calculations have been used to examine potential structures for several of the smaller ions while multistage mass spectrometry experiments have been used to probe their unimolecular reactivity (via collision-induced dissociation (CID)) and bimolecular reactivity (via ion-molecule reactions with the neutral reagents acetonitrile, methanol, butylamine and pyridine). DFT calculations of neutral adenine tautomers and their silver ion adducts provide insights into the binding modes of adenine. We find that the most stable [Ad + Ag](+) ion does not correspond to the most stable neutral adenine tautomer, consistent with previous studies that have shown that transition metal ions can stabilize rare tautomeric forms of nucleobases. Both the charge and the stoichiometry of the [Ad(x)+ Ag(y)-zH]((y-z)+) complexes play pivotal roles in directing the types of fragmentation and ion-molecule reactions observed. Thus, [Ad(2)+ Ag(2)](2+) is observed to dissociate to [Ad + Ag](+) and to react with butylamine via proton transfer, while [Ad(2)+ Ag(2)- H](+) fragments via loss of neutral adenine to form the [Ad + Ag(2)- H](+) ion and does not undergo proton transfer to butylamine. DFT calculations on several isomeric [Ad(2)+ Ag(2)](2+) ions suggest that planar centrosymmetric cations, in which two adjacent silver atoms are bridged by two N7H adenine tautomers via N(3),N(9)-bidentate interactions, are the most stable. The [Ad + Ag(2)-H](+) ion adds two neutral reagents in ion-molecule reactions, consistent with the presence of two vacant coordination sites. It undergoes a silver atom loss to form the [Ad + Ag - H](+) radical cation, which in turn fragments quite differently to the even electron [Ad + Ag](+) ion. Several other pairs of radical cation/even electron adenine-silver complexes were also found to undergo different fragmentation reactions.     

Gas-phase synthesis and reactivity of the organomagnesates [CH3MgL2]- (L = Cl and O2CCH3): from ligand effects to catalysis

Multistage mass spectrometry experiments combined with density functional theory (DFT) calculations were used to examine the gas-phase synthesis and ion-molecule reactions of the organomagnesates [CH(3)MgL(2)](-) (L = Cl and O(2)CCH(3)). Neutral species containing an acidic proton (HX) react with the [CH(3)MgL(2)](-) ions via addition with concomitant elimination of methane to form [XMgL(2)](-) ions. Kinetic measurements combined with DFT calculations revealed reduced reactivity of [CH(3)Mg(O(2)CCH(3))(2)](-) toward water, caused by the bidentate binding mode of acetate, which induces overcrowding of the Mg coordination sphere. The [CH(3)MgL(2)](-) ions reacted with (i) aldehydes with enolizable protons via enolization rather than the Grignard reaction and (ii) CH(3)CO(2)H to complete a catalytic cycle for the decarboxylation of acetic acid. Other electrophilic reagents such as pivaldehyde, benzaldehyde, methyl iodide, and trimethylborate are unreactive. DFT calculations on the competition between enolization and the Grignard reaction for [CH(3)MgCl(2)](-) ions reacting with acetaldehyde suggest that while the latter has a smaller barrier, it is entropically disfavored.     

The Performance of an Electrorheological Fluid in Dynamic Squeeze Flow: The Influence of Solid Phase Size

This paper is concerned with an experimental investigation of a comparison of the rheological performance of an ER fluid, consisting of a carrier with a range of solid phase sizes, in oscillatory squeeze-flow under DC conditions. The fluid is sandwiched between two parallel plane electrodes, the upper one stationary and the lower one oscillating normal to its plane. It is seen that the dynamic performance of the fluid, in terms of the capacity for the transmission of imposed forces across the fluid, is highly dependent on the size of the dispersed solid phase and has an optimum value which is dependent on the mean value of the interelectrode gap. In addition the paper includes some measurements of the current through the fluid which may help to shed some further light on the mechanism of the ER effect. Finally the implications of the results to vibration control are discussed. Copyright 1999 Academic Press.     

Ultrasonic study of molecular interaction in binary liquid mixtures at 30°C

Densities ρ and ultrasonic speeds u of the binary mixtures of tetrahydrofuran (THF) with 1-butanol and tert-butanol, at 30°C, over the entire composition range were measured. From these data isentropic compressibility, K _s, intermolecular free length L _f, relative association R _A, acoustic impedance Z, molar sound speed R _m, deviations in isentropic compressibility ΔK _s, and excess volume V ^E were calculated. The variation of these parameters with composition of the mixture helps us in understanding the nature and extent of interaction between unlike molecules in the mixtures. Further, theoretical values of ultrasonic speed were evaluated using theories and empirical relations. The relative merits of these theories and relations were discussed.