Junction conditions at the boundary of a charged viscous-fluid sphere

Junction conditions are studied at the boundary of a sphere consisting of a charged viscous fluid with outgoing heat and radiation flux. The motion is anisotropic and the matching is done with the exterior Reissner-Nordström-Vaidya metric. A general relation in terms of the energy-momentum tensor componentsT ₁ ¹ andT ₄ ¹ is satisfied at the boundary hypersurface and this relation gives appropriate physical conditions in different special cases, some of which were obtained previously.     

Oxidative addition of different electrophiles with rhodium(I) carbonyl complexes of unsymmetrical phosphine–phosphine monoselenide ligands

Dimeric chlorobridge complex [Rh(CO)₂Cl]₂ reacts with two equivalents of a series of unsymmetrical phosphine–phosphine monoselenide ligands, Ph₂P(CH₂)_nP(Se)Ph₂ {n = 1( a ), 2( b ), 3( c ), 4( d )}to form chelate complex [Rh(CO)Cl(P∩Se)] ( 1a ) {P∩Se = η²‐(P,Se) coordinated} and non‐chelate complexes [Rh(CO)₂Cl(P～Se)] ( 1b–d ) {P～Se = η¹‐(P) coordinated}. The complexes 1 undergo oxidative addition reactions with different electrophiles such as CH₃I, C₂H₅I, C₆H₅CH₂Cl and I₂ to produce Rh(III) complexes of the type [Rh(COR)ClX(P∩Se)] {where R = ? C₂H₅ ( 2a ), X = I; R = ? CH₂C₆H₅ ( 3a ), X = Cl}, [Rh(CO)ClI₂(P∩Se)] ( 4a ), [Rh(CO)(COCH₃)ClI(P～Se)] ( 5b–d ), [Rh(CO)(COH₅)ClI‐(P～Se)] ( 6b–d ), [Rh(CO)(COCH₂C₆H₅)Cl₂(P～Se)] ( 7b–d ) and [Rh(CO)ClI₂(P～Se)] ( 8b–d ). The kinetic study of the oxidative addition (OA) reactions of the complexes 1 with CH₃I and C₂H₅I reveals a single stage kinetics. The rate of OA of the complexes varies with the length of the ligand backbone and follows the order 1a > 1b > 1c > 1d . The CH₃I reacts with the different complexes at a rate 10–100 times faster than the C₂H₅I. The catalytic activity of complexes 1b–d for carbonylation of methanol is evaluated and a higher turnover number (TON) is obtained compared with that of the well‐known commercial species [Rh(CO)₂I₂]^?. Copyright © 2006 John Wiley & Sons, Ltd.     

Hopping of chaotic dynamics in a doubly resonant parametric oscillator

We study a doubly resonant optical parametric oscillator where the pump can feed two pairs of signal-idler modes. We assume the presence of gain at the pump frequency. We investigate the various oscillation states of interest, namely, when only the first pair oscillates with the other pair having null amplitudes and vice versa. We demonstrate the exchange of dynamics between the mode pairs when the relevant parameters of the cavity, namely, the phase mismatch factors or the decay rates switch because of fluctuations. The exchange of dynamics is shown to be independent of the nature of dynamics, i.e. independent of whether the motion isn-periodic or chaotic. We also investigate the case where both the pairs can exhibit chaotic dynamics though these states are difficult to realize because of fluctuations.     

A finite element model for nonlinear behaviour of piezoceramics under weak electric fields

It has been experimentally observed that piezoceramic materials exhibit different types of nonlinearities under different combinations of electric and mechanical fields. When excited near resonance in the presence of weak e to a Duffinor such as jump phenomena and presence of superharmonics in the response spectra. There has not been much work in the litrature to model these types of nonlinearities. Some authors have developed one-dimensional models for the above phenomenon and derived closed-form solutions for the displacement response of piezo-actuators. However, the generalized three-dimensional (3-D) formulation of electric enthalpy, the variational formulation and the FEM implementation have not yet been addressed, which are the focus of this paper. In this work, these nonlinearities have been modelled in a 3-D piezoelectric continuum using higher order quadratic and cubic terms in the generalized electric enthalpy density function. The coupled nonlinear finite element equations have been derived using variational formulation. A special linearization technique for assembling the nonlinear matrices and solution of the resulting nonlinear equations has been developed. The method has been used for simulating the nonlinear frequency response of a lead zirconate titanate plate excited near its first in-plane vibration resonance frequency with sinusoidal excitations of different electric field strengths. The results have been compared with those of the experiment.     

New algorithms for constrained minimax optimization

A constrained minimax problem is converted to minimization of a sequence of unconstrained and continuously differentiable functions in a manner similar to Morrison's method for constrained optimization. One can thus apply any efficient gradient minimization technique to do the unconstrained minimization at each step of the sequence. Based on this approach, two algorithms are proposed, where the first one is simpler to program, and the second one is faster in general. To show the efficiency of the algorithms even for unconstrained problems, examples are taken to compare the two algorithms with recent methods in the literature. It is found that the second algorithm converges faster with respect to the other methods. Several constrained examples are also tried and the results are presented.     

Macrocyclic paracyclophane synthesis

Macrocyclic stilbene derivatives are prepared using strong base to couple the terminal carbons of 1,12-bis-[4-chloromethylphenyl]-dodecane and its homologs.     

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

A new approach to irreversibility from maximum entropy estimation

This paper deals with the study of some irreversible processes like slow heating of a thermodynamic system or of inhomogeneity, i.e. spatially local equilibrium in it, based on the principle of maximum entropy estimation, in a stochastic model.     

DNA damage by fasicularin

Fasicularin is a structurally novel thiocyanate-containing alkaloid isolated from the ascidian Nephteis fasicularis. Early biological experiments suggested that this compound's cytotoxic properties may stem from its ability to damage cellular DNA. Sequence gel analysis reveals that treatment of a 5'-32P-labeled DNA duplex with fasicularin in pH 7.0 buffer causes strand cleavage selectively at guanine residues. Further experiments indicate that production of these base-labile lesions in DNA involves alkylation of guanine residues by a fasicularin-derived aziridinium ion. This work reveals fasicularin as the first natural product found to generate a DNA-alkylating aziridinium ion via a mechanism analogous to the clinically used anticancer drugs mechlorethamine, melphalan, and chlorambucil.