Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

A short range many-body potential for modelling bcc metals

The problem considered is the fitting of a many-body interaction potential to bulk crystal data. A parameterisation of the potential is assumed which is based on physical considerations. The free parameters are determined by using global optimization to perform a least squares fit, to a large number of crystal properties. This has been achieved for body centered cubic (bcc) materials. The approach adopted here fits the bcc crystal structure, as the preferred minimum energy configuration for tungsten, and also fits the dimer energetics and the elastic properties of crystalline tungsten.     

Temperature effects in proton exchanged LiNbO<Subscript>3</Subscript> waveguides

Temperature effects on single, homogeneous phases of proton exchanged LiNbO₃ waveguides have been studied. The refractive index of -phase guides on z-cut and x-cut congruent substrates monotonically increases with temperature, the thermo-optical coefficient being similar to that of the substrate. In ₂-phases on z-cut congruent substrates and in ₁-phases on z-cut and x-cut congruent and quasi-stoichiometric substrates, the thermo-optical coefficient is smaller than that of the substrate below 60 °C and higher above this temperature. A rather similar effect has been observed in ₁-phases on z-cut and x-cut congruent substrates in the linear expansion coefficient. The microscopic origin of the phase transition is not known for the moment. PACS Provide PACS codes please.     

Alcaloides steroidiques—LII Alcaloides du buxus balearica Willd.: Cycloprotobuxine-D, buxamine-E, buxaminol-E, N-isobutyryl-baleabuxidine-F, N-benzoyl-baleabuxidine-F, baleabuxoxazine-C, N-isobutyryl-baleabuxidienine-F, N-benzoyl-baleabuxidienine-F, N-isobutyryl-baleabuxaline-F

The following alkaloides have been extracted from the leaves of Buxus balearica Willd.: cyclomicrophylline-B, cycloprotobuxines A, C and D, baleabuxine (N-isobutyryl-baleabuxine-F), buxamine-E and buxaminol-E (already reported), N-isobutyryl- and N-benzoyl-baleabuxidine-F, baleabuxoxazine-C, N-isobutyryl- and N-benzoyl-baleabuxidienine-F, N-isobutyryl-baleabuxaline-F, the structures of which are proposed. The stereochemistry of baleabuxidines and baleabuxoxazines is established on the base of chemical correlations between these two groups and cyclomicrophyllines.     

Tuning of magnetic properties of polynuclear lanthanide(III)-octacyanotungstate(V) systems: determination of ligand-field parameters and exchange interaction

The self-assembly reaction between trivalent lanthanide ions, 2,2':6',2' '-terpyridine (terpy) ligand, and octacyanotungstate(V) leads to the formation of two series of isomorphous cyano-bridged compounds: (i) one-dimensional (1-D) chains [Ln(terpy)(DMF)(4)][W(CN)(8)].6H(2)O.C(2)H(5)OH (Ln = Ce-Dy) and (ii) dinuclear molecules [Ln(terpy)(DMF)(2)(H(2)O)(2)][W(CN)(8)].3H(2)O (Ln = Ho, Er, Yb) and the ionic [Tm(III)(terpy)(DMF)(2)(H(2)O)(3)][WV(CN)(8)].4H(2)O.DMF (DMF = N,N-dimethylformamide) system. The crystal structures of 1-D chains consist of alternating {[W(CN)(8)]} and {[Ln(terpy)]} building blocks. The neighboring chains are weakly linked through the pi-pi stacking interactions of the aromatic rings, leading to two-dimensional supramolecular layers. The dinuclear species are weakly linked through the hydrogen bonds between H2O molecules and terminal cyano ligands resulting in a columnlike arrangement of dimers. Taking into account the ligand-field splitting and the exchange interaction, we have estimated the magnetic couplings between the Ln(III) and WV centers in a series of polycrystalline 1-D chains and in dimeric systems. The corresponding exchange constants have been shown to change the sign along the series of chains. The coupling is antiferromagnetic for 1 (J = -0.24 cm(-1)) and 2 (J = -0.07 cm(-1)), whereas 3 (J = +0.47 cm(-1)), 7 (J = +0.28 cm(-1)), and 8 (J = +0.23 cm(-1)) have ferromagnetic character. In the case of dimeric systems, the coupling constants seem to be independent of the lanthanide center. The splitting structures of the ground-state multiplets of the Ln(III) centers have been shown to explain the temperature dependences of the magnetic susceptibilities.     

W-knotted chain {[Cu(II)(dien)]4[W(V)(CN)8]}(5+)∞: synthesis, crystal structure, magnetism, and theory

The self-assembly of [Cu(II)(dien)(H(2)O)(2)](2+) and [W(V)(CN)(8)](3-) in aqueous solution leads to the formation (H(3)O){[Cu(II)(dien)](4)[W(V)(CN)(8)]}[W(V)(CN)(8)](2)·6.5H(2)O (1). The crystal structure of 1 consists of an unprecedented {[Cu(II)(dien)](4)[W(V)(CN)(8)]}(5+)(∞) chain of (2,8) topology, nonbridging [W(CN)(8)](3-) anions, and crystallization water molecules. The analysis of magnetic behavior of 1 was performed by the density functional theory (DFT) method and magnetic susceptibility measurements. The DFT broken symmetry approach gave two J(CuW) coupling constants: J(ax) = +2.9 cm(-1) assigned to long and strongly bent W-CN-Cu linkage, and the J(eq) = +1.5 cm(-1) assigned to short and less bent W-CN-Cu linkage, located at the axial and the equatorial positions of square pyramidal Cu(II) centers, respectively, in the hexanuclear {W(2)Cu(4)} chain subunit. The dominance of weak-to-moderate ferromagnetic coupling within the chain was confirmed by magnetic calculations. Zero-field susceptibility of the full chain segment {WCu(4)}(n) was calculated by a semiclassical analytical approach assuming that only one W(V) out of five ? spins of the chain unit WCu(4) is treated as a classical commuting variable. The calculation of the field dependence of the magnetization was performed separately by replacing the same spin with the Ising variable and applying the standard transfer matrix technique. The intermolecular coupling between the chain segments and off-chain [W(CN)(8)](3-) entities was resolved using the mean-field approximation set to be of antiferromagnetic character. The magnetic coupling parameters are compared with those of other low dimensional {Cu(II)-[M(V)(CN)(8)]} systems.