An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

Neutron quasi-elastic scattering in disordered solids: a Monte Carlo study of metal-hydrogen systems

The dynamic structure factor of neutron quasi-elastic scattering has been calculated by Monte Carlo methods for atoms diffusing on a disordered lattice. The disorder includes not only variation in the distances between neighbouring atomic sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent intermediate scattering function which translate into a significant increase in the intensity in the wings of the quasi-elastic spectrum as compared with the Lorentzian form. The effect is particularly marked at high values of the momentum transfer and at site occupancies of the order of unity. The MC calculations demonstrate how the degree of disorder may be derived from experimental measurements of the quasi-elastic scattering. The model structure factors are compared with the experimental quasi-elastic spectrum of an amorphous metal-hydrogen alloy.

Low temperature X-ray structures of two crystalline forms (I) and (II) of the pyrimidine derivative and sodium channel blocker BW1003C87: 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine

The X-ray crystal structures of two crystalline forms of 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine, C10H7Cl3N4 (code name BW1003C87) (I) and (II), have been carried out at liquid nitrogen temperature. A detailed comparison of the two structures is given. Both are centrosymmetric, with structure (I) in the triclinic space group P (1) over bar unit cell a = 6.4870(10), b = 9.216(2), c = 12.016(2) angstrom, alpha = 75.78(3)degrees, beta = 89.95(3)degrees, gamma = 83.45(3)degrees, V = 691.5(2) angstrom(3), Z = 2 and density (calculated) = 1.544 Mg/m(3); and (II) in the monoclinic space group P2(1)/c, unit cell a = 12.000(2), b = 7.518(2), c = 13.450(3) angstrom, beta = 97.87(3)degrees, V = 1202.0(5) angstrom(3), Z = 4, Density (calculated) = 1.600 Mg/m(3). Structure (I) includes a solvated CH3OH in the lattice. Final R indices [I > 2sigma(I)] are R1 = 0.0427, wR2 = 0.1075 for (I) and R1 = 0.0487, wR2 = 0.1222 for (II). R indices (all data) are R1 = 0.0470, wR2 = 0.1118 for (I) and R1 = 0.0623, wR2 = 0.1299 for (II). 5-Phenyl-2,4 diaminopyrimidine and 6-phenyl-1,2,4 triazine derivatives, which include lamotrigine (3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine), have been investigated for some time for their effects on the central nervous system. Both lamotrigine and 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine (code name BW1003C87), the subject of the present study, are anticonvulsant as well as neuroprotective in models of brain ischaemia and in a model of white matter ischaemia. BW1003C87 is a sodium channel blocker which also reduces the release of the neurotransmitter glutamate. The three dimensional structures reported here form part of a newly developed data base for the detailed investigation of members of this drug family and their biological activities.