The Photochemistry of 2-Cyclopentenyl Methyl Ketones

2-Cyclopentenyl and 3-phenyl-2-cyclopentenyl methyl ketones (15–18, 30, 31) undergo a 1,3-acetyl shift on direct irradiation, and the oxa-di-π-methane rearrangement to photochemically non-interconverting endo and exo bicyclo-[2.1.0]pentyl methyl ketones on triplet sensitization. Exceptions include the 2-methyl-3-phenyl-2-cyclopentenyl methyl ketone 32 and the 1-phenyl-2-cyclo-pentenyl methyl ketone 44 which are unreactive on direct irradiation and on triplet sensitization, respectively, and the 2-phenyl-2-cyclopentenyl methyl ketones 42 and 43 which do not react under either condition. The reactive triplet of the 3-phenyl-2-cyclopentenyl methyl ketone 30 has been identified as the localized styrene π,π*-state of E_T=59 kcal/mol by comparison of its phosphorescence at 77K in rigid glasses with that of 1-phenyl-cyclopentene, and by the independence of the quantum yield on sensitizer energy in the range of 61–74 kcal/mol.     

Algorithms for cardinal interpolation using box splines and radial basis functions

Summary We describe an algorithm for (bivariate) cardinal interpolation which can be applied to translates of basis functions which include box splines or radial basis functions. The algorithm is based on a representation of the Fourier transform of the fundamental interpolant, hence Fast Fourier Transform methods are available. In numerical tests the 4-directional box spline (transformed to the characteristical submodule of ²), the thin plate spline, and the multiquadric case give comparably equal and good results.     

Monte Carlo simulation of phase separation and clustering in the ABV model

As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump rates _A and _B, respectively. For a small concentration of vacancies (c _v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk ₁(t),k ₂ ² (t) is studied during the early stages of phase separation, for several choices of concentrationc _B of B atoms. Forc _B=0.18 also the time evolution of the cluster size distribution is studied. Apart from very early times, the mean cluster sizel(t) as well as the moments of the structure function depend on timet and the ratio of the jump rates (= _B/ _A) only via a scaled timet/(). Qualitatively, the behavior is very similar to the direct exchange model containing no vacancies. Consequences for phase separation of real alloys are briefly discussed.     

Neutron diffraction study of the heavy fermion superconductors UM2Al3(M=Pd,Ni)

An elastic neutron scattering study was performed on the new superconducting heavy fermion systems UPd₂Al₃ and UNi₂Al₃. The neutron diffraction patterns reveal unambiguously long range antiferromagnetic order in UPd₂Al₃ with an ordered magnetic moment _U = (0.85±0.03) _B , which coexists with the superconducting state. This is by far the largest _U value observed for any heavy fermion superconductor. For UNi₂Al₃, no long-range magnetic order could be observed for temperaturesT1.5 K, yielding an upper limit of the ordered moment of 0.2 _B .