QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Evaluation of intramolecular energy transfer process in the lanthanide(III) bis- and tris-(TTA) complexes: Photoluminescent and triboluminescent behavior

This work reports the energy transfer mechanism process of [Eu(TTA)(2)(NO(3))(TPPO)(2)] (bis-TTA complex) and [Eu(TTA)(3)(TPPO)(2)] (tris-TTA complex) based on experimental and theoretical spectroscopic properties, where TTA = 2-thienoyltrifluoroacetone and TPPO = triphenylphosphine oxide. These complexes were synthesized and characterized by elemental analyses, infrared spectroscopy and thermogavimetric analysis. The theoretical complexes geometry data by using Sparkle model for the calculation of lanthanide complexes (SMLC) is in agreement with the crystalline structure determined by single-crystal X-ray diffraction analysis. The emission spectra for [Gd(TTA)(3)(TPPO)(2)] and [Gd(TTA)(2) (NO(3))(TPPO)(2)] complexes are associated to T -> S(0) transitions centered on coordinated TTA ligands. Experimental luminescent properties of the bis-TTA complex have been quantified through emission intensity parameters Omega(lambda)(lambda = 2 and 4), spontaneous emission rates (A(rad)), luminescence lifetime (tau), emission quantum efficiency (eta) and emission quantum yield (q), which were compared with those for tris-TTA complex. The experimental data showed that the intensity parameter value for bis-TTA complex is twice smaller than the one for tris-TTA complex, indicating the less polarizable chemical environment in the system containing nitrate ion. A good agreement between the theoretical and experimental quantum yields for both Eu(Ill) complexes was obtained. The triboluminescence (TL) of the [Eu(TTA)(2)(NO(3))(TPPO)(2)] complexes are discussed in terms of ligand-to-metal energy transfer. (c) 2007 Elsevier B.V. All fights reserved.