Particle and particle pair dispersion in turbulence modeled with spatially and temporally correlated stochastic processes

In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles, which are modeled by stochastic processes correlated in time. We are able to reproduce the ballistic regime in the mean squared displacement of single particles and the transition to a normal diffusion regime for long times. For the dispersion of particle pairs we find a $t^{2}$-dependence of the mean squared separation at short times and a $t$-dependence for long ones. For intermediate times indications for a Richardson $t^{3}$ law are observed in certain situations. Finally the influence of inertia of real particles on the dispersion is investigated.Comment: 10 pages, 7 figures, 1 tabl

Purification, growth, and characterization of Zn(x)Cd(1-x)Se crystals

The purification of starting materials which were used in the growth of Zn(x)Cd(1-x)Se (x = 0.2) single crystals using the traveling solution method (TSM) is reported. Up to 13 cm long single crystals and as grown resistivities of 6 x 10(exp 12) ohm/cm could be achieved. Infrared and Raman spectra of Zn(0.2)Cd(0.8)Se are also presented and discussed

The poverty of journal publishing

The article opens with a critical analysis of the dominant business model of for-profit, academic publishing, arguing that the extraordinarily high profits of the big publishers are dependent upon a double appropriation that exploits both academic labour and universities’ financial resources. Against this model, we outline four possible responses: the further development of open access repositories, a fair trade model of publishing regulation, a renaissance of the university presses, and, finally, a move away from private, for-profit publishing companies toward autonomous journal publishing by editorial boards and academic associations. </jats:p

The essential Mcm7 protein PROLIFERA is localized to the nucleus of dividing cells during the G(1) phase and is required maternally for early Arabidopsis development

PROLIFERA (PRL) encodes a homologue of the DNA replication licensing factor Mcm7, a highly conserved protein found in all eukaryotes. Insertions in the PROLIFERA gene are lethal, resulting in decreased transmission through the female gametophyte, and homozygous embryonic lethality. We show here that PROLIFERA is specifically expressed in populations of dividing cells in sporophytic tissues of the plant body, such as the palisade layer of the leaf and founder cells of initiating flower primordia, Gene fusions with the green fluorescent protein (GFP) reveal that the PROLIFERA protein accumulates during the G(1) phase of the cell cycle, and is transiently localized to the nucleus. During mitosis, the fusion protein rapidly disappears, returning to daughter nuclei during G(1), PROLIFERA::GUS fusions are strongly expressed in the central cell nucleus of mature megagametophytes, which have a variety of arrest points reflecting a leaky lethality. Expression is also observed in the endosperm of mutant prl embryo sacs that arrest following fertilization. Crosses with wild-type pollen result in occasional embryonic lethals that also stain for GUS activity, In contrast, embryos resulting from crosses of wild-type carpels with PRL::GUS pollen do not stain and are phenotypically normal. In situ hybridization of GUS fusion RNA indicates transcription is equivalent from maternally and paternally derived alleles, so that accumulation of maternally derived gametophytic protein is likely to be responsible for the 'maternal' effect

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.Comment: 41 page

Schubert varieties and generalizations

This contribution reviews the main results on Schubert varieties and their generalizations It covers more or less the material of the lectures at the Seminar These were partly expository introducing material needed by other lecturers In particular Section reviews classical material used in several of the other contribution