Differential Geometry of the Vortex Filament Equation

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting flows is shown to be hereditary. The system is shown to have a description with a Hamiltonian pair. Master symmetries are found and are applied to deriving an expression of the constants of motion in involution. The expression agrees with the inspection of Langer and Perline.Comment: 20 pages, LaTeX, no figure

Vortex Filament in Three-manifold and the Duistermaat-Heckman Formula

Symplectic geometry of the vortex filament in a curved three-manifold is investigated. There appears an infinite sequence of constants of motion in involution in the case of constant curvature. The Duistermaat-Heckman formula is examined perturbatively for the classical partition function in our model and verified up to the 3-loop order.Comment: Revised to include Figure2 (a PostScript file). 15 pages, LaTex2e, 2 figure

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Stochastic Cahn-Hilliard equation with singular nonlinearity and reflection

We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space-time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical penalization method, which uses a crucial monotonicity property. Being inspired by the works of Debussche and Zambotti, we use a method based on infinite dimensional equations, approximation by regular equations and convergence of the approximated semi-group. We obtain existence and uniqueness of solution for nonnegative intial conditions, results on the invariant measures, and on the reflection measures

Young Clusters in the Magellanic Clouds II

We present the results of a quantitative study of the degree of extension to the boundary of the classical convective core within intermediate mass stars. The basis of our empirical study is the stellar population of four young populous clusters in the Magellanic Clouds which has been detailed in Keller, Bessell & Da Costa (2000). The sample affords a meaningful comparison with theoretical scenarios with varying degrees of convective core overshoot and binary star fraction. Two critical properties of the population, the main-sequence luminosity function and the number of evolved stars, form the basis of our comparison between the observed data set and that simulated from the stellar evolutionary models. On the basis of this comparison we conclude that the case of no convective core overshoot is excluded at a 2 sigma level.Comment: 27 pages, 12 figures, AJ accepte

Specific staining of human chromosomes in Chinese hamster x man hybrid cell lines demonstrates interphase chromosome territories

In spite of Carl Rabl's (1885) and Theodor Boveri's (1909) early hypothesis that chromosomes occupy discrete territories or domains within the interphase nucleus, evidence in favor pf this hypothesis has been limited and indirect so far in higher plants and animals. The alternative possibility that the chromatin fiber of single chromosomes might be extended throughout the major part of even the whole interphase nucleus has been considered for many years. In the latter case, chromosomes would only exist as discrete chromatin bodies during mitosis but not during interphase. Both possibilities are compatible with Boveri's well established paradigm of chromosome individuality. Here we show that an active human X chromosome contained as the only human chromosome in a Chinese hamster x man hybrid cell line can be visualized both in metaphse plates and in interphase nuclei after in situ hybridization with either 3H- or biotin-labeled human genomic DNA. We demonstrate that this chromosome is organized as a distinct chromatin body throughout interphase. In addition, evidence for the territorial organization of human chromosomes is also presented for another hybrid cell line containing several autosomes and the human X chromosome. These findings are discussed in the context of our present knowledge of the organization and topography of interphase chromosomes. General applications of a strategy aimed at specific staining of individual chromosomes in experimental and clinical cytogenetics are briefly considered

Light nuclei in galactic globular clusters : constraints on the self-enrichment scenario from nucleosynthesis

Hydrogen-burning is the root cause of the star-to-star abundance variations of light nuclei in Galactic globular clusters (GC). In the present work we constrain the physical conditions that gave rise to the observed abundance patterns of Li, C, N, O, Na, Mg, Al, as well as Mg isotopes in the typical case of NGC6752. We perform nucleosynthesis calculations at constant temperature, adopting realistic initial abundances for the proto-cluster gas. We use a detailed nuclear reaction network and state-of-the-art nuclear reaction rates. Although simplistic, our analysis provides original results and new constraints on the self-enrichment scenario for GCs. Our parametrized calculations allow us to determine a narrow range of temperature where the observed extreme abundances of all light elements and isotopes in NGC6752 are nicely reproduced simultaneously. This agreement is obtained after mixing of the H-processed material with 30 % of unprocessed gas. The observed C-N, O-Na, Mg-Al, Li-Na and F-Na anticorrelations, as well as the behaviour of the Mg isotopes can be recovered by assuming mixing with even larger dilution factors. Li production by the stars that build up the other abundance anomalies is not mandatory in the case of NGC 6752. Observations of O, Na, Mg and Al constrain the temperature range for H-burning; such temperatures are encountered in the two main candidate ``polluters'' proposed for GCs, namely massive AGBs and the most massive main-sequence stars. (Abridged).Comment: 15 pages, 8 figures, accepted in Astronomy and Astrophysic

In vivo biocompatibility and biodegradability of dextrin-based hydrogels

The in vivo biocompatibility of dextrin hydrogels obtained by polymerization of dextrin-hydroxyethylmethacrylate (dextrin-HEMA) and dextrin-vinyl acrylate (dextrin-VA) are reported in this work. The histological analysis of subcutaneous implants of these hydrogels, featuring inflammatory and reabsorption events, were carried out over a 16-week period in mice. The dextrin-HEMA hydrogel was quickly and completely degraded and reabsorbed, whereas the dextrin-VA degradation occurred slowly and a thin fibrous capsule surrounded the nondegradable hydrogel. The dextrin-HEMA was degraded after 16 weeks with only mild inflammation and a few detectable foamy macrophages around the implant. These events were followed by complete resorption and no sign of capsule formation or fibrosis associated to the implants. The results indicate that the dextrin hydrogels are biocompatible because no toxicity on the tissues surrounding the implants was found. It may be speculated that a controlled degradation rate of the hydrogels may be obtained by grafting dextrin to HEMA and VA in different proportions.Funding from FCT through POCTI program is acknowledged. The authors Susana Moreira and Rui M. Gil da Costa are recipients of a PhD fellowship from Fundacao para a Ciencia e a Tecnologia (FCT, Portugal)

Structure formation in active networks

Structure formation and constant reorganization of the actin cytoskeleton are key requirements for the function of living cells. Here we show that a minimal reconstituted system consisting of actin filaments, crosslinking molecules and molecular-motor filaments exhibits a generic mechanism of structure formation, characterized by a broad distribution of cluster sizes. We demonstrate that the growth of the structures depends on the intricate balance between crosslinker-induced stabilization and simultaneous destabilization by molecular motors, a mechanism analogous to nucleation and growth in passive systems. We also show that the intricate interplay between force generation, coarsening and connectivity is responsible for the highly dynamic process of structure formation in this heterogeneous active gel, and that these competing mechanisms result in anomalous transport, reminiscent of intracellular dynamics