Sticky behavior of fluid particles in the compressible Kraichnan model

We consider the compressible Kraichnan model of turbulent advection with small molecular diffusivity and velocity field regularized at short scales to mimic the effects of viscosity. As noted in ref.[5], removing those two regularizations in two opposite orders for intermediate values of compressibility gives Lagrangian flows with quite different properties. Removing the viscous regularization before diffusivity leads to the explosive separation of trajectories of fluid particles whereas turning the regularizations off in the opposite order results in coalescence of Lagrangian trajectories. In the present paper we re-examine the situation first addressed in ref.[6] in which the Prandtl number is varied when the regularizations are removed. We show that an appropriate fine-tuning leads to a sticky behavior of trajectories which hit each other on and off spending a positive amount of time together. We examine the effect of such a trajectory behavior on the passive transport showing that it induces anomalous scaling of the stationary 2-point structure function of an advected tracer and influences the rate of condensation of tracer energy in the zero wavenumber mode.Comment: latex, 35 page

Lagrangian dispersion in Gaussian self-similar ensembles

We analyze the Lagrangian flow in a family of simple Gaussian scale-invariant velocity ensembles that exhibit both spatial roughness and temporal correlations. We show that the behavior of the Lagrangian dispersion of pairs of fluid particles in such models is determined by the scale dependence of the ratio between the correlation time of velocity differences and the eddy turnover time. For a non-trivial scale dependence, the asymptotic regimes of the dispersion at small and large scales are described by the models with either rapidly decorrelating or frozen velocities. In contrast to the decorrelated case, known as the Kraichnan model and exhibiting Lagrangian flows with deterministic or stochastic trajectories, fast separating or trapped together, the frozen model is poorly understood. We examine the pair dispersion behavior in its simplest, one-dimensional version, reinforcing analytic arguments by numerical analysis. The collected information about the pair dispersion statistics in the limiting models allows to partially predict the extent of different phases and the scaling properties of the Lagrangian flow in the model with time-correlated velocities.Comment: 43 pages, 10 figure

Prognostic impact of reduced connexin43 expression and gap junction coupling of neoplastic stromal cells in giant cell tumor of bone

Missense mutations of the GJA1 gene encoding the gap junction channel protein connexin43 (Cx43) cause bone malformations resulting in oculodentodigital dysplasia (ODDD), while GJA1 null and ODDD mutant mice develop osteopenia. In this study we investigated Cx43 expression and channel functions in giant cell tumor of bone (GCTB), a locally aggressive osteolytic lesion with uncertain progression. Cx43 protein levels assessed by immunohistochemistry were correlated with GCTB cell types, clinico-radiological stages and progression free survival in tissue microarrays of 89 primary and 34 recurrent GCTB cases. Cx43 expression, phosphorylation, subcellular distribution and gap junction coupling was also investigated and compared between cultured neoplastic GCTB stromal cells and bone marow stromal cells or HDFa fibroblasts as a control. In GCTB tissues, most Cx43 was produced by CD163 negative neoplastic stromal cells and less by CD163 positive reactive monocytes/macrophages or by giant cells. Significantly less Cx43 was detected in alpha-smooth muscle actin positive than alpha-smooth muscle actin negative stromal cells and in osteoclast-rich tumor nests than in the adjacent reactive stroma. Progressively reduced Cx43 production in GCTB was significantly linked to advanced clinico-radiological stages and worse progression free survival. In neoplastic GCTB stromal cell cultures most Cx43 protein was localized in the paranuclear-Golgi region, while it was concentrated in the cell membranes both in bone marrow stromal cells and HDFa fibroblasts. In Western blots, alkaline phosphatase sensitive bands, linked to serine residues (Ser369, Ser372 or Ser373) detected in control cells, were missing in GCTB stromal cells. Defective cell membrane localization of Cx43 channels was in line with the significantly reduced transfer of the 622 Da fluorescing calcein dye between GCTB stromal cells. Our results show that significant downregulation of Cx43 expression and gap junction coupling in neoplastic stromal cells are associated with the clinical progression and worse prognosis in GCTB

Advection passive par des champs de vitesse stochastiques.

The principal aim of this thesis is to study various aspects of the evolution of some scalar or vector field, advected by a velocity field who's statistics is given independently of the advected field. As a byproduct, we also come to study integral curves of the velocity field, known as Lagrangian trajectories. After a synthetic introduction, several models and problems are approached. Our main model -- named after R. H. Kraichnan -- uses velocity fields that are Gaussian delta-correlated in time. The cases, where the spatial structure of the velocity field is either smooth or is a (multidimensional) fractional Brownian motion, are studied. A model of time correlated velocity field is also considered. Among problems studied, one finds the anisotropic sector of the advected quantity, emergence of spatial intermittency, and taking different limits of the velocity field statistics.L'objet principal de cette thèse est d'étudier divers aspects de l'évolution d'un champ scalaire ou vectoriel, transporté par un champ de vitesse dont la statistique est donnée indépendamment du champ advecté. Ce faisant, on est amené également à étudier les courbes intégrales du champ de vitesse, appelées trajectoires Lagrangiennes. Après une introduction synthétique, plusieurs modèles et problèmes sont abordés. Notre modèle principal - baptisé après R. H. Kraichnan - suppose des champs de vitesse gaussiens delta-corrélés en temps. Sont étudiés les cas où la structure spatiale du champ de vitesse est soit lisse soit brownien fractionnaire (multidimensionnel). Un modèle où le champ de vitesse est corrélé en temps est également abordé. Parmi les problèmes étudiés sont les secteurs anisotropes de la quantité advectée, l'apparition d'intermittence spatiale, ou encore différents passages à la limite dans la statistique du champ de vitesse

Advection passive par des champs de vitesse stochastiques

PALAISEAU-Polytechnique (914772301) / SudocSudocFranceF