A laboratory Study of Polymer Rheology in Bulk and in Sandstone Cores with Application to German Oilfields

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Mathematical study of degenerate boundary layers: A Large Scale Ocean Circulation Problem

This paper is concerned with a complete asymptoticanalysis as $\mathfrak{E} \to 0$ of the stationary Munk equation $\partial\_x\psi-\mathfrak{E} \Delta^2 \psi=\tau$ in a domain $\Omega\subset \mathbf{R}^2$, supplemented with boundaryconditions for $\psi$ and $\partial\_n \psi$. This equation is a simplemodel for the circulation of currents in closed basins, the variables$x$ and $y$ being respectively the longitude and the latitude. A crudeanalysis shows that as $\mathfrak{E} \to 0$, the weak limit of $\psi$ satisfiesthe so-called Sverdrup transport equation inside the domain, namely$\partial\_x \psi^0=\tau$, while boundary layers appear in the vicinity ofthe boundary.These boundary layers, which are the main center of interest of thepresent paper, exhibit several types of peculiar behaviour. First, thesize of the boundary layer on the western and eastern boundary, whichhad already been computed by several authors, becomes formally verylarge as one approaches northern and southern portions of the boudary,i.e. pieces of the boundary on which the normal is vertical. Thisphenomenon is known as geostrophic degeneracy. In order to avoid suchsingular behaviour, previous studies imposed restrictive assumptionson the domain $\Omega$ and on the forcing term $\tau$. Here, we provethat a superposition of two boundary layers occurs in the vicinity ofsuch points: the classical western or eastern boundary layers, andsome northern or southern boundary layers, whose mathematicalderivation is completely new. The size of northern/southern boundarylayers is much larger than the one of western boundary layers($\mathfrak{E}^{1/4}$ vs. $\mathfrak{E}^{1/3}$). We explain in detail how the superpositiontakes place, depending on the geometry of the boundary.Moreover, when the domain $\Omega$ is not connex in the $x$ direction,$\psi^0$ is not continuous in $\Omega$, and singular layers appear inorder to correct its discontinuities. These singular layers areconcentrated in the vicinity of horizontal lines, and thereforepenetrate the interior of the domain $\Omega$. Hence we exhibit some kindof boundary layer separation. However, we emphasize that we remainable to prove a convergence theorem, so that the singular layerssomehow remain stable, in spite of the separation.Eventually, the effect of boundary layers is non-local in severalaspects. On the first hand, for algebraic reasons, the boundary layerequation is radically different on the west and east parts of theboundary. As a consequence, the Sverdrup equation is endowed with aDirichlet condition on the East boundary, and no condition on the Westboundary. Therefore western and eastern boundary layers have in factan influence on the whole domain $\Omega$, and not only near theboundary. On the second hand, the northern and southern boundary layerprofiles obey a propagation equation, where the space variable $x$plays the role of time, and are therefore not local.Comment: http://www.ams.org/books/memo/1206/memo1206.pd

Measurement of an excess in the yield of J/ψ\psi at very low-pTp_{\rm T} in Pb--Pb collisions with the ALICE detector

We report on the measurement of J/$\psi$ production at very low transverse momentum ($p_{\rm T} <$ 300 MeV/$c$) in Pb--Pb collisions performed with the ALICE detector at the LHC. We find an excess in the yield of J/$\psi$ with respect to expectations from hadronic production. Coherent photo-production of J/$\psi$ is proposed as a plausible origin of this excess. We show the nuclear modification factor of very low-$p_{\rm T}$ J/$\psi$ as a function of centrality. Then we measure the J/$\psi$ coherent photoproduction cross section in peripheral events assuming that it is the mechanism at the origin of the measured excess. It's worth noting that the observation of J/$\psi$ coherent photoproduction in Pb--Pb collisions at impact parameters smaller than twice the nuclear radius has never been observed so far and would open new theoretical challenges.Comment: Proceeding of EDS Blois Conference, 29th June - 4th July 2015, Borgo, Corsic

Maximally selected chi-square statistics and binary splits of nominal variables

We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a pregnancy and birth data set

Long time behaviour of viscous scalar conservation laws

This paper is concerned with the stability of stationary solutions of the conservation law $\partial_t u + \mathrm{div}_y A(y,u) -\Delta_y u=0$, where the flux $A$ is periodic with respect to its first variable. Essentially two kinds of asymptotic behaviours are studied here: the case when the equation is set on $\R$, and the case when it is endowed with periodic boundary conditions. In the whole space case, we first prove the existence of viscous stationary shocks - also called standing shocks - which connect two different periodic stationary solutions to one another. We prove that standing shocks are stable in $L^1$, provided the initial disturbance satisfies some appropriate boundedness conditions. We also extend this result to arbitrary initial data, but with some restrictions on the flux $A$. In the periodic case, we prove that periodic stationary solutions are always stable. The proof of this result relies on the derivation of uniform $L^\infty$ bounds on the solution of the conservation law, and on sub- and super-solution techniques.Comment: 36 page

PLS dimension reduction for classification of microarray data

PLS dimension reduction is known to give good prediction accuracy in the context of classification with high-dimensional microarray data. In this paper, PLS is compared with some of the best state-of-the-art classification methods. In addition, a simple procedure to choose the number of components is suggested. The connection between PLS dimension reduction and gene selection is examined and a property of the first PLS component for binary classification is proven. PLS can also be used as a visualization tool for high-dimensional data in the classification framework. The whole study is based on 9 real microarray cancer data sets

On the equivalence of some eternal additive coalescents

In this paper, we study additive coalescents. Using their representation as fragmentation processes, we prove that the law of a large class of eternal additive coalescents is absolutely continuous with respect to the law of the standard additive coalescent on any bounded time interval