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

Geometry of Schreieder's varieties and some elliptic and K3 moduli curves

We study the geometry of a class of $n$-dimensional smooth projective varieties constructed by Schreieder for their noteworthy Hodge-theoretic properties. In particular, we realize Schreieder's surfaces as elliptic modular surfaces and Schreieder's threefolds as one-dimensional families of Picard rank $19$ $K3$ surfaces.Comment: 28 pages. Contains arXiv:1603.0561

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

Dirac's Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac's canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As result the quantum system is simply modeled by the original quantum Hamiltonian.Comment: 12 pages, Open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0