Analyse mathématique d'un systéme de transport-diffusion-réaction modélisant la restauration biologique d'un milieu poreux

Sin resume

Atom lithography without laser cooling

Using direct-write atom lithography, Fe nanolines are deposited with a pitch of 186 nm, a full width at half maximum (FWHM) of 50 nm, and a height of up to 6 nm. These values are achieved by relying on geometrical collimation of the atomic beam, thus without using laser collimation techniques. This opens the way for applying direct-write atom lithography to a wide variety of elements.Comment: 7 pages, 11 figure

Incompressible flow in porous media with fractional diffusion

In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove global existence of weak solutions for different cases. Moreover, we obtain the decay of the solution in $L^p$, for any $p\geq2$, and the asymptotic behavior is shown. Finally, we prove the existence of an attractor in a weak sense and, for the sub-critical dissipative case with $\alpha\in (1,2]$, we obtain the existence of the global attractor for the solutions in the space $H^s$ for any $s > (N/2)+1-\alpha$

A Sucrose Solution Application to the Study of Model Biological Membranes

The small-angle X-ray and neutron scattering, time resolved X-ray small-angle and wide-angle diffraction coupled with differential scanning calorimetry have been applied to the investigation of unilamellar and multilamellar dimyristoylphosphatidylcholine (DMPC) vesicles in sucrose buffers with sucrose concentrations from 0 to 60%. Sucrose buffer decreased vesicle size and polydispersity and increased an X-ray contrast between phospholipid membrane and bulk solvent sufficiently. No influence of sucrose on the membrane thickness or mutual packing of hydrocarbon chains has been detected. The region of sucrose concentrations 30%-40% created the best experimental conditions for X-ray small-angle experiments with phospholipid vesicles.Comment: PDF: 10 pages, 6 figures. MS Word sours

Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems

On bounded three-dimensional domains, we consider divergence-type operators including mixed homogeneous Dirichlet and Neumann boundary conditions and discontinuous coefficient functions. We develop a geometric framework in which it is possible to prove that the operator provides an isomorphism of suitable function spaces. In particular, in these spaces, the gradient of solutions turns out to be integrable with exponent larger than the space dimension three. Relevant examples from real-world applications are provided in great detail

Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential

A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle \K is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed $n$-dimensional simplex, we prove that the long-time behavior of the solution semigroup associated with this problem can be described in terms of an exponential attractor. In particular, the latter means that the fractal dimension of the associated global attractor is also finite

Global and exponential attractors for a Ginzburg-Landau model of superfluidity

The long-time behavior of the solutions for a non-isothermal model in superfluidity is investigated. The model describes the transition between the normal and the superfluid phase in liquid 4He by means of a non-linear differential system, where the concentration of the superfluid phase satisfies a non-isothermal Ginzburg-Landau equation. This system, which turns out to be consistent with thermodynamical principles and whose well-posedness has been recently proved, has been shown to admit a Lyapunov functional. This allows to prove existence of the global attractor which consists of the unstable manifold of the stationary solutions. Finally, by exploiting recent techniques of semigroups theory, we prove the existence of an exponential attractor of finite fractal dimension which contains the global attractor.Comment: 39 page