Enhancement of magnetic coercivity in Fe/Mn and Co/Mn bilayers

The dependence of the coercive field and saturated magnetization on the interfacial width is studied to understand the driving mechanism of the coercive enhancement in Fe/Mn and Co/Mn bilayers. We establish a controlled annealing procedure to reveal the origin of this enhancement. Using a model, we reveal that the full interfacial width plays a keyrole, and that no Mn based finite size effects drive the mechanism. We show that this mechanism is common to both type of bilayers.     

The tensor product of f-algebras

In this paper we prove that the Fremlin tensor product of two f-algebras can be endowed with an f-algebra structure and satisfies an appropriate universal property. In particular, the Riesz tensor product of C(X) and C(Y), where X and Y are topological spaces, is an f-subalgebra of C(X × Y).     

Prime Orders All of Whose Prime Suborders Are Selfdual

Let P be an order on a set V. A subset A of V is autonomous in P if every element of V not in A is either less than or greater than or incomparable to all elements of A. The empty set, the singletons from V and the set V are autonomous sets and are called trivial. Call an order prime if all its autonomous sets are trivial. We give the complete list of all finite prime orders all of whose prime suborders are selfdual.     

Observabilité et contrôlabilité exacte indirecte interne par un contrôle localement distribué de systèmes d'équations couplées

We study the observability and the exact controllability of a weakly coupled system with an internal locally control acting on only one equation. We show that, for sufficiently large time, the observation of the velocity of the first component of the solution on a neighborhood of a part of the boundary allows us to get back a weakened energy of initial data of the second component, this if the coupling parameter is sufficiently small, but non-vanishing. This result leads to a uniqueness theorem and, by the HUM method, we prove that the total system is exactly controllable.     

Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of Markov chain Monte Carlo) and are compounded by high dimensionality of the posterior. We address these challenges by introducing truncated Karhunen–Loève expansions, based on the prior distribution, to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior. We seek a solution of this problem using Galerkin projection on a polynomial chaos basis, and use the solution to construct a reduced-dimensionality surrogate posterior density that is inexpensive to evaluate. We demonstrate the formulation on a transient diffusion equation with prescribed source terms, inferring the spatially-varying diffusivity of the medium from limited and noisy data.     

On Bounded Solutions for Nonlinear Parabolic Equations with Degenerate Coercivity

Mediterranean Journal of Mathematics - By means of Stampacchia’s lemma, we prove an existence result of bounded solutions for some nonlinear parabolic equations with degenerate coercivity.     

Ultra‐Tuning of the Rare‐Earth fcu‐MOF Aperture Size for Selective Molecular Exclusion of Branched Paraffins

Using isoreticular chemistry allows the design and construction of a new rare‐earth metal (RE) fcu ‐MOF with a suitable aperture size for practical steric adsorptive separations. The judicious choice of a relatively short organic building block, namely fumarate, to bridge the 12‐connected RE hexanuclear clusters has afforded the contraction of the well‐defined RE‐ fcu ‐MOF triangular window aperture, the sole access to the two interconnected octahedral and tetrahedral cages. The newly constructed RE (Y³⁺ and Tb³⁺) fcu ‐MOF analogues display unprecedented total exclusion of branched paraffins from normal paraffins. The resultant window aperture size of about 4.7 Å, regarded as a sorbate‐size cut‐off, enabled a complete sieving of branched paraffins from normal paraffins. The results are supported by collective single gas and mixed gas/vapor adsorption and calorimetric studies.