Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Approximate controllability of the Schrödinger Equation with a polarizability term in higher Sobolev norms

Abstract: This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field induced dipole moment. Sufficient conditions for approximate controllability are given. For transfers between eigenstates of the free Hamiltonian, the control laws are explicitly given. The results apply also for unbounded or non-regular potentials.

Nearest embedded and embedding self-nested trees

Abstract: Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by directed acrylic graph (DAG) compression. A method for quantifying the degree of self-similarity of plants through self-nested trees was introduced by Godin and Ferraro in 2010. The procedure consists of computing a self-nested approximation, called the nearest embedding self-nested tree, that both embeds the plant and is the closest to it. In this paper, we propose a new algorithm that computes the nearest embedding self-nested tree with a smaller overall complexity, but also the nearest embedded self-nested tree. We show from simulations that the latter is mostly the closest to the initial data, which suggests that this better approximation should be used as a privileged measure of the degree of self-similarity of plants.

Two finiteness theorem for $(a,b)$-modules

Abstract: 1. For a proper holomorphic function \ $ f : X \to D$ \ of a complex manifold \ $X$ \ on a disc such that \ $\{ df = 0 \} \subset f^{-1}(0)$, we construct, in a functorial way, for each integer \ $p$, a geometric (a,b)-module \ $E^p$ \ associated to the (filtered) Gauss-Manin connexion of \ $f$.\\ This first theorem is an existence/finiteness result which shows that geometric (a,b)-modules may be used in global situations. 2. For any regular (a,b)-module \ $E$ \ we give an integer \ $N(E)$, explicitely given from simple invariants of \ $E$, such that the isomorphism class of \ $E\big/b^{N(E)}.E$ \ determines the isomorphism class of \ $E$.\\ This second result allows to cut asymptotic expansions (in powers of \ $b$) \ of elements of \ $E$ \ without loosing any information.

Control systems of zero curvature are not necessarily trivializable

Abstract: A control system $\dot{q} = f(q,u)$ is said to be trivializable if there exists local coordinates in which the system is feedback equivalent to a control system of the form $\dot{q} = f(u)$. In this paper we characterize trivializable control systems and control systems for which, up to a feedback transformation, $f$ and $\partial f/\partial u$ commute. Characterizations are given in terms of feedback invariants of the system (its control curvature and its centro-affine curvature) and thus are completely intrinsic. To conclude we apply the obtained results to Zermelo-like problems on Riemannian manifolds.

On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals

Abstract: We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which include both spatial heterogeneity and anisotropy. In particular, we introduce the notion of deciding factors which single out a nonlocal diffusion model and typically consist of the total jump rate and the average jump length. In this framework, we also discuss the dependence of the profile of the steady state solutions on these deciding factors, thus shedding light on the preferential position of individuals.