On the reachable states for the boundary control of the heat equation

We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions onsome square of C, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controlsthat are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class witha specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function

Null controllability of one-dimensional parabolic equations by the flatness approach

We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular.Considering generalized Robin-Neumann boundary conditions at both extremities, we prove the null controllability with one boundary control by following the flatness approach, which providesexplicitly the control and the associated trajectory as series. Both the control and the trajectory have a Gevrey regularity in time related to the $L^p$ class of the coefficient in front of $u\_t$.The approach applies in particular to the (possibly degenerate or singular) heat equation $(a(x)u\_x)\_x-u\_t=0$ with a(x)\textgreater{}0 for a.e. $x\in (0,1)$ and $a+1/a \in L^1(0,1)$, or to the heat equation with inverse square potential $u\_{xx}+(\mu / |x|^2)u-u\_t=0$with $\mu\ge 1/4$

Null controllability of the 1D heat equation using flatness

We derive in a straightforward way the null controllability of a 1-D heat equation with boundary control. We use the so-called {\em flatness approach}, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control law achieving the exact steering to zero. We also give accurate error estimates when the various series involved are replaced by their partial sums, which is paramount for an actual numerical scheme. Numerical experiments demonstrate the relevance of the approach

Controllability of the 1D Schrodinger equation by the flatness approach

We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a "flat output". This provides an explicit control input achieving the exact controllability in the energy space. As an application, we derive an explicit pair of control inputs achieving the exact steering to zero for a simply-supported beam

Null controllability of the 2D heat equation using flatness

International audienceWe derive in a direct and rather straightforward way the null controllability of the N -dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder. We use the so-called flatness approach, which consists in param-eterizing the solution and the control by the derivatives of a "flat output". This yields an explicit control law achieving the exact steering to zero. Replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds. Numerical experiments demonstrate the relevance of the approach

Null controllability of the structurally damped wave equation with moving point control

International audienceWe investigate the internal controllability of the wave equation with structural damping on the one-dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions

La Fasciathérapie Méthode Danis Bois et la récupération physique, mentale et somato-psychique du sportif de haut niveau: Evaluation quantitative et qualitative auprès d’une population de sportifs de haut niveau

Tese apresentada à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de Doutor em Ciências Sociais, especialidade em PsicopedagogiaThis work focuses on fasciatherapy applied to the recovery of high level athletes and attempts to answer the question “How and in what way does fasciatherapy participate in the physical, mental and somato-psychic recovery of high level athletes?” In order to do this, I have presented the theoretical side of the therapies addressing the fascia and in particular the Danis Bois fasciatherapy method, as well as the theoretical side of physical, psychological and somato-psychic recovery in the field of sports. I have approached this research from the viewpoint of a practitioner-researcher in order to gain better understanding of the somato-psychic impact of fasciatherapy on the recovery of ten high level athletes who are deemed to be "in good shape" and who practice sports intensively on a daily basis. This research uses a mixed methodology. The first one is qualitative and is based on interviews. It develops an analysis inspired by phenomenology on a case by case basis and a transverse hermeneutic interpretation. The second one is quantitative and uses a questionnaire based on Likert scales. This research translates the impact of fasciatherapy on seventeen indicators of physical, psychological and somato-psychic recovery.Ce travail porte sur la fasciathérapie appliquée à la récupération des sportifs de haut niveau et tente de répondre à la question « En quoi et comment la fasciathérapie participe-t-elle à la récupération physique, mentale et somato-psychique des sportifs de haut niveau ? » Pour cela, j’ai présenté le champ théorique des thérapies s’adressant aux fascias et notamment la fasciathérapie méthode Danis Bois, ainsi que le champ théorique de la récupération physique, psychique et somato-psychique dans le domaine du sport. J’ai abordé cette recherche avec une posture de praticien-chercheur afin de mieux comprendre les impacts somato-psychiques de la fasciathérapie sur la récupération de dix sportifs de haut niveau réputés « en pleine forme », confrontés à leur pratique sportive intensive quotidienne. Cette recherche déploie une méthodologie mixte. La première, qualitative, est basée sur des entretiens et développe une analyse d’inspiration phénoménologique cas par cas et une interprétation herméneutique tranversale. La seconde, quantitative, est basée sur un questionnaire à base d’échelles de Likert. Cette recherche traduit l’impact de la fasciathérapie sur dix-sept indicateurs de la récupération physique, psychique et somato-psychique.Este trabalho sobre a fasciaterapia aplicada à recuperação dos atletas de alto nível, tenta responder à questão "De que forma a fasciaterapia participa na recuperação física, psicológica e somático-psíquica dos atletas de alta competição?" Para tal, o trabalho teórico apresentado incide nas terapias fasciais (fascia), nomeadamente a fasciaterapia método Danis Bois, e na recuperação física, psicológica e somáticopsíquica no domínio desportivo. Assumi esta investigação adoptando uma postura de praticante-investigador no âmbito de compreender melhor os impactos somatopsíquicos da fasciaterapia na recuperação de 10 atletas considerados "em boa forma" e confrontados a uma prática desportiva quotidiana. Esta investigação desenvolve uma metodologia mista. A primeira, qualitativa, é baseada em entrevistas e desenvolve uma análise de inspiração fenomenológica caso a caso e uma interpretação hermenêutica transversal. A segunda, quantitativa, é baseada num questionário baseado nas escalas de Likert. Esta pesquisa reflecte o impacto da fasciaterapia sobre 17 indicadores de recuperação física, psicológica e somático-psíquica

Chapman-Enskog derivation of the generalized Smoluchowski equation

We use the Chapman-Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations associated with generalized free energy functionals. We mention applications of these results to systems with long-range interactions (self-gravitating systems, 2D vortices, bacterial populations,...). In that case, the Smoluchowski equation is non-local. In the limit of short-range interactions, it reduces to a generalized form of the Cahn-Hilliard equation. These equations are associated with an effective generalized thermodynamical formalism.Comment: In pres

Present eternity : quests of temporality in the literary production of the "extrême contemporain" in France (The Writings of Dominique Fourcade and Emmanuel Hocquard)

The term \uab extr\ueame contemporain \ubb is an expression currently used by scholars to indicate the French literary production of the last 20 years. This term was used in a work of literature for the first time by the French poet Dominique Fourcade in 1986 (\uc9l\ue9gie L apostrophe E.C.) in reference to an epoch, but also to a new sense of experiencing time and space in the so-called \uab age of digital reproducibility \ubb. The aim of this paper is to consider how the change in temporal protocols due to the triumph of Big Optics (Paul Virilio) affects the sense of teleology (destiny) and the quest for experience in French contemporary poetry (in particular, in the genre of the elegy). Including both memory and anticipation, the \uab extr\ueame contemporain \ubb production seems to prefer the \u201ctime of now\u201d, Jetz-zeit in Benjamin\u2019s words, to past or testimony, and speaks to the present, whose responsibility is to give voice to a space where everything is simply allowed to happen