Spectra of Graphs and the Spectral Criterion for Property (T)

For a finite connected graph $X$, we consider the graph $RX$ obtained from $X$ by associating a new vertex to every edge of $X$ and joining by edges the extremities of each edge of $X$ to the corresponding new vertex. We express the spectrum of the Laplace operator on $RX$ as a function of the corresponding spectrum on $X$. As a corollary, we show that $X$ is a complete graph if and only if \lambda_1(RX)>\frac{1}{2}. We give a re-interpretation of the correspondence $X\mapsto RX$ in terms of the right-angled Coxeter group defined by $X$

Paradox management delegation: inter and intra-individual variability

While paradox is increasingly presented in organisational literature as a normal, even advisable element, it is still seen as a problem by individuals who are confronted with it on a daily basis. Thus there is a clear gap between researchers' conclusions and real-life situations experienced by practitioners, or maybe a tension between two levels of analysis, organisational and individual levels. We have found that this tension has seldom been studied. In a nutshell, existing literature tends to be divided into two groups. Our research work therefore aims to study the positions of health sector professionals with respect to the paradox management that has been delegated to them, to analyse the extent to which this delegation might alter the pluralistic organisational management of paradoxes. To this end, we conducted semi-structured interviews with 14 of 16 new physician-managers working in a large teaching hospital where the reform was initiated. Our results show that individuals adopt four types of positions when faced with paradox : rejection, detachment, absorption, and transcendence.Paradox ; management ; delegation ; individual variability

Elastic instability in stratified core annular flow

We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -- it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure rheological properties of dilute polymer solutions that are difficult to assess otherwise.Comment: 4 pages, 4 figure

A New Family of Planets ? "Ocean Planets"

A new family of planets is considered which is between rochy terrestrial planets and gaseous giant ones: "Ocean-Planets". We present the possible formation, composition and internal models of these putative planets, including that of their ocean, as well as their possible Exobiology interest. These planets should be detectable by planet detection missions such as Eddington and Kepler, and possibly COROT (lauch scheduled in 2006). They would be ideal targets for spectroscopic missions such as Darwin/TPF.Comment: 15 pages, 3 figures submitted to Icarus notes (10 july 2003

Quand l'information échappe à ses créateurs : le cas de l'artificialisation des terres agricoles en Languedoc-Roussillon

International audienceThis article aims to describe how the quantification of a phenomenon in relation to a specific worldview spreads and is distorted. This project has been supported by a regional public authority in Languedoc-Roussillon (France), and consisted in the production of information so to quantify and qualify the farmland decrease due to urban sprawl. The paper is based on Latour's actor-network theory; it characterizes the process of enrolment, and the development of dissidences. Identifying contradictory logics and dissidences help questioning the complexity of ‘closing the black-box' regarding information production and of sensemaking between heterogeneous actants involved in a supposed-to-be public debate.Cet article vise à spécifier comment la quantification d'un phénomène fondée sur une certaine vision du monde se propage et se déforme. Ce projet a été porté par une direction déconcentrée de l'Etat soucieuse de l'emprise croissante du bâti sur les terres agricoles en Languedoc-Roussillon. Le cadre théorique mobilisé, la sociologie de la traduction, permet d'identifier les grandes étapes d'intéressement, d'enrôlement, ainsi que le développement de controverses. Les difficultés rencontrées interrogent sur la complexité de clôture de processus innovants s'agissant de production d'information et de co-construction de sens associant des actants hétérogènes impliqués dans des procédures de débat public

Mesures de facteurs spectroscopiques de 61Ni par réaction (d, p) en régime sous-coulombien

Nous avons utilisé la réaction (d, p) en régime sous-coulombien pour mesurer les facteurs spectroscopiques de deux états excités par transferts l = 0 et l = 2 dans 61Ni au voisinage de 4,8 MeV. Nos résultats confirment que la règle de somme pour le remplissage des couches 3s1/2 et 2d n'est satisfaite qu'à 50 % dans 61Ni

Phase field modeling of electrochemistry I: Equilibrium

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories. We calculate the surface energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4, SIUnits.sty. Precedes cond-mat/030817

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Isometric group actions on Banach spaces and representations vanishing at infinity

Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property ({\BP}_0^V), for $V$ be a Banach space: a locally compact group $G$ has property ({\BP}_0^V) if every affine isometric action of $G$ on $V$, such that the linear part is a $C_0$-representation of $G$, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic groups over a local field of characteristic zero, have property ({\BP}_0^V). As a consequence for unitary representations, we characterize those groups in the latter classes for which the first cohomology with respect to the left regular representation on $L^2(G)$ is non-zero; and we characterize uniform lattices in those groups for which the first $L^2$-Betti number is non-zero.Comment: 28 page