The Generalized Graetz Problem in Finite Domains

We consider the generalized Graetz problem associated with stationary convection-diffusion inside a domain having any regular three-dimensional translationally invariant section and finite or semi-infinite extent. Our framework encompasses any previous “extended” and “conjugated” Graetz generalizations and provides theoretical bases for computing the orthogonal set of generalized two-dimensional Graetz modes. The theoretical framework includes both heterogeneous and possibly anisotropic diffusion tensors. In the case of semi-infinite domains, the existence of a bounded solution is shown from the analysis of two-dimensional operator eigenvectors which form a basis of L2 . In the case of finite domains a similar basis can be exhibited, and the mode’s amplitudes can be obtained from the inversion of newly defined finite domain operator. Our analysis includes both the theoretical and practical issues associated with this finite domain operator inversion as well as its interpretation as a multireflection image method. Error estimates are provided when numerically truncating the spectrum to a finite number of modes. Numerical examples are validated for reference configurations and provided in nontrivial cases. Our methodology shows how to map the solution of stationary convection-diffusion problems in finite three-dimensional domains into a two-dimensional operator spectrum, which leads to a drastic reduction in computational cost

Shape optimization for the generalized Graetz problem

We apply shape optimization tools to the generalized Graetz problem which is a convection-diffusion equation. The problem boils down to the optimization of generalized eigen values on a two phases domain. Shape sensitivity analysis is performed with respect to the evolution of the interface between the fluid and solid phase. In particular physical settings, counterexamples where there is no optimal domains are exhibited. Numerical examples of optimal domains with different physical parameters and constraints are presented. Two different numerical methods (level-set and mesh-morphing) are show-cased and compared

Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials

Let $\R$ be a real closed field, ${\mathcal Q} \subset \R[Y_1,...,Y_\ell,X_1,...,X_k],$ with \deg_{Y}(Q) \leq 2, \deg_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m, and ${\mathcal P} \subset \R[X_1,...,X_k]$ with \deg_{X}(P) \leq d, P \in {\mathcal P}, #({\mathcal P})=s. Let $S \subset \R^{\ell+k}$ be a semi-algebraic set defined by a Boolean formula without negations, with atoms $P=0, P \geq 0, P \leq 0, P \in {\mathcal P} \cup {\mathcal Q}$. We describe an algorithm for computing the the Betti numbers of $S$. The complexity of the algorithm is bounded by $(\ell s m d)^{2^{O(m+k)}}$. The complexity of the algorithm interpolates between the doubly exponential time bounds for the known algorithms in the general case, and the polynomial complexity in case of semi-algebraic sets defined by few quadratic inequalities known previously. Moreover, for fixed $m$ and $k$ this algorithm has polynomial time complexity in the remaining parameters.Comment: 24 pages, 3 figure

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Background Light in Potential Sites for the ANTARES Undersea Neutrino Telescope

The ANTARES collaboration has performed a series of {\em in situ} measurements to study the background light for a planned undersea neutrino telescope. Such background can be caused by $^{40}$K decays or by biological activity. We report on measurements at two sites in the Mediterranean Sea at depths of 2400~m and 2700~m, respectively. Three photomultiplier tubes were used to measure single counting rates and coincidence rates for pairs of tubes at various distances. The background rate is seen to consist of three components: a constant rate due to $^{40}$K decays, a continuum rate that varies on a time scale of several hours simultaneously over distances up to at least 40~m, and random bursts a few seconds long that are only correlated in time over distances of the order of a meter. A trigger requiring coincidences between nearby photomultiplier tubes should reduce the trigger rate for a neutrino telescope to a manageable level with only a small loss in efficiency.Comment: 18 pages, 8 figures, accepted for publication in Astroparticle Physic

Community psychiatric nurses and the care co-ordinator role: squeezed to provide ‘limited nursing’.

Background: The Care Programme Approach (CPA) is the key policy underpinning community-focused mental health services but has been unevenly implemented and is associated with increased inpatient bed use. The care co-ordinator role is central to the CPA and is most often held by Community Psychiatric Nurses (CPNs), but there has been little research into how this role is conducted or how it impacts on the work of CPNs and their ability to meet the needs of service users. Aim: The study aimed to identify and illuminate the factors that either facilitated or constrained the ability of CPNs, in their role as care co-ordinators, to meet service users’ and carers’ needs. Methods: A multiple case study of seven sectorised community mental health teams was employed over two years using predominantly qualitative methods of participant observation, semi-structured interviews and document review. Findings: Additional duties and responsibilities specifically associated with the care co-ordinator role and multidisciplinary working, combined with heavy workloads, combined to produce ‘limited nursing’, whereby CPNs are unable to provide evidence-based psychosocial interventions that are recognised to reduce relapse amongst people with severe mental illness. Conclusions: The role of the CPA care co-ordinator was not designed to support the provision of psychosocial interventions. Consequently, CPNs in the co-ordinator role faced with competing demands are unable to provide the range of structured, evidence-based interventions required. This may partially account for the increased inpatient bed use associated with the CPA

Evolutionary history of hepatitis C virus genotype 5a in France, a multicenter ANRS study

The epidemic history of HCV genotype 5a is poorly documented in France, where its prevalence is very low, except in a small central area, where it accounts for 14.2% of chronic hepatitis C cases. A Bayesian coalescent phylogenetic investigation based on the E1 envelope gene and a non-structural genomic segment (NS3/4) was carried out to trace the origin of this epidemic using a large sample of genotype 5a isolates collected throughout France. The dates of documented transmissions by blood transfusion were used to calibrate five nodes in the phylogeny. The results of the E1 gene analysis showed that the best-fitting population dynamic model was the expansion growth model under a relaxed molecular clock. The rate of nucleotide substitutions and time to the most recent common ancestors (tMRCA) of genotype 5a isolates were estimated. The divergence of all the French HCV genotype 5a strains included in this study was dated to 1939 [95% HPD: 1921–1956], and the tMRCA of isolates from central France was dated to 1954 [1942–1967], which is in agreement with epidemiological data. NS3/4 analysis provided similar estimates with strongly overlapping HPD values. Phylodynamic analyses give a plausible reconstruction of the evolutionary history of HCV genotype 5a in France, suggesting the concomitant roles of transfusion, iatrogenic route and intra-familial transmission in viral diffusion

Sedimentation and Fouling of Optical Surfaces at the ANTARES Site

ANTARES is a project leading towards the construction and deployment of a neutrino telescope in the deep Mediterranean Sea. The telescope will use an array of photomultiplier tubes to detect the Cherenkov light emitted by muons resulting from the interaction with matter of high energy neutrinos. In the vicinity of the deployment site the ANTARES collaboration has performed a series of in-situ measurements to study the change in light transmission through glass surfaces during immersions of several months. The average loss of light transmission is estimated to be only ~2% at the equator of a glass sphere one year after deployment. It decreases with increasing zenith angle, and tends to saturate with time. The transmission loss, therefore, is expected to remain small for the several year lifetime of the ANTARES detector whose optical modules are oriented downwards. The measurements were complemented by the analysis of the ^{210}Pb activity profile in sediment cores and the study of biofouling on glass plates. Despite a significant sedimentation rate at the site, in the 0.02 - 0.05 cm.yr^{-1} range, the sediments adhere loosely to the glass surfaces and can be washed off by water currents. Further, fouling by deposits of light-absorbing particulates is only significant for surfaces facing upwards.Comment: 18 pages, 14 figures (pdf), submitted to Astroparticle Physic

Locative Media and Sociability:Using Location-Based Social Networks to Coordinate Everyday Life

Foursquare was a mobile social networking application that enabled people to share location with friends in the form of “check-ins.” The visualization of surrounding known social connections as well as unknown others has the potential to impact how people coordinate social encounters and forge new social ties. While many studies have explored mobile phones and sociability, there is a lack of empirical research examining location-based social network’s (LSBNs) from a sociability perspective. Drawing on a dataset of original qualitative research with a range of Foursquare users, the paper examines the application in the context of social coordination and sociability in three ways. First, the paper explores if Foursquare is used to organize certain social encounters, and if so, why. Second, the paper examines the visualization of surrounding social connections and whether this leads to “serendipitous encounters.” Lastly, the paper examines whether the use of Foursquare can produce new social relationships