Quantitative and Algorithmic aspects of Barrier Synchronization in Concurrency

In this paper we address the problem of understanding Concurrency Theory from a combinatorial point of view. We are interested in quantitative results and algorithmic tools to refine our understanding of the classical combinatorial explosion phenomenon arising in concurrency. This paper is essentially focusing on the the notion of synchronization from the point of view of combinatorics. As a first step, we address the quantitative problem of counting the number of executions of simple processes interacting with synchronization barriers. We elaborate a systematic decomposition of processes that produces a symbolic integral formula to solve the problem. Based on this procedure, we develop a generic algorithm to generate process executions uniformly at random. For some interesting sub-classes of processes we propose very efficient counting and random sampling algorithms. All these algorithms have one important characteristic in common: they work on the control graph of processes and thus do not require the explicit construction of the state-space

Interface dynamics in the two-dimensional quantum Ising model

In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this paper, we elaborate more on the issue. First, we discuss two classes of initial states on the square lattice, the dynamics of which is driven by complementary terms in the effective Hamiltonian and may be solved exactly: (a) strips of consecutive neighbouring spins aligned in the opposite direction of the surrounding spins, and (b) a large class of initial states, characterized by the presence of a well-defined "smooth" interface separating two infinitely extended regions with oppositely aligned spins. The evolution of the latter states can be mapped onto that of an effective one-dimensional fermionic chain, which is integrable in the infinite-coupling limit. In this case, deep connections with noteworthy results in mathematics emerge, as well as with similar problems in classical statistical physics. We present a detailed analysis of the evolution of these interfaces both on the lattice and in a suitable continuum limit, including the interface fluctuations and the dynamics of entanglement entropy. Second, we provide analytical and numerical evidence supporting the conclusion that the observed non-ergodicity -- arising from Stark localization of the effective fermionic excitations -- persists away from the infinite-Ising-coupling limit, and we highlight the presence of a timescale $T\sim e^{c L\ln L}$ for the decay of a region of large linear size $L$. The implications of our work for the classic problem of the decay of a false vacuum are also discussed.Comment: 33 pages, 12 figures. Comments are welcome

Modelling local scour around bridge piers using TELEMAC

Scour at bridge crossings is a major cause of bridge failure. There are several different types of scour such as general scour, constriction scour and local scour. One of the most serious types is local scour which occurs as a result of vortex formation around bridge piers and abutments (Hoffmans & Verheij, 1997; Raudkivi, 1998; Melville & Coleman, 2000; Richardson & Davis, 2001; Armitage & McGahey, 2003). Local scour is also one of the most difficult to predict accurately. If not adequately designed for, local scour of a riverbed at a bridge pier may become deep enough to undermine the pier foundation and eventually cause the bridge to collapse. Complete protection against scour is expensive and therefore not a favourable design option. It is generally cheaper to ensure that the foundation lies below the maximum expected scour depth. Traditionally, the maximum scour depth is predicted from empirical equations derived from simple laboratory tests without much regard for local conditions. Alternatively, smaIlscale hydraulic models, which are laborious and time intensive, are widely used. In view of the above, increasing attention is being paid to the use of Computational Fluid Dynamics (CFD) based modelling for the prediction of local scour and its opposite, local deposition. The ever-improving capabilities of computers and the increasing availability of powerful and flexible CFD codes have further assisted in this process. This study is a contribution in this direction

Copula models for epidemiological research and practice

Investigating associations between random variables (rvs) is one of many topics in the heart of statistical science. Graphical displays show emerging patterns between rvs, and the strength of their association is conventionally quantified via correlation coefficients. When two or more of these rvs are thought of as outcomes, their association is governed by a joint probability distribution function (pdf). When the joint pdf is bivariate normal, scalar correlation coefficients will produce a satisfactory summary of the association, otherwise alternative measures are needed. Local dependence functions, together with their corresponding graphical displays, quantify and show how the strength of the association varies across the span of the data. Additionally, the multivariate distribution function can be explicitly formulated and explored. Copulas model joint distributions of varying shapes by combining the separate (univariate) marginal cumulative distribution functions of each rv under a specified correlation structure. Copula models can be used to analyse complex relationships and incorporate covariates into their parameters. Therefore, they offer increased flexibility in modelling dependence between rvs. Copula models may also be used to construct bivariate analogues of centiles, an application for which few references are available in the literature though it is of particular interest for many paediatric applications. Population centiles are widely used to highlight children or adults who have unusual univariate outcomes. Whilst the methodology for the construction of univariate centiles is well established there has been very little work in the area of bivariate analogues of centiles where two outcomes are jointly considered. Conditional models can increase the efficiency of centile analogues in detection of individuals who require some form of intervention. Such adjustments can be readily incorporated into the modelling of the marginal distributions and of the dependence parameter within the copula model

Étude de la formation de boues dans la cellule Hall-Héroult

La production d’aluminium comme un procédé métallurgique énergivore, joue un rôle majeur dans l’économie du Québec. Un facteur qui peut augmenter la consommation d'énergie correspondante est la formation de dépôts résistifs (des boues) à la surface de la cathode. Par conséquent, l'objectif de cette thèse est de clarifier davantage la nature complexe de la formation de boues dans le procédé Hall-Héroult, en tant que le procédé principal de production d'aluminium. Les objectifs de recherche sont: a) étudier l’effet possible de la nuance de cathode sur la formation ou la dissolution des boues; b) déterminer l'importance relative de trois paramètres opérationnels, à savoir la température d’opération, le ratio de cryolite (CR) ainsi que la nuance de cathode; c) étudier de façon expérimentale des boues induites chimiquement (c'est-à-dire précipitation des espèces cryolitiques dues au changement de la chimie du bain comme la consommation d'alumine ou la polarisation de concentration de sodium). La méthodologie expérimentale comporte une configuration expérimentale à l'échelle du banc d’essai, cinq nuances cathodiques différentes, une conception de plan expérimental factoriel complet ayant trois variables et deux niveaux pour chaque paramètre, à savoir la température d’opération (940 et 960 ° C), le ratio de cryolite (2,2 et 3,8) et deux nuances cathodiques. Les résultats de cette recherche sont: i. une combinaison de porosité ouverte et de perméabilité à l'air des cathodes affecte l'épaisseur des couches de carbure d'aluminium; ii. parmi plusieurs propriétés, la conductivité thermique et la porosité ouverte des cathodes affectent la tendance à la formation de boues en raison de la perte de chaleur au fond de la cellule et des phénomènes interfaciaux; iii. l'influence significative de la température d’opération par rapport au ratio de cryolite et à la nuance de cathode; iv. la précipitation des espèces cryolitiques solides est accélérée grâce à la polarisation de concentration plus élevée et le taux d'épuisement de l'aluminium plus rapide; v. le temps de réalimentation des boues est plus élevé pour les cathodes à porosités ouvertes plus élevées en raison de l'interaction des boues, avec des couches de carbure plus épaisses et des espèces carbonées au fond de la cellule