Braiding and knotting for amateurs,

Mode of access: Internet.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Experimental assessment of an innovative strengthening material for brick masonry infills

The vulnerability of masonry infill walls has been highlighted in recent earthquakes in which severe inplane damage and out-of-plane collapse developed, justifying the investment in the proposal of strengthening solutions aiming to improve the seismic performance of these construction elements. Therefore, this work presents an innovative strengthening solution to be applied in masonry infill walls, in order to avoid brittle failure and thus minimize the material damage and human losses. The textilereinforced mortar technique (TRM) has been shown to improve the out-of-plane resistance of masonry and to enhance its ductility, and here an innovative reinforcing mesh composed of braided composite rods is proposed. The external part of the rod is composed of braided polyester whose structure is defined so that the bond adherence with mortar is optimized. The mechanical performance of the strengthening technique to improve the out-of-plane behaviour of brick masonry is assessed based on experimental bending tests. Additionally, a comparison of the mechanical behaviour of the proposed meshes with commercial meshes is provided. The idea is that the proposed meshes are efficient in avoiding brittle collapse and premature disintegration of brick masonry during seismic events.

Influence of design parameters on the mechanical behavior and porosity of braided fibrous stents

In spite of all innovations in stent design, commonly used metallic stents present several problems such as corrosion, infection and restenosis, leading to health complications or even death of patients. In this context, the present paper reports a systematic investigation on designing and development of 100% fiber based stents, which can eliminate or minimize the problems with existing metallic stents. For this purpose, braided stents were produced by varying different materials, structural and process parameters such as mono-filament type and diameter, braiding angle and mandrel diameter. The influence of these design parameters on mechanical behavior as well as stent's porosity was thoroughly investigated, and suitable parameters were selected for developing a stentwith mechanical characteristics and porosity matching with the commercial stents. According to the experimental results, the best performance was achieved with a polyester stent designed with 0.27 mm monofilament diameter, braiding angle of 35° and mandrel diameter of 6 mm, providing similar properties to commercial Nitinol stents.

Antibacterial properties of fibrous stents coated with silver oxide nanocoatings

Stents are rigid and perforated tubular structures, which are inserted into blood vessels in order to prevent or inhibit the constriction of blood flow, restoring the normal blood flow, when blood vessels are clogged, being used in 70% of angioplasties. These medical devices assume great importance in the treatment of cardiovascular diseases (CVD) which are the leading cause of death worldwide. In the European Union CVD account for 40% of deaths and assume an estimated annual cost of 196 billion euros[1]. Stents must possess certain requirements, in order to, adequately, perform its function, such as biocompatibility (so that its use does not c ause damage on the health of its user), mechanical strength, radiopacity (so that it is easy to view), longitudinal flexibility, ease of handling, corrosion resistance and having high strength and high radial expansion ability to recover. Stents can be made of different materials, but metals, particularly stainless steel, are the most common. However, metallic stents present several dRawbacks such as corrosion and restenosis, leading to health complications for the patient, or even death. In order to minimize these disadvantages, new materials, like fibrous materials, have been used [2]. Monofilaments present high potential for stents development because, in addition to its biocompatibility, these materials allow the application of various surface treatments, such as antibacterial coatings. Furthermore, monofilament exhibit excellent mechanical properties, like greater stiffness and good results when subjected to compression, tensile and bending forces, since these forces will be directly supported by the monofilament [3]. To minimize the reaction of the human body and Limit the adhesion of microorganisms to the stent surface, some coatings have been developed, including the use of novel metals with antimicrobial properties, like silver. The main objective of this study was the development of fibrous stents, incorporation of silver oxide nanocoating. For the development of the stent, polyester monofilaments with 0.27mm of diameter were used in braiding technology, with a mandrel diameter of 6mm and a braiding angle of 35⁰. The mechanical behaviour of the stent were evaluated by mechanical testing under longitudinal and radial compression, bending. The results of compressive strength tests are according with value from literature: 1.13 to 2.9 N for radial compression and 0. 16-5.28N to longitudinal compression. From literature is also possible to verify that stents must present 75% of unchanged diameter during the bending test and must possess a porosity between 70% and 80% [4]. The produced polyester stent presents values of 1.29N for radial compression, 0.23N for longitudinal compression, 80% of porosity and 85.5% of unchanged diameter, during bending tests. For the antibacterial functionalization, silver oxide nanocoatings were prepared, through reactive magnetron g, with an Ag target in an Ar +O2 atmosphere. In order to evaluate the nanostructure and morphology of the coatings, d ifferent technique s like X-ray diffraction (XRD), scanning electron microscopy (SEM) and and X- ray photoelectron spectroscopy (XPS were used. From the analyses of XRD it is possible to verify that the peaks corresponds to planes of Ag2 O and MATERIAIS 2015 Porto, 21-23 June, 2015 characterize a cubic phase. The presence of Ag2 O is corroborated by XPS spectrum, where it is possible to observe silver, not only, in oxide state, but a lso in mettalic state, and it is possible to verify the presence of silver clusters, confirmed by SEM analysis. Films’ roughness and topography, parameters influencing the wettability of the surface and microorganism adhesion, were measured by Atomic Force Microscopy (AFM), and it was observed that the roughness is very low (under 10 nm). Coatings’ hydrophobicity and surface tension parameters were determined by contact angle measurement, and it was verified the hydrophobic behavior of the coatings. For antibacterial tests were used Staphylococcus epidermidis strain (IE186) and Staphylococcus aureus(ATCC 6538), and halo inhibition zone tests were realized. Ag+release rates were studied by means of inductively coupled plasma mass spectrometry (ICP -MS). The obtained results suggest that silver oxide coatings do not modify significantly surface properties of the substrate, like hydrophobicity and roughness, and present antimicrobial properties for both bacteria used.

Late migration of percutaneous bio-absorbable devices--a word of caution.

BACKGROUND: Closures of atrial septal defects or a patent foramen ovale (PFO) are increasingly performed percutaneously. The experience of late migration of a new bio-absorbable device is presented here, followed by conceptual discussion. METHODS: Six months post PFO closure with a BioSTAR® device a patient presented with chest pain. Echocardiography showed a hyperechogenic structure perforating the aortic wall. RESULTS: Surgical exploration showed a perforation of the ascending aorta by one metallic, non absorbable arm. This is the second case of late (>6 months) dislocation of the residual framework of the occluder. CONCLUSIONS: The overall incidence of perforation of cardiac structures due to secondary dislocation is low. However this complication exists and should kept in mind in symptomatic patients with new onset of chest pain, after percutaneous procedures. The concept of biodegradation, with residual, non absorbable metal braiding, should be reviewed, analyzing in particular long term results and incidence of secondary dislocation.

Entrepreneurial structure of the mercantile company in pre-industrial Catalonia

The mercantile company was the basic form of enterprise in pre-industrial Catalonia. The aim of this paper is to study the formation and development of the mercantile companies in Barcelona whose end was the wholesale and retail sale of textiles in the botigues de teles (textile retail shops) throughout the eighteenth century. These firms were officially registered before a notary and their deeds reveal how these establishments were administered and managed.The study covers a sample of 121 mercantile companies, and the articles and documentation that were put into effect by 32 notaries who were active in Barcelona in the 18th century have been consulted in their entirety. From an initial selection of documentation, a total of 228 deeds registering companies have been found, 107 of which (47%) relate to the creation of companies whose various activities were centred in taverns, textile manufacturing, braiding.... While the 121 companies, which make up our sample and which account for 53% of the deeds registered with the notaries mentioned above, focused exclusively on the management of textile retail shops located in the commercial heart of the city. Thus one point of interest that the documentation reveals is that the majority of the mercantile companies registered by Barcelona notaries throughout the 18th century were establishments which traded in textiles. The first part of the article focuses on the structural characteristics of these enterprises, the number and socio-professional status of the partners and the extent of each partner s involvement in the administration and management. The second part of the article examines the capital investment made by each partner, their rights and obligations agreed on, the sharing out of profits and possible losses and the duration of the companies. The final aim of the paper is to highlight the evolution of these companies through one specific case.

Flow structures at an idealized bifurcation : a numerical experiment

River bifurcations are key nodes within braided river systems controlling the flow and sediment partitioning and therefore the dynamics of the river braiding process. Recent research has shown that certain geometrical configurations induce instabilities that lead to downstream mid-channel bar formation and the formation of bifurcations. However, we currently have a poor understanding of the flow division process within bifurcations and the flow dynamics in the downstream bifurcates, both of which are needed to understand bifurcation stability. This paper presents results of a numerical sensitivity experiment undertaken using computational fluid dynamics (CFD) with the purpose of understanding the flow dynamics of a series of idealized bifurcations. A geometric sensitivity analysis is undertaken for a range of channel slopes (0.005 to 0.03), bifurcation angles (22 degrees to 42 degrees) and a restricted set of inflow conditions based upon simulating flow through meander bends with different curvature on the flow field dynamics through the bifurcation. The results demonstrate that the overall slope of the bifurcation affects the velocity of flow through the bifurcation and when slope asymmetry is introduced, the flow structures in the bifurcation are modified. In terms of bifurcation evolution the most important observation appears to be that once slope asymmetry is greater than 0.2 the flow within the steep bifurcate shows potential instability and the potential for alternate channel bar formation. Bifurcation angle also defines the flow structures within the bifurcation with an increase in bifurcation angle increasing the flow velocity down both bifurcates. However, redistributive effects of secondary circulation caused by upstream curvature can very easily counter the effects of local bifurcation characteristics. Copyright (C) 2011 John Wiley & Sons, Ltd.

Temporal and spatial dynamics of benthic invertebrate communities in an alpine glacier-fed alluvial system

Summary The present thesis work focused on the ecology of benthic invertebrates in the proglacial floodplain of the Rhone in the Swiss Alps. The main glacial Rhone River and a smaller glacial tributary, the Mutt River, joined and entered a braiding multi-thread area. A first part concentrated on the disruption of the longitudinal patterns of environmental conditions and benthic invertebrate fauna in the Rhone by its tributary the Mutt. The Mutt had less harsh environmental conditions, higher taxonomic richness and more abundant zoobenthos compared to the Rhone upstream of the confluence. Although the habitat conditions in the main stream were little modified by the tributary, the fauna was richer and more diverse below the confluence. Colonisation from the Mutt induced the occurrence of faunal elements uncommon of glacial streams in the upper Rhone, where water temperature remains below 4°C. Although the glacial Rhone dominated the system with regard to hydrology and certain environmental conditions, the Mutt tributary has to be seen as the faunal driver of the system. The second part of the study concerned the spatio-temporal differentiation of the habitats and the benthic communities along and across the flood plain. No longitudinal differentiation was found. The spatial transversal differentiation of three habitat types with different environmental characteristics was successfully reflected in the spatial variability of benthic assemblages. This typology separated marginal sites of the flood plain, left bank sites under the influence of the Mutt, and the right bank sites under the influence of the Rh6ne. Faunistic spatial differences were emphasized by the quantitative structure of the fauna, richness, abundances and Simpson index of diversity. Seasonal environmental variability was positively related with Simpson index of diversity and the total richness per site. Low flow conditions were the most favourable season for the fauna and November was characterized by low spatial environmental heterogeneity, high spatial heterogeneity of faunal assemblage, maximum taxonomic richness, a particular taxonomic composition, highest abundances, as well as the highest primary food resources. The third part studied the egg development of three species of Ephemeroptera in the laboratory at 1.5 to 7°C and the ecological implications in the field. Species revealed very contrasting development strategies. Baetis alpinus has a synchronous and efficient egg development, which is faster in warmer habitats, enabling it to exploit short periods of favourable conditions in the floodplain. Ecdyonurus picteti has a very long development time slightly decreasing in warmer conditions. The high degree of individual variation suggests a genetic determination of the degree-days demand. Combined with the glacial local conditions, this strategy leads to an extreme delay of hatching and allows it to develop in very unpredictable habitats. Rhithrogena nivata is the second cold adapted species in Ephemeroptera. The incubation duration is long and success largely depends on the timing of hatching and the discharge conditions. This species is able to exploit extremely unstable and cold habitats where other species are limited by low water temperatures. The fourth part dealt with larval development in different habitats of the floodplain. Addition of data on egg development allowed the description of the life histories of the species from oviposition until emergence. Rhithrogena nivata and loyolaea generally have a two-year development, with the first winter passed as eggs and the second one as larvae. Development of Ecdyonurus picteti is difficult to document but appears to be efficient in a harsh and unpredictable environment. Baetis alpinus was studied separately in four habitats of the floodplain system with contrasting thermal regimes. Differences in success and duration of larval development and in growth rates are emphasised. Subvention mechanisms between habitats by migration of young or grown larvae were demonstrated. Development success and persistence of the populations in the system were thus increased. Emergence was synchronised to the detriment of the optimisation of the adult's size and fecundity. These very different development strategies induce a spatial and temporal distribution in the use of food resources and ecological niches. The last part of this work aimed at the synthesis of the characteristics and the ecological features of three distinct compartments of the system that are the upper Rhone, the Mutt and the floodplain. Their particular role as well as their inter-dependence concerning the structure and the dynamics of the benthic communities was emphasised. Résumé Ce travail de thèse est consacré à l'écologie des invertébrés benthiques dans la zone alluviale proglaciaire du Rhône dans les Alpes suisses. Le Rhône, torrent glaciaire principal, reçoit les eaux de la Mutt, affluent glaciaire secondaire, puis pénètre dans une zone de tressage formée de plusieurs bras. La première partie de l'étude se concentre sur la disruption par la Mutt des processus longitudinaux, tant environnementaux que faunistiques, existants dans le Rhône. Les conditions environnementales régnant dans la Mutt sont moins rudes, la richesse taxonomique plus élevée et le zoobenthos plus abondant que dans le Rhône en amont de la confluence. Bien que les conditions environnementales dans le torrent principal soient peu modifiées par l'affluent, la faune s'avère être plus riche et plus diversifiée en aval de la confluence. La colonisation depuis la Mutt permet l'occurrence de taxons inhabituels dans le Rhône en amont de la confluence, où la température de l'eau se maintient en dessous de 4°C. Bien que le Rhône, torrent glaciaire principal, domine le système du point de vu de l'hydrologie et de certains paramètres environnementaux, l'affluent Mutt doit être considéré comme l'élément structurant la faune dans le système. La deuxième partie concerne la différentiation spatiale et temporelle des habitats et des communautés benthiques à travers la plaine alluviale. Aucune différentiation longitudinale n'a été mise en évidence. La différentiation transversale de trois types d'habitats sur la base des caractéristiques environnementales a été confirmée par la variabilité spatiale de la faune. Cette typologie sépare les sites marginaux de la plaine alluviale, ceux sous l'influence de la Mutt (en rive gauche) et ceux sous l'influence du Rhône amont (en rive droite). Les différences spatiales de la faune sont mises en évidence par la structure quantitative de la faune, la richesse, les abondances et l'indice de diversité de Simpson. La variabilité saisonnière du milieu est positivement liée avec l'indice de diversité de Simpson et la richesse totale par site. L'étiage correspond à la période la plus favorable pour la faune et novembre réunit des conditions de faible hétérogénéité spatiale du milieu, de forte hétérogénéité spatiale de la faune, une richesse taxonomique maximale, une composition faunistique particulière, les abondances ainsi que les ressources primaires les plus élevées. La troisième partie est consacrée à l'étude du développement des oeufs de trois espèces d'Ephémères au laboratoire à des températures de 1.5 à 7°C, ainsi qu'aux implications écologiques sur le terrain. Ces espèces présentent des stratégies de développement très contrastées. Baetis alpinus a un développement synchrone et efficace, plus rapide en milieu plus chaud et lui permettant d'exploiter les courtes périodes de conditions favorables. Ecdyonurus picteti présente une durée de développement très longue, diminuant légèrement dans des conditions plus chaudes. L'importante variation interindividuelle suggère un déterminisme génétique de la durée de développement. Cette stratégie, associée aux conditions locales, conduit à un décalage extrême des éclosions et permet à l'espèce de se développer dans des habitats imprévisibles. Rhithrogena nivata est la seconde espèce d'Ephémères présentant une adaptation au froid. L'incubation des oeufs est longue et son succès dépend de la période des éclosions et des conditions hydrologiques. Cette espèce est capable d'exploiter des habitats extrêmement instables et froids, où la température est facteur limitant pour d'autres espèces. La quatrième partie traite du développement larvaire dans différents habitats de la plaine alluviale. Le développement complet est décrit pour les espèces étudiées de la ponte jusqu'à l'émergence. Rhithrogena nivata et loyolaea atteignent généralement le stade adulte en deux ans, le premier hiver étant passé sous forme d'oeuf et le second sous forme de larve. Le développement de Ecdyonurus picteti est difficile à documenter, mais s'avère cependant efficace dans un environnement rude et imprévisible. Baetis alpinus a été étudié séparément dans quatre habitats de la plaine ayant des régimes thermiques contrastés. La réussite et la durée du développement embryonnaire ainsi que les taux de croissance y sont variables. Des mécanismes de subvention entre habitats sont possibles par la migration de larves juvéniles ou plus développées, augmentant ainsi la réussite du développement et le maintien des populations dans le système. L'émergence devient synchrone, au détriment de l'optimisation de la taille et de la fécondité des adultes. Ces stratégies très différentes induisent une distribution spatiale et temporelle dans l'usage des ressources et des niches écologiques. La dernière partie synthétise les caractéristiques écologiques des trois compartiments du système que sont le Rhône amont, la Mutt et la zone alluviale. Leurs rôles particuliers et leurs interdépendances du point de vue de la structure et de la dynamique des communautés benthiques sont mis en avant.

Probing the large-scale topology of the heliospheric magnetic field using Jovian electrons

Jupiter’s magnetosphere acts as a point source of near-relativistic electrons within the heliosphere. In this study, three solar cycles of Jovian electron data in near-Earth space are examined. Jovian electron intensity is found to peak for an ideal Parker spiral connection, but with considerable spread about this point. Assuming the peak in Jovian electron counts indicates the best magnetic connection to Jupiter, we find a clear trend for fast and slow solar wind to be over- and under-wound with respect to the ideal Parker spiral, respectively. This is shown to be well explained in terms of solar wind stream interactions. Thus, modulation of Jovian electrons by corotating interaction regions (CIRs) may primarily be the result of changing magnetic connection, rather than CIRs acting as barriers to cross-field diffusion. By using Jovian electrons to remote sensing magnetic connectivity with Jupiter’s magnetosphere, we suggest that they provide a means to validate solar wind models between 1 and 5 AU, even when suitable in situ solar wind observations are not available. Furthermore, using Jovian electron observations as probes of heliospheric magnetic topology could provide insight into heliospheric magnetic field braiding and turbulence, as well as any systematic under-winding of the heliospheric magnetic field relative to the Parker spiral from footpoint motion of the magnetic field.

Agências reguladoras e contrato de gestão, limites e potencialidades

A presente dissertação tem por objetivo estudar como foram idealizados e como foram implementados os contatos de gestão, tendo por fim abordar limites e potencialidades deste instrumento, em relação as agências reguladoras federais, com uma abordagem mais dedicada a Agência Nacional de Saúde Suplementar, trançando um histórico do setor de saúde suplementar, porém com apontamentos de todas as agências reguladoras federais, quanto a utilização do contrato de gestão. O estudo foi desenvolvido com a apresentação de um breve retrato histórico desse instrumento, sua evolução e aspectos dos momentos histórico de sua implementação pelo governo federal. São apresentadas definições conceituais sobre contrato de gestão, descrição de sua organização e como se dá sua implementação nas agências reguladoras, como essas se organizam e utilizam essa ferramenta. Em seguida é feita uma breve abordagem de projeto de lei que entre outros assuntos trata sobre o contrato de gestão. Por fim, são apresentadas considerações sobre estudo realizado e apresenta-se a proposição de continuidade de novos estudos sobre o tema.

Suitability of carbon fiber-reinforced polymers as power cable cores: Galvanic corrosion and thermal stability evaluation

The increasing demand for electrical energy and the difficulties involved in installing new transmission lines presents a global challenge. Transmission line cables need to conduct more current, which creates the problem of excessive cable sag and limits the distance between towers. Therefore, it is necessary to develop new cables that have low thermal expansion coefficients, low densities, and high resistance to mechanical stress and corrosion. Continuous fiber-reinforced polymers are now widely used in many industries, including electrical utilities, and provide properties that are superior to those of traditional ACSR (aluminum conductor steel reinforced) cables. Although composite core cables show good performance in terms of corrosion, the contact of carbon fibers with aluminum promotes galvanic corrosion, which compromises mechanical performance. In this work, three different fiber coatings were tested (phenol formaldehyde resin, epoxy-based resin, and epoxy resin with polyester braiding), with measurements of the galvanic current. The use of epoxy resin combined with polyester braiding provided the best inhibition of galvanic corrosion. Investigation of thermal stability revealed that use of phenol formaldehyde resin resulted in a higher glass transition temperature. On the other hand, a post-cure process applied to epoxy-based resin enabled it to achieve glass transition temperatures of up to 200 degrees C. (C) 2014 Elsevier Ltd. All rights reserved.

Représentations et fusion des algèbres de Temperley-Lieb originale et diluée

Les algèbres de Temperley-Lieb originales, aussi dites régulières, apparaissent dans de nombreux modèles statistiques sur réseau en deux dimensions: les modèles d'Ising, de Potts, des dimères, celui de Fortuin-Kasteleyn, etc. L'espace d'Hilbert de l'hamiltonien quantique correspondant à chacun de ces modèles est un module pour cette algèbre et la théorie de ses représentations peut être utilisée afin de faciliter la décomposition de l'espace en blocs; la diagonalisation de l'hamiltonien s'en trouve alors grandement simplifiée. L'algèbre de Temperley-Lieb diluée joue un rôle similaire pour des modèles statistiques dilués, par exemple un modèle sur réseau où certains sites peuvent être vides; ses représentations peuvent alors être utilisées pour simplifier l'analyse du modèle comme pour le cas original. Or ceci requiert une connaissance des modules de cette algèbre et de leur structure; un premier article donne une liste complète des modules projectifs indécomposables de l'algèbre diluée et un second les utilise afin de construire une liste complète de tous les modules indécomposables des algèbres originale et diluée. La structure des modules est décrite en termes de facteurs de composition et par leurs groupes d'homomorphismes. Le produit de fusion sur l'algèbre de Temperley-Lieb originale permet de «multiplier» ensemble deux modules sur cette algèbre pour en obtenir un autre. Il a été montré que ce produit pouvait servir dans la diagonalisation d'hamiltoniens et, selon certaines conjectures, il pourrait également être utilisé pour étudier le comportement de modèles sur réseaux dans la limite continue. Un troisième article construit une généralisation du produit de fusion pour les algèbres diluées, puis présente une méthode pour le calculer. Le produit de fusion est alors calculé pour les classes de modules indécomposables les plus communes pour les deux familles, originale et diluée, ce qui vient ajouter à la liste incomplète des produits de fusion déjà calculés par d'autres chercheurs pour la famille originale. Finalement, il s'avère que les algèbres de Temperley-Lieb peuvent être associées à une catégorie monoïdale tressée, dont la structure est compatible avec le produit de fusion décrit ci-dessus. Le quatrième article calcule explicitement ce tressage, d'abord sur la catégorie des algèbres, puis sur la catégorie des modules sur ces algèbres. Il montre également comment ce tressage permet d'obtenir des solutions aux équations de Yang-Baxter, qui peuvent alors être utilisées afin de construire des modèles intégrables sur réseaux.

A mixer design for the pigtail braid

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called "pigtail braid", in which three stirring rods execute the usual "over-under" motion associated with braiding plaiting) hair. We show how to achieve this optimal braiding motion straightforwardly: one stirring rod is driven in a figure-of-eight motion, while the other two rods are baffles, which rotate episodically about their common centre. We also explore the extent to which the physical baffles may be replaced by flow structures (such as periodic islands).

Représentations et fusion des algèbres de Temperley-Lieb originale et diluée

Les algèbres de Temperley-Lieb originales, aussi dites régulières, apparaissent dans de nombreux modèles statistiques sur réseau en deux dimensions: les modèles d'Ising, de Potts, des dimères, celui de Fortuin-Kasteleyn, etc. L'espace d'Hilbert de l'hamiltonien quantique correspondant à chacun de ces modèles est un module pour cette algèbre et la théorie de ses représentations peut être utilisée afin de faciliter la décomposition de l'espace en blocs; la diagonalisation de l'hamiltonien s'en trouve alors grandement simplifiée. L'algèbre de Temperley-Lieb diluée joue un rôle similaire pour des modèles statistiques dilués, par exemple un modèle sur réseau où certains sites peuvent être vides; ses représentations peuvent alors être utilisées pour simplifier l'analyse du modèle comme pour le cas original. Or ceci requiert une connaissance des modules de cette algèbre et de leur structure; un premier article donne une liste complète des modules projectifs indécomposables de l'algèbre diluée et un second les utilise afin de construire une liste complète de tous les modules indécomposables des algèbres originale et diluée. La structure des modules est décrite en termes de facteurs de composition et par leurs groupes d'homomorphismes. Le produit de fusion sur l'algèbre de Temperley-Lieb originale permet de «multiplier» ensemble deux modules sur cette algèbre pour en obtenir un autre. Il a été montré que ce produit pouvait servir dans la diagonalisation d'hamiltoniens et, selon certaines conjectures, il pourrait également être utilisé pour étudier le comportement de modèles sur réseaux dans la limite continue. Un troisième article construit une généralisation du produit de fusion pour les algèbres diluées, puis présente une méthode pour le calculer. Le produit de fusion est alors calculé pour les classes de modules indécomposables les plus communes pour les deux familles, originale et diluée, ce qui vient ajouter à la liste incomplète des produits de fusion déjà calculés par d'autres chercheurs pour la famille originale. Finalement, il s'avère que les algèbres de Temperley-Lieb peuvent être associées à une catégorie monoïdale tressée, dont la structure est compatible avec le produit de fusion décrit ci-dessus. Le quatrième article calcule explicitement ce tressage, d'abord sur la catégorie des algèbres, puis sur la catégorie des modules sur ces algèbres. Il montre également comment ce tressage permet d'obtenir des solutions aux équations de Yang-Baxter, qui peuvent alors être utilisées afin de construire des modèles intégrables sur réseaux.