Invariant Variation Problems

The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker), Weyl and Klein for special infinite groups. Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may refer to the concluding remarks of Klein's Note.Comment: M. A. Tavel's English translation of Noether's Theorems (1918), reproduced by Frank Y. Wang. Thanks to Lloyd Kannenberg for corrigend

Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR

Prebiotic effects: metabolic and health benefits

The different compartments of the gastrointestinal tract are inhabited by populations of micro-organisms. By far the most important predominant populations are in the colon where a true symbiosis with the host exists that is a key for well-being and health. For such a microbiota, 'normobiosis' characterises a composition of the gut 'ecosystem' in which micro-organisms with potential health benefits predominate in number over potentially harmful ones, in contrast to 'dysbiosis', in which one or a few potentially harmful micro-organisms are dominant, thus creating a disease-prone situation. The present document has been written by a group of both academic and industry experts (in the ILSI Europe Prebiotic Expert Group and Prebiotic Task Force, respectively). It does not aim to propose a new definition of a prebiotic nor to identify which food products are classified as prebiotic but rather to validate and expand the original idea of the prebiotic concept (that can be translated in 'prebiotic effects'), defined as: 'The selective stimulation of growth and/or activity(ies) of one or a limited number of microbial genus(era)/species in the gut microbiota that confer(s) health benefits to the host.' Thanks to the methodological and fundamental research of microbiologists, immense progress has very recently been made in our understanding of the gut microbiota. A large number of human intervention studies have been performed that have demonstrated that dietary consumption of certain food products can result in statistically significant changes in the composition of the gut microbiota in line with the prebiotic concept. Thus the prebiotic effect is now a well-established scientific fact. The more data are accumulating, the more it will be recognised that such changes in the microbiota's composition, especially increase in bifidobacteria, can be regarded as a marker of intestinal health. The review is divided in chapters that cover the major areas of nutrition research where a prebiotic effect has tentatively been investigated for potential health benefits. The prebiotic effect has been shown to associate with modulation of biomarkers and activity(ies) of the immune system. Confirming the studies in adults, it has been demonstrated that, in infant nutrition, the prebiotic effect includes a significant change of gut microbiota composition, especially an increase of faecal concentrations of bifidobacteria. This concomitantly improves stool quality (pH, SCFA, frequency and consistency), reduces the risk of gastroenteritis and infections, improves general well-being and reduces the incidence of allergic symptoms such as atopic eczema. Changes in the gut microbiota composition are classically considered as one of the many factors involved in the pathogenesis of either inflammatory bowel disease or irritable bowel syndrome. The use of particular food products with a prebiotic effect has thus been tested in clinical trials with the objective to improve the clinical activity and well-being of patients with such disorders. Promising beneficial effects have been demonstrated in some preliminary studies, including changes in gut microbiota composition (especially increase in bifidobacteria concentration). Often associated with toxic load and/or miscellaneous risk factors, colon cancer is another pathology for which a possible role of gut microbiota composition has been hypothesised. Numerous experimental studies have reported reduction in incidence of tumours and cancers after feeding specific food products with a prebiotic effect. Some of these studies (including one human trial) have also reported that, in such conditions, gut microbiota composition was modified (especially due to increased concentration of bifidobacteria). Dietary intake of particular food products with a prebiotic effect has been shown, especially in adolescents, but also tentatively in postmenopausal women, to increase Ca absorption as well as bone Ca accretion and bone mineral density. Recent data, both from experimental models and from human studies, support the beneficial effects of particular food products with prebiotic properties on energy homaeostasis, satiety regulation and body weight gain. Together, with data in obese animals and patients, these studies support the hypothesis that gut microbiota composition (especially the number of bifidobacteria) may contribute to modulate metabolic processes associated with syndrome X, especially obesity and diabetes type 2. It is plausible, even though not exclusive, that these effects are linked to the microbiota-induced changes and it is feasible to conclude that their mechanisms fit into the prebiotic effect. However, the role of such changes in these health benefits remains to be definitively proven. As a result of the research activity that followed the publication of the prebiotic concept 15 years ago, it has become clear that products that cause a selective modification in the gut microbiota's composition and/or activity(ies) and thus strengthens normobiosis could either induce beneficial physiological effects in the colon and also in extra-intestinal compartments or contribute towards reducing the risk of dysbiosis and associated intestinal and systemic pathologies

Patterns and flow in frictional fluid dynamics

Pattern-forming processes in simple fluids and suspensions have been studied extensively, and the basic displacement structures, similar to viscous fingers and fractals in capillary dominated flows, have been identified. However, the fundamental displacement morphologies in frictional fluids and granular mixtures have not been mapped out. Here we consider Coulomb friction and compressibility in the fluid dynamics, and discover surprising responses including highly intermittent flow and a transition to quasi-continuodynamics. Moreover, by varying the injection rate over several orders of magnitude, we characterize new dynamic modes ranging from stick-slip bubbles at low rate to destabilized viscous fingers at high rate. We classify the fluid dynamics into frictional and viscous regimes, and present a unified description of emerging morphologies in granular mixtures in the form of extended phase diagrams

Influence d'un traitement d'implantation diffusion d'azote à flux élevé sur la résistance à l'usure d'un acier austénitique

La résistance à l'usure des aciers austénitiques est insuffisante pour de nombreuses applications à cause de leur dureté assez faible, mais elle peut être améliorée par un traitement de durcissement superficiel par nitruration. Il est cependant nécessaire que le traitement soit effectué à température modérée si l'on veut éviter la formation de nitrure de chrome et conserver les propriétés inoxydables de l'acier. Des études récentes ont montré la possibilité de former des couches nitrurées épaisses (2-10µm) et concentrées (25at%) en réalisant à une température modérée (400°C) une implantation d'azote à basse énergie (1keV) et flux élevé (1mA.cm2). Dans ces conditions, pour un traitement d'une heure à 400°C d'un acier austénitique 304, on forme en surface sur environ 5µm une solution solide interstitielle d'azote (austénite dilatée γN) qui augmente fortement la dureté de 280 à environ 800 Kg/mm2. Les expériences d'usure sont faites sous eau déminéralisée en mode glissement et en contact sphère-plan sous des pressions de Hertz très inférieures à la limite élastique de l'acier. Le traitement de nitruration a été appliqué aux disques et aux pions dans quatre configurations : pion traité (ou non) sur disque traité (ou non). Quel que soit le traitement du disque on obtient une baisse notable de l'usure du pion, par contre dans le cas ou le pion non traité frotte sur un disque traité, l'usure du pion est très fortement augmentée de même que les faciès de dégradation sont fortement modifiés

Evaluations of phylogenetic proximity in a group of 67 dogs with osteosarcoma: a pilot study

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