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The average conformation tensor of inter-atomic bonds as an alternative state variable to the strain tensor: definition and first application — the case of nanoelasticity
No full textMost of the mechanical models for solid state materials are in a methodological framework where a strain tensor, whatever it is, is considered as a thermodynamic state variable. As a consequence, the Cauchy stress tensor is expressed as a function of a strain tensor—and, in many cases, of one or more other state variables, such as the temperature. Such a choice for the kinematic state variable is clearly relevant in the case of infinitesimal or finite elasticity. However, one can ask whether an alternative state variable could not be considered. In the case of finite elastoplasticity, the choice of a strain tensor as the basic, kinematic state variable is not totally without issue, in particular in relation to the physical meaning of the internal state variable describing the permanent strains. In any case, this paper proposes an alternative to the strain tensor as a state variable, which is not based on the deformation (Lagrangian) gradient: the average conformation tensor of inter-atomic bonds. The purpose, however, is restricted to (1) a particular type of materials, namely the pure substances (copper or aluminum, for instance), (2) the nanoscale, and (3) the case of elasticity. The very simple case of two atoms of a pure substance in the solid state is first considered. It is shown that the kinematics of the inter-atomic bond can be characterized by a so called ``conformation'' tensor, and that the tensorial internal force acting on it can be immediately deduced from a single scalar function, depending only on the conformation tensor: the state potential of free energy (or interaction potential). Using an averaging procedure, these notions are then extended to a finite set of atoms, namely an atom and its first neighbours, which can be seen as the ``unit cell'' of a pure substance in the solid state considered as a discrete medium. They are also transposed to the Continuum case, where an expression of the Cauchy stress tensor is proposed as the first derivative of a state potential of density (per unit mass) of average free energy of inter-atomic bonds, which is an explicit function of the average conformation tensor of inter-atomic bonds. By applying a standard procedure in Continuum Thermodynamics, it is then shown that the objective part of the material derivative of this new state variable, at least in the case when the pure substance can be considered as an elastic medium, is equal to the symmetric part of the Eulerian velocity gradient, that is the rate of deformation tensor. In the case of uniaxial tension, a simple relationship is eventually set out between the average conformation tensor and a strain tensor, which is correctly approximated by the usual infinitesimal strain tensor as long as the conformation variations (from an initial state of conformation) are ``small''. From this latter result, and assuming an elastic behavior, a simple expression for the state potential of density of average free energy is inferred, showing great similarities with—but not equivalent to—the classical model of isotropic, linear elasticity (Hooke's law)
The cotangent bundle of K3 surfaces of degree two
No full textK3 surfaces have been studied from many points of view, but the positivity ofthe cotangent bundle is not well understood. In this paper we explore thesurprisingly rich geometry of the projectivised cotangent bundle of a verygeneral polarised K3 surface of degree two. In particular, we describe thegeometry of a surface that plays a similarrole to the surface of bitangents for a quartic in .Comment: 30 page
A simple polynomial-time approximation algorithm for the total variation distance between two product distributions
No full textWe give a simple polynomial-time approximation algorithm for the totalvariation distance between two product distributions
La réception en France de la musique soviétique : l'évolution de la censure de 1948 à 1958
No full textThis paper offers a study of the way Soviet authorities’ discourses on music were received in France. The post-war period is very interesting in many aspects. The political landscape changed following Zhdanov and Stalin’s deaths, and two decrees regarding music production were published in 1948 and 1958. The press bulletins of the Ministry of Foreign Affairs as well as the journalistic and intellectual production with scholarly pretensions of the PCF inform us about the reception of Soviet music in the French public space. We understand the evolution of censorship in the USSR thanks to the discourse in France about the professional Soviet musician and about the Soviet opera. Since censorship in the USSR was not always controlled, it is appropriate to question the role of Soviet and French communist intellectuals. As such, we study socialist realism in music, but also the conflicts that the enforcement of such ideological principles produces. Moreover, although French sympathizers covered Soviet musical news extensively, we observe divergences of opinion resulting from the diversity of the editorial frameworks.Cet article étudie la réception en France des discours des autorités soviétiques sur la musique. La période de l’après-guerre est intéressante à plus d’un titre. Le paysage politique évolue avec les décès de Jdanov et Staline et deux décrets relatifs à la production musicale sont publiés en 1948 et 1958. Les bulletins de presse du ministère des Affaires étrangères et la production journalistique et intellectuelle à prétention savante du PCF sont des indicateurs de la réception de la musique soviétique dans l’espace public français. Nous apprécions l’évolution de la censure en URSS grâce aux discours en France sur le musicien professionnel et l’opéra soviétiques. La censure en URSS n’ayant pas toujours été maîtrisée, il convient de questionner le rôle des intellectuels communistes soviétiques et français. Nous appréhendons ainsi le réalisme socialiste en musique, mais aussi les désaccords que produit l’application de tels principes idéologiques. Bien que les sympathisants français traitent abondamment les actualités musicales soviétiques, on est amené à observer des divergences d’opinion, résultats de la diversité des cadres éditoriaux
Le rôle de la caricature et du cinéma dans la construction de la mémoire collective de l'émigration russe après la Révolution de 1917
No full textPour une mise en ligne sur ÉpisciencesThis article addresses the problem of preserving the memory of first-wave Russian emigrants who settled in France between the two world wars. The author is interested in the visual and audiovisual heritage of exiles, in particular, press caricatures and cinema, one of whose functions was to transmit not only current events but also life experiences of Russians in all their forms (various emotions and feelings, sublimations of traumas, memories of the past). The author studies some examples of visual representations of exile and emigrants in cinema and caricature, selected from a large corpus of nearly 1,000 drawings and 50 films preserved today in library collections and audiovisual archives in France.Cet article aborde le problème de la préservation de la mémoire des émigrés russes de la première vague installés en France pendant l’entre-deux-guerres. L’autrice s’intéresse au patrimoine visuel et audiovisuel des exilés, notamment à la caricature de presse et au cinéma, dont l’une des fonctions était de transmettre non seulement l’actualité, mais aussi le vécu des Russes sous toutes ses formes (divers émotions et sensations, sublimations des traumatismes, souvenirs du passé). L’autrice propose d’étudier quelques exemples de représentations visuelles de l’exil et des émigrés dans le cinéma et la caricature, sélectionnés parmi un corpus large de près de 1 000 dessins et 50 films conservés aujourd’hui dans des fonds de bibliothèques et d’archives audiovisuelles en France
Exact Wirelength of Embedding 3-Ary n-Cubes into certain Cylinders and Trees
No full textGraph embeddings play a significant role in the design and analysis ofparallel algorithms. It is a mapping of the topological structure of a guestgraph G into a host graph H, which is represented as a one-to-one mapping fromthe vertex set of the guest graph to the vertex set of the host graph. Inmultiprocessing systems the interconnection networks enhance the efficientcommunication between the components in the system. Obtaining minimumwirelength in embedding problems is significant in the designing of network andsimulating one architecture by another. In this paper, we determine thewirelength of embedding 3-ary n-cubes into cylinders and certain trees.Comment: 13 pages, 5 figure
Méthode de quantification des flux des mines urbaines : cas des briques en terre cuite en Ile de France
No full textsoumission à EpisciencesThe building sector is a large consumer of resources and a major producer of waste. In a context of resource depletion, the building sector will have to implement strategies to become more circular. One possible solution is to resort to urban mining, i.e., to see existing buildings as a resource pool available for future construction or renovation of the building stock during their deconstruction or renovation. This article proposes a method to compare the quantities generated by deconstruction and renovation to the needs of new construction or renovation projects. After deconstruction, building components may be suitable for various secondary uses from reuse to recycling. The uses issued from reuse and recycling are identified and the quantities of materials corresponding to each of them are determined with adequate units (m2, kg...) to be compared with the new buildings’ project’s needs. These units facilitate the comparison between the recovered materials and the demand of components and materials. The method assumes that circular economy is fully developed and that the focus is only on the technical feasibility of recovery methods, ignoring the socio-economic obstacles to reuse and recycling. To illustrate the method, the case of clay bricks in Ile-de-France is detailed. During the year 2020, 153 kt of clay bricks were produced by the demolition of buildings in this territory, allowing to obtain, for example, a maximum surface of more than 21,000 m2 of masonry bricks, in reuse, and 9.2 kt of aggregates for concrete manufacturing.Le secteur du bâtiment est un grand consommateur de ressources et producteur de déchets. Dans un contexte d’épuisement des ressources, on peut imaginer qu’il devra mettre en place des stratégies pour devenir davantage circulaire. Une solution possible est d’avoir recours aux mines urbaines, c’est-à-dire, de voir les bâtiments existants comme un gisement de ressources disponibles pour les futurs constructions ou rénovations du parc immobilier lors de leur déconstruction ou rénovation. Cet article propose une méthode pour mettre en relation des quantités de matériaux issus de la déconstruction et de la rénovation avec les besoins du secteur du bâtiment neuf ou de la rénovation. Après leur extraction des mines urbaines, les éléments de construction peuvent convenir à divers usages secondaires. Les usages possibles en sortie des filières de réemploi, réutilisation et de recyclage sont identifiés et les quantités de matériaux répondant à chacun de ceux-ci sont déterminés avec des unités adéquates (m2, kg…). Ces unités facilitent la comparaison entre les matériaux valorisés et la demande. La méthode se veut prospective en considérant comme hypothèse que l’économie circulaire est pleinement développée et que l’accent n’est mis que sur la faisabilité technique des modes de valorisation. Afin d’illustrer la méthode, le cas des briques en terre cuite en Ile-de-France est développé. Durant l’année 2020, 153 kt de briques en terre cuite ont été produites par la démolition de bâtiments sur ce territoire, permettant d’obtenir au maximum (et sous réserve d’une bonne qualité de tri et des matériaux déconstruits), une surface de plus de 21 000 m2 de parois en briques de maçonnerie, par exemple, et 9,2 kt de granulats destinés à la fabrication de béton
Zero-sum partitions of Abelian groups of order
No full textThe following problem has been known since the 80's. Let be anAbelian group of order (denoted ), and let and , , be positive integers such that .Determine when , the set of non-zero elements of, can be partitioned into disjoint subsets , ,such that and for every , 1 \leq i \leqt. It is easy to check that (for every , ) and are necessary conditions for the existence of suchpartitions, where is the set of involutions of . It wasproved that the condition is sufficient if and only if. For other groups (i.e., for which and ), only the case of any group with for some positive integer has been analyzed completelyso far, and it was shown independently by several authors that issufficient in this case. Moreover, recently Cichacz and Tuza proved that, if is large enough and , then is sufficient.In this paper we generalize this result for every Abelian group of order .Namely, we show that the condition is sufficient for suchthat and , for every positive integer . Wealso present some applications of this result to graph magic- andanti-magic-type labelings
How to construct the symmetric cycle of length 5 using Haj\'os construction with an adapted Rank Genetic Algorithm
No full textIn 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to theclass of digraphs and generalized several results for vertex colorings indigraphs. Although, as a consequence of these results, a digraph can beobtained by Haj\'os constructions (directed Haj\'os join and identifyingnon-adjacent vertices), determining the Haj\'os constructions to obtain thedigraph is a complex problem. In particular, Bang-Jensen et al. posed theproblem of determining the Haj\'os operations to construct the symmetric5-cycle from the complete symmetric digraph of order 3 using only Haj\'osconstructions. We successfully adapted a rank-based genetic algorithm to solvethis problem by the introduction of innovative recombination and mutationoperators from graph theory. The Haj\'os Join became the recombination operatorand the identification of independent vertices became the mutation operator. Inthis way, we were able to obtain a sequence of only 16 Haj\'os operations toconstruct the symmetric cycle of order 5.Comment: 11 pages, 5 figures, 6 algoritm
Learning of Structurally Unambiguous Probabilistic Grammars
No full textThe problem of identifying a probabilistic context free grammar has twoaspects: the first is determining the grammar's topology (the rules of thegrammar) and the second is estimating probabilistic weights for each rule.Given the hardness results for learning context-free grammars in general, andprobabilistic grammars in particular, most of the literature has concentratedon the second problem. In this work we address the first problem. We restrictattention to structurally unambiguous weighted context-free grammars (SUWCFG)and provide a query learning algorithm for \structurally unambiguousprobabilistic context-free grammars (SUPCFG). We show that SUWCFG can berepresented using \emph{co-linear multiplicity tree automata} (CMTA), andprovide a polynomial learning algorithm that learns CMTAs. We show that thelearned CMTA can be converted into a probabilistic grammar, thus providing acomplete algorithm for learning a structurally unambiguous probabilisticcontext free grammar (both the grammar topology and the probabilistic weights)using structured membership queries and structured equivalence queries. Asummarized version of this work was published at AAAI 21.Comment: arXiv admin note: substantial text overlap with arXiv:2011.0747