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An explicit dynamics framework suited to highly non-smooth interface behaviors
No full textDynamic systems, and in particular mechanical structures, may be subjected to non-smooth loadings such as impacts or shocks. Moreover, their behavior itself may exhibit more or less non-smooth evolutions, as when fracture occurs. Therefore, robust simulation models are of interest to capture such behaviors. A particular focus is made herein on time-stepping explicit dynamics schemes to allow efficient simulations, and non-smoothness is embedded within the discrete resolution model, so that robust simulations can be obtained, with a minimum number of numerical parameters. The original contributions of this article lie in the way the non-smooth behavior is formulated to be embedded in an explicit dynamics framework. This study focuses on the solver for dynamics with non-smooth interface behavior, rather than on the behavior models themselves. The applications concern non-smooth interface behaviors at macroscopic scale, between displacement jump on the 2D interface surface with no thickness, and interfacial force distributions acting on the bodies apart the interface. The proposed test cases which can serve as benchmarks for simulation codes, concern in a first step contact and perfectly plastic interface behavior (for illustrative purpose, on a 0D example). The last numerical test deals with contact, friction, fracture and adhesion for an extrinsic perfectly brittle interface behavior, to exemplify the feasibility on a full 3D finite element model
Елизавета Ахматова: забытое громкое имя русской культуры?
No full textThe paper focuses on Elizaveta Akhmatova (1820-1904) – translator, editor and writer, the “first pioneer”, in her own words, of women’s literary work. The purpose of this research was to describe the conditions for entry into the profession (translation, publishing, writing), to present the results of her editorial activity (published periodicals), and to look at the reception of Akhmatova’s work by her contemporariesCet article est consacré à Élizavéta Akhmatova (1820-1904), traductrice, éditrice et écrivaine, « première pionnière », comme elle le disait elle-même, du travail littéraire féminin. L’objectif de cette recherche est triple : décrire l’entrée d’Akhmatova dans le métier (traduction, édition, écriture), présenter les résultats de sa démarche (revues périodiques publiées), ainsi qu’examiner la réception réservée à son travail par ses contemporains (O. Senkovski, N. Leskov, A. Droujinine,M. Sémevski, A. Skabitchevski). Ceci nous permettra de proposer une première réflexion sur le rôle, la place et la réputation littéraire de cette « première pionnière » dans le monde culturel et éditorial.Статья посвящена Елизавете Николаевне Ахматовой (1820-1904) – переводчице, издательнице и писательнице, «первой пионерке», как она сама говорила о себе, женского литературного труда. Особое внимание в статье уделяется следующим вопросам: начало профессиональной деятельности Ахматовой (переводческая и писательская работа), описание издаваемых ей периодических журналов и переводных собраний сочинений, отклики современников на ее литературно-издательскую работу (О. Сенковский, Н. Лесков, А. Дружинин, М. Семевский, А. Скабичевский). Созданный набросок к портрету Ахматовой позволяет очертить ее место и роль в издательском мире, а также воссоздать литературную репутацию этой «первой пионерки» женского труда
Inner isotopes associated with automorphisms of commutative associative algebras
No full textThe principal observation of the present paper is that an inner isotopy (i.e.a principal isotopy defined by an algebra endomorphism) is a very helpfulinstrument in constructing and studying interesting classes of nonassociativealgebras. By using methods developed in the paper, we define a new class ofcommutative nonassociative algebras obtained by inner isotopy from commutativeassociative polynomial algebras. There is a natural bijection betweenisomorphism classes of our algebras and integer partitions of the algebradimensions. Among the interesting features of the nonassociative algebrasconstructed are that these algebras are generic, some of examples are axial andmetrized algebras. We completely describe both the set of algebra idempotentsand their spectra
Zeta Functions and the (Linear) Logic of Markov Processes
No full textThe author introduced models of linear logic known as ''Interaction Graphs''which generalise Girard's various geometry of interaction constructions. Inthis work, we establish how these models essentially rely on a deep connectionbetween zeta functions and the execution of programs, expressed as a cocycle.This is first shown in the simple case of graphs, before begin lifted todynamical systems. Focussing on probabilistic models, we then explain how thenotion of graphings used in Interaction Graphs captures a natural class ofsub-Markov processes. We then extend the realisability constructions and thenotion of zeta function to provide a realisability model of second-order linearlogic over the set of all (discrete-time) sub-Markov processes
On two-variable guarded fragment logic with expressive local Presburger constraints
No full textWe consider the extension of the two-variable guarded fragment logic withlocal Presburger quantifiers. These are quantifiers that can express propertiessuch as "the number of incoming blue edges plus twice the number of outgoingred edges is at most three times the number of incoming green edges" andcaptures various description logics with counting, but without constantsymbols. We show that the satisfiability problem for this logic isEXP-complete. While the lower bound already holds for the standard two-variableguarded fragment logic, the upper bound is established by a novel, yet simpledeterministic graph-based algorithm
Deterministic pushdown automata can compress some normal sequences
No full textIn this paper, we give a deterministic pushdown transducer and a normalsequence of digits compressed by it. This solves positively a question leftopen in a previous paper by V. Becher, P. A. Heiber and the first author
Wind-wave interaction in finite depth: linear and nonlinear approaches, blow-up and soliton breaking in finite time, integrability perspectives
No full textThis work is an analytical investigation of the evolution of surface waterwaves in Miles and Jeffreys theories of wind wave interaction in water offinite depth. The present review is divided into two major parts. The firstcorresponds to the surface water waves in a linear regime and its nonlinearextensions. In this part, Miles theory of wave amplification by wind isextended to the case of finite depth. The dispersion relation provides a wavegrowth rate depending on depth. Our theoretical results are in good agreementwith the data from the Australian Shallow Water Experiment and the data fromthe Lake George experiment. In the second part of this study, Jeffreys theoryof wave amplification by wind is extended to the case of finite depth, wherethe Serre-Green-Naghdi is derived. We find the solitary wave solution of thesystem, with an increasing amplitude under the action of the wind. Thiscontinuous increase in amplitude leads to the soliton breaking and blow-up ofthe surface wave in finite time. The theoretical blow-up time is calculatedbased on actual experimental data. By applying an appropriate perturbationmethod, the SGN equation yields Korteweg de Vries Burger equation (KdVB). Weshow that the continuous transfer of energy from wind to water results in thegrowth of the KdVB soliton amplitude, velocity, acceleration, and energy overtime while its effective wavelength decreases. This phenomenon differs from theclassical results of Jeffreys approach due to finite depth. Again, blow-up andbreaking occur in finite time. These times are calculated and expressed forsoliton- and wind-appropriate parameters and values. These values aremeasurable in usual experimental facilities. The kinematics of the breaking isstudied, and a detailed analysis of the breaking time is conducted usingvarious criteria. Finally, some integrability perspectives are presented
Pattern Avoidance in Weak Ascent Sequences
No full textIn this paper, we study pattern avoidance in weak ascent sequences, givingsome results for patterns of length 3. This is an analogous study to one givenby Duncan and Steingr\'imsson (2011) for ascent sequences. More precisely, weprovide systematically the generating functions for the number of weak ascentsequences avoiding the patterns , and . Additionally,we establish bijective connections between pattern-avoiding weak ascentsequences and other combinatorial objects, such as compositions, uppertriangular 01-matrices, and plane trees
Midy's Theorem in non-integer bases and divisibility of Fibonacci numbers
No full textFractions with prime denominator written indecimal have a curious property described by Midy's Theorem, namely that twohalves of their period (if it is of even length ) sum up to . Anumber of results generalise Midy's theorem to expansions of indifferent integer bases, considering non-prime denominators, or dividing theperiod into more than two parts. We show that a similar phenomena can bestudied even in the context of numeration systems with non-integer bases, asintroduced by R\'enyi. First we define the Midy property for a general realbase and derive a necessary condition for validity of the Midyproperty. For we characterize prime denominators, which satisfy the property
Sur une équation définie par une réduction de la hiérarchie de Drinfeld et Sokolov
No full textA seventh order ordinary differential equation (ODE) arising by reduction of the Drinfeld-Sokolov hierarchyis shown to be identical to a similarity reduction of an equationin the hierarchy of Sawada-Kotera.We also exhibit its link with a particular F-VI,a fourth order ODE isolated by Cosgrove which is likely to define a higher order Painlev\'e function