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Mesh Density and Geodesic Tortuosity in Planar Triangular Tesselations Devoted to Fracture Mechanics
No full textIn fracture mechanics, the mesh sensitivity is a key issue. It is particularly true concerning cohesive volumetric finite element methods in which the crack path and the overall behavior are respectively influenced by the mesh topology and the mesh density. Poisson-Delaunay tessellations parameters, including the edge length distributions, were widely studied in the literature but very few works concern the mesh density and topology in Delaunay type meshes suitable for finite element simulations, which is of crucial interest for practical use. Starting from previous results concerning Poisson-Delaunay tessellations and studying in detail the Lloyd relaxation algorithm, we propose estimates for the probability density functions of the edge length and triangle top angles sets. These estimates depend both on the intensity of the underlying point process and on an efficiency index associated to the global quality of the mesh. The global and local accuracies of these estimates are checked for various standard mesh generators. Finally the mesh density and geodesic tortuosity are estimated for standard random or structured triangular meshes typically used in finite element simulations. These results provide practical formulas to estimate bias introduced by the mesh density and topology on the results of cohesive-volumetric finite element simulations
Plaie de paturon combinée à une fracture de type II de la troisième phalange chez un mulet
No full textAn adult mule was presented with a purulent wound on the distal and medial third of the pastern of his right forelimb (MAD) accompanied by grade 5 lameness. A type II fracture of the third phalanx (P3) was diagnosed by radiological examination. Treatment consisted of analgesics, antibiotics, wound care and a flanged boot bandage, replaced by a Monkey splint the following week. Six (6) months later, a follow-up clinical examination showed a clear reduction in lameness estimated at grade 2 and a clear reduction in pain on palpation.Un mulet adulte est présenté avec une plaie purulente sur le tiers distal et médial du paturon de son membre antérieur droit (MAD) accompagné d’une boiterie de grade 5. Une fracture de type II de la troisième phalange (P3) a été diagnostiqué par examen radiologique. Le traitement a consisté en l’administration d’antalgique, d’antibiotiques, de soins de la plaie et de la mise en place d’un bandage renforcé par chaussure à rebord remplacé par une attelle de Monkey la semaine suivante. Six (6) mois plus tard, un examen clinique de suivi a montré une nette diminution de la boiterie estimée au grade 2 et une nette diminution de douleur à la palpation
Advanced Model Consistency Restoration with Higher-Order Short-Cut Rules
No full textSequential model synchronisation is the task of propagating changes from onemodel to another correlated one to restore consistency. It is challenging toperform this propagation in a least-changing way that avoids unnecessarydeletions (which might cause information loss). From a theoretical point ofview, so-called short-cut (SC) rules have been developed that enable provablycorrect propagation of changes while avoiding information loss. However, to beable to react to every possible change, an infinite set of such rules might benecessary. Practically, only small sets of pre-computed basic SC rules havebeen used, severely restricting the kind of changes that can be propagatedwithout loss of information. In this work, we close that gap by developing anapproach to compute more complex required SC rules on-the-fly duringsynchronisation. These higher-order SC rules allow us to cope with more complexscenarios when multiple changes must be handled in one step. We implemented ourapproach in the model transformation tool eMoflon. An evaluation shows that theoverhead of computing higher-order SC rules on-the-fly is tolerable and attimes even improves the overall performance. Above that, completely newscenarios can be dealt with without the loss of information
An implicit staggered algorithm for CPFEM-based analysis of aluminum
No full textIn this paper, we propose an implicit staggered algorithm for crystal plasticity finite element methodwhich makes use of dynamic relaxation at the constitutive integration level. An uncoupled version ofthe constitutive system consists of a multi-surface flow law complemented by an evolution law for thehardening variables. Since a saturation law is adopted for hardening, a sequence of nonlinear iterationfollowed by a linear system is feasible. To tie the constitutive unknowns, the dynamic relaxation method isadopted. A Green-Nagdhi plasticity model is adopted based on the Hencky strain calculated using a[2/2] Padé approximation. For the incompressible case, the approximation error is calculated exactly.A enhanced-assumed strain element technology is adopted, which was found to be especially suitedto localization problems such as the ones resulting from crystal plasticity plane slipping. Analysis ofthe results shows significant reduction of drift and well defined localization without spurious modes orhourglassing
Line game-perfect graphs
No full textThe -edge colouring game is played with a set of colours on agraph with initially uncoloured edges by two players, Alice (A) and Bob(B). The players move alternately. Player has the first move.. If , then only player may skip any move,otherwise skipping is not allowed for any player. A move consists of colouringan uncoloured edge with one of the colours such that adjacent edges havedistinct colours. When no more moves are possible, the game ends. If every edgeis coloured in the end, Alice wins; otherwise, Bob wins. The -game chromatic index is the smallestnonnegative integer such that Alice has a winning strategy for the-edge colouring game played on with colours. The graph iscalled line -perfect if, for any edge-induced subgraph of , where denotes the cliquenumber of the line graph of . For each of the six possibilities , wecharacterise line -perfect graphs by forbidden (edge-induced) subgraphsand by explicit structural descriptions, respectively
Preservation theorems for Tarski's relation algebra
No full textWe investigate a number of semantically defined fragments of Tarski's algebraof binary relations, including the function-preserving fragment. We address thequestion whether they are generated by a finite set of operations. We obtainseveral positive and negative results along these lines. Specifically, thehomomorphism-safe fragment is finitely generated (both over finite and overarbitrary structures). The function-preserving fragment is not finitelygenerated (and, in fact, not expressible by any finite set of guardedsecond-order definable function-preserving operations). Similarly, thetotal-function-preserving fragment is not finitely generated (and, in fact, notexpressible by any finite set of guarded second-order definabletotal-function-preserving operations). In contrast, the forward-lookingfunction-preserving fragment is finitely generated by composition,intersection, antidomain, and preferential union. Similarly, theforward-and-backward-looking injective-function-preserving fragment is finitelygenerated by composition, intersection, antidomain, inverse, and an `injectiveunion' operation
A study on the domain independence of the Laurent property, the irreducibility and the coprimeness in lattice equations
No full textWe study the Laurent property, the irreducibility and the coprimeness forlattice equations (partial difference equations), mainly focusing on how thechoice of initial value problem (the choice of domain) affects theseproperties. We show that these properties do not depend on the choice of domainas long as they are considered together. In other words, these properties areinherent to a difference equation. Applying our result, we discuss thereductions of lattice equations. We show that any reduction of a Laurentsystem, even if the lattices have torsion elements, preserves the Laurentproperty
Game Comonads & Generalised Quantifiers
No full textGame comonads, introduced by Abramsky, Dawar and Wang and developed byAbramsky and Shah, give an interesting categorical semantics to someSpoiler-Duplicator games that are common in finite model theory. In particularthey expose connections between one-sided and two-sided games, and parameterssuch as treewidth and treedepth and corresponding notions of decomposition. Inthe present paper, we expand the realm of game comonads to logics withgeneralised quantifiers. In particular, we introduce a comonad graded by twoparameters such that isomorphisms in the resulting Kleisli categoryare exactly Duplicator winning strategies in Hella's -bijection game with pebbles. We define a one-sided version of this game which allows us toprovide a categorical semantics for a number of logics with generalisedquantifiers. We also give a novel notion of tree decomposition that emergesfrom the construction
Modelling the governance of European medium-sized port-cities
No full textThe paper presents a model designed to analyse port governance. It considers that thestakeholders ability to adopt cooperative behaviors constitutes the key element to portdevelopment. Its focus is on medium-sized European ports and fifteen cases were studied. Eachterritory was first subject to a qualitative survey and analysis of the contents of local stakeholdersdiscourse (over 80 interviews conducted). The material is rich, allowing for the comparisonbetween two or even three ports, yet the delicate nature of the relations brought to light addsconsiderable complexity to the comparison within a larger ensemble. The paper, therefore,proposes a semi-automatic treatment which helps to mitigate this difficulty by means of acomputer model based on graph theory. It involves a modelling system based on the relationsbetween the entities of the system. In this context, the relations between stakeholders wereanalysed in order to create typologies and eventually envisage some standard models ofgovernance. In order to territorialize the subject, six typical cases out of fifteen were used: LeHavre, Nantes-Saint Nazaire, Dunkirk (France), Gdynia (Poland), Klaipėda (Lituania), Hamina-Kotka (Finland).All these port environments modelled according to a single format (i.e. a graph) led to theapplication of a certain number of metrics which enables them to be compared. Two mainmetrics were presented in the framework of this paper for illustrative purposes: “Density” and“S_metric”. These metrics originating in graph theory, coupled with other indicators (distributionof degrees and number of hubs per port), allowed to measure the relationships' intensity and thedistribution of these intensities among the stakeholders, and to identify the main stakeholders orconversely the least influential
