The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

How the obscuration-zone hypothesis affects fragmentation: Illustration with the cohesive-element method

The problem of fragmentation prediction is at the origin of various analytical models. Among them, we focus on the ones introducing the idea of obscured zones. They assume that when a crack initiates at a defect, a stress release wave propagates away from the crack and protects the region encompassed by the wave from any further crack initiation. In this paper, we show by the use of numerical simulations that this assumption is only valid at high strain rates. The limit of its accuracy is even pushed to higher strain rates when the fragmentation process becomes more complex, that is to say when crack propagation, bifurcation or coalescence together with wave reflections are implied. In these cases, fragmentation lasts longer than the time needed to completely obscure the whole specimen and the obscured zone theory for fragmentation appears inadequate. We use the cohesive-element method to describe the damage and failure of the material considere

How the obscuration-zone hypothesis affects fragmentation: Illustration with the cohesive-element method

The problem of fragmentation prediction is at the origin of various analytical models. Among them, we focus on the ones introducing the idea of obscured zones. They assume that when a crack initiates at a defect, a stress release wave propagates away from the crack and protects the region encompassed by the wave from any further crack initiation. In this paper, we show by the use of numerical simulations that this assumption is only valid at high strain rates. The limit of its accuracy is even pushed to higher strain rates when the fragmentation process becomes more complex, that is to say when crack propagation, bifurcation or coalescence together with wave reflections are implied. In these cases, fragmentation lasts longer than the time needed to completely obscure the whole specimen and the obscured zone theory for fragmentation appears inadequate. We use the cohesive-element method to describe the damage and failure of the material considered

The Context-Freeness Problem Is coNP-Complete for Flat Counter Systems

International audienceBounded languages have recently proved to be an important class of languages for the analysis of Turing-powerful models. For instance, bounded context-free languages are used to under-approximate the behav-iors of recursive programs. Ginsburg and Spanier have shown in 1966 that a bounded language L ⊆ a * 1 · · · a * d is context-free if, and only if, its Parikh image is a stratifiable semilinear set. However, the question whether a semilinear set is stratifiable, hereafter called the stratifiability problem, was left open, and remains so. In this paper, we give a partial answer to this problem. We focus on semilinear sets that are given as finite systems of linear inequalities, and we show that stratifiability is coNP-complete in this case. Then, we apply our techniques to the context-freeness problem for flat counter systems, that asks whether the trace language of a counter system intersected with a bounded regular language is context-free. As main result of the paper, we show that this problem is coNP-complete

Experimental validation of an anisotropic delay damage model for impact on reinforced concrete structures

International audienceImpact problems on reinforced concrete structures are usually computed with models coupling plasticity and isotropic damage. The induced damage anisotropy observed for quasi-brittle materials such as concrete is often reproduced considering different variables for tension and compression (not consistent with the thermodynamic framework). Introducing viscosity for both damage and plasticity evolutions enables to reproduce the strength enhancement due to rate effects. Such kinds of models present the main advantage to describe precisely each phenomenon locally observed (different rate effects in traction and compression, compaction under confined loadings ...) but require a large number of parameters. Anisotropic damage is quite relevant to describe the micro-cracking pattern and the failure conditions of quasi-brittle materials and structures. In concrete, a state of micro-cracks orthogonal to the loading direction in tension and parallel to it in compression is easily described by a second order damage variable. This anisotropic delay-damage model, used in this work, introduces only few parameters (7 including elasticity parameters E and ν) compared to the ones mentioned higher. The efficiency and the validation of such an approach is illustrated with its application on impacted reinforced concrete beams and dynamic Brazilian tests. The test has been performed with the drop-weight tower ORION of the CEA Saclay for two kinds of beam geometries in order to exhibit flexion and shear rupture. 1 INTRODUCTION The challenge of understanding the behavior of civil engineering structures under dynamic loading is usually linked to security issues but also some economic problems. Advances in instrumentation continue to improve our understanding on these subjects, so one continues around the world to develop impact tests on reinforced concrete structures. The civil engineering is one area where the tests are the most numerous. Indeed, it's only repeating the experiments and varying the parameters that we managed to understand the behavior of structures. But few cases where experiments are conducted on real structures with the stresses actually envisaged, are available. Moreover these experiments do not always provide more information than mockup models. Therefore, we find in the literature a large number of tests on simple structures such as slabs or beams. The philosophy of these kind of tests is to demonstrate on simple structures (beams, slabs) a number of local and global phenomena to allow modeling of more complex cases. Tests developed in the Dynamics Laboratory (DYN) of the CEA Saclay during this work include in this perspective. Two types of tests on a drop-weight tower were made: dynamic Brazilian tests and impact tests on beams. The dynamic Brazilian tests are relatively uncommon in the literature ((Tedesco, Ross, and Kuennen 1993) made the first dynamic Brazilian tests on split Hopkinson bars), but very interesting. A fast digital camera has been used in addition to more traditional, but precise and efficient, instrumentations (accelerometer, displacement measurement by camera, force sensors). The recorded images are analyzed by Digital Image Correlation with the software CORRELI developed at the LMT Cachan (Besnard, Hild, and Roux 2006). The impact tests on beams were designed to study the transition from a ductile failure mode (flexural) to a brittle fracture mode (shear cone). The two factors influencing this study are the slenderness of the beam and the transverse reinforcement (stirrups). An anisotropic delay-damage model has been developed during this work and it is presented in the last section. Finally this model is used to model the tests realized on the drop-weight tower

Mixing lossy and perfect fifo channels

We consider asynchronous networks of finite-state systems communicating via a combination of reliable and lossy fifo channels. Depending on the topology, the reachability problem for such networks may be decidable. We provide a complete classification of network topologies according to whether they lead to a decidable reachability problem. Furthermore, this classification can be decided in polynomial-time

On the influence of transgranular and intergranular failure mechanisms during dynamic loading of silicon nitride

Plane-strain tensile loading numerical simulations of dynamic crack propagation in silicon nitride microstructures are conducted. The strength and toughness are evaluated as a function of strain rate and microstructural parameters, including grain size and density of needle-shaped grains. The silicon nitride microstructures are built using Voronoi tessellation for constructing regular grains and a merging procedure to generate elongated grains. Dynamic insertion of cohesive elements representing transgranular and intergranular cracking is a key feature of the modeling. The results show that inertia and elongated grains both contribute to the rate hardening of the specimen. The simulations reveal the existence of a threshold opening rate for intergranular cracks to transform into transgranular ones. Moreover, a higher percentage of transgranular fracture causes higher toughness. (c) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets

www.lsv.ens-cachan.fr/~phs Abstract. We prove that coverability and termination are not primitive-recursive for lossy counter machines and for Reset Petri nets.