Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16

Crack Front Waves and the dynamics of a rapidly moving crack

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport energy, generate surface structure and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to crack instabilities, yields both inhomogeneity and scaling behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure

Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Additional information can be obtained from http://gershwin.msd.anl.gov/theor

Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication

Elastic forces that do no work and the dynamics of fast cracks

Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is used to propose a universal scenario, in which three dimensionality is essential, for the dynamic instability of fast cracks in thin brittle materials.Comment: 8 pages Latex, 1 Postscript figur

Development of a PCI Express Based Readout Electronics for the XPAD3 X-Ray Photon Counting Image

International audienceXPAD3 is a large surface X-ray photon counting imager with high count rates, large counter dynamics and very fast data readout. Data are readout in parallel by a PCI Express interface using DMA transfer. The readout frame rate of the complete detector comprising 0.5 MPixels amounts to 500 images per second without dead-time

XPAD: pixel detector for material sciences

Currently available 2D detectors do not make full use of the high flux and high brilliance of third generation synchrotron sources. The XPAD prototype, using active pixels, has been developed to fulfil the needs of materials science scattering experiments. At the time, its prototype is build of eight modules of eight chips. The threshold calibration of /spl ap/4 10/sup 4/ pixels is discussed. Applications to powder diffraction or SAXS experiments prove that it allows to record high quality data