Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur

A Very Low Resource Language Speech Corpus for Computational Language Documentation Experiments

Most speech and language technologies are trained with massive amounts of speech and text information. However, most of the world languages do not have such resources or stable orthography. Systems constructed under these almost zero resource conditions are not only promising for speech technology but also for computational language documentation. The goal of computational language documentation is to help field linguists to (semi-)automatically analyze and annotate audio recordings of endangered and unwritten languages. Example tasks are automatic phoneme discovery or lexicon discovery from the speech signal. This paper presents a speech corpus collected during a realistic language documentation process. It is made up of 5k speech utterances in Mboshi (Bantu C25) aligned to French text translations. Speech transcriptions are also made available: they correspond to a non-standard graphemic form close to the language phonology. We present how the data was collected, cleaned and processed and we illustrate its use through a zero-resource task: spoken term discovery. The dataset is made available to the community for reproducible computational language documentation experiments and their evaluation.Comment: accepted to LREC 201

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

A prototypical model for tensional wrinkling in thin sheets

The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians and engineers. This has been triggered by the growing interest in developing technologies at ever decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. While the most basic buckling instability of uniaxially compressed plates was understood by Euler more than 200 years ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length - a sheet under axisymmetric tensile loads. This geometry, whose first study is attributed to Lam´e, allows us to construct\ud a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that for thin sheets the far-from-threshold regime is expected to emerge under extremely small compressive loads, emphasizing the relevance of our analysis for nanomechanics applications

First Order Phase Transition of a Long Polymer Chain

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.Comment: 11 pages, 7 figure

Roughness of moving elastic lines - crack and wetting fronts

We investigate propagating fronts in disordered media that belong to the universality class of wetting contact lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we study their roughness using the self-consistent expansion. When neglecting the irreversibility of fracture and wetting processes, we find a possible dynamic rough phase with a roughness exponent of $\zeta=1/2$ and a dynamic exponent of z=2. When including the irreversibility, we conclude that the front propagation can become history dependent, and thus we consider the value $\zeta=1/2$ as a lower bound for the roughness exponent. Interestingly, for propagating contact line in wetting, where irreversibility is weaker than in fracture, the experimental results are close to 0.5, while for fracture the reported values of 0.55--0.65 are higher.Comment: 15 pages, 6 figure

Casimir Effects in Renormalizable Quantum Field Theories

We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.Comment: 27 pp., 11 EPS figures, LaTeX using ijmpa1.sty; email correspondence to R.L. Jaffe ; based on talks presented by the authors at the 5th workshop `QFTEX', Leipzig, September 200

Scale relativity and fractal space-time: theory and applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the Evolution and Development of the Universe,8th - 9th October 2008, Paris, Franc