Stability and roughness of tensile cracks in disordered materials

We study the stability and roughness of propagating cracks in heterogeneous brittle two-dimensional elastic materials. We begin by deriving an equation of motion describing the dynamics of such a crack in the framework of Linear Elastic Fracture Mechanics, based on the Griffith criterion and the Principle of Local Symmetry. This result allows us to extend the stability analysis of Cotterell and Rice to disordered materials. In the stable regime we find stochastic crack paths. Using tools of statistical physics we obtain the power spectrum of these paths and their probability distribution function, and conclude they do not exhibit self-affinity. We show that a real-space fractal analysis of these paths can lead to the wrong conclusion that the paths are self-affine. To complete the picture, we unravel the systematic bias in such real-space methods, and thus contribute to the general discussion of reliability of self-affine measurements.Comment: 32 pages, 12 figures, accepted to Physical Review

Career progression and formal versus on-the-job training

We model the choice of individuals to follow or not apprenticeship training and their subsequent career. We use German administrative data, which records education, labour market transitions and wages to estimate a dynamic discrete choice model of training choice, employment and wage growth. The model allows for returns to experience and tenure, match specific effects, job mobility and search frictions. We show how apprenticeship training affects labour market careers and we quantify its benefits, relative to the overall costs. We then use our model to show how two welfare reforms change life-cycle decisions and human capital accumulation: One is the introduction of an Earned Income Tax Credit in Germany, and the other is a reform to Unemployment Insurance. In both reforms we find very significant impacts of the policy on training choices and on the value of realized matches, demonstrating the importance of considering such longer term implications

A model for hierarchical patterns under mechanical stresses

We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.Comment: To appear in Philosophical Magazine. 18 pages, 8 figure

Cloaking by coating: How effectively does a thin, stiff coating hide a soft substrate?

From human tissue to fruits, many soft materials are coated by a thin layer of a stiffer material. While the primary role of such a coating is often to protect the softer material, the thin, stiff coating also has an important effect on the mechanical behaviour of the composite material, making it appear significantly stiffer than the underlying material. We study this cloaking effect of a coating for the particular case of indentation tests, which measure the `firmness' of the composite solid: we use a combination of theory and experiment to characterize the firmness quantitatively. We find that the indenter size plays a key role in determining the effectiveness of cloaking: small indenters feel a mixture of the material properties of the coating and of the substrate, while large indenters sense largely the unadulterated substrate

Seismic Radiation From Simple Models of Earthquakes

We review some basic features of shear wave generation and energy balance for a 2D anti plane rupture. We first study the energy balance for a flat fault, and for a fault that contains a single localized kink. We determine an exact expression for the partition between strain energy flow released from the elastic medium surrounding the fault, radiated energy flow and energy release rate. This balance depends only on the rupture speed and the residual stress intensity factor. When the fault contains a kink, the energy available for fracture is reduced so that the rupture speed is reduced. When rupture speed changes abruptly, the radiated energy flow also changes abruptly. As rupture propagates across the kink, a shear wave is emitted that has a displacement spectral content that decreases like ω^(-2) at high frequencies. We then use spectral elements to model the propagation of an antiplane crack with a slip-weakening friction law. Since the rupture front in this case has a finite length scale, the wave emitted by the kink is smoothed at very high frequencies but its general behavior is similar to that predicted by the simple sharp crack model. A model of a crack that has several kinks and wanders around a mean rupture directions, shows that kinks reduce the rupture speed along the average rupture direction of the fault. Contrary to flat fault models, a fault with kinks produces high frequency waves that are emitted every time the rupture front turns at a kink. Finally, we discuss the applicability of the present results to a 3D rupture model

Measuring order in the isotropic packing of elastic rods

The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic two-dimensional confinement of a rod by a central force. We seek to measure how ordered is a folded configuration and we identify two key quantities. A geometrical characterization is given by the number of superposed layers in the configuration. Using temporal modulations of the confining force, we probe the mechanical properties of the configuration and we define and measure its effective compressibility. These two quantities may be used to build a statistical framework for packed elastic systems.Comment: 4 pages, 5 figure

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 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