New model for surface fracture induced by dynamical stress

We introduce a model where an isotropic, dynamically-imposed stress induces fracture in a thin film. Using molecular dynamics simulations, we study how the integrated fragment distribution function depends on the rate of change and magnitude of the imposed stress, as well as on temperature. A mean-field argument shows that the system becomes unstable for a critical value of the stress. We find a striking invariance of the distribution of fragments for fixed ratio of temperature and rate of change of the stress; the interval over which this invariance holds is determined by the force fluctuations at the critical value of the stress.Comment: Revtex, 4 pages, 4 figures available upon reques

Rupture Pressure Prediction for Composite High Pressure Tanks Using Acoustic Emission

The French Aerospace company AEROSPATIALE manufactures high pressure tanks for helium gas storage. Because these tanks are critical elements for rockets and satellites, a new approach has been developed to have a better knowledge of the structure reliability. Although numerical tools such as finite elements codes are used for the design of such structures and. quality rules are imposed to insure that the tanks manufactured are in accordance to the definition, it is conceivable that even a successful proof test could actually damage the composite and lead to a residual SF less than 2

Tri-critical behavior in rupture induced by disorder

We discover a qualitatively new behavior for systems where the load transfer has limiting stress amplification as in real fiber composites. We find that the disorder is a relevant field leading to tri--criticality, separating a first-order regime where rupture occurs without significant precursors from a second-order regime where the macroscopic elastic coefficient exhibit power law behavior. Our results are based on analytical analysis of fiber bundle models and numerical simulations of a two-dimensional tensorial spring-block system in which stick-slip motion and fracture compete.Comment: Revtex, 10 pages, 4 figures available upon reques

Log-periodic route to fractal functions

Log-periodic oscillations have been found to decorate the usual power law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes characterized by the amplitudes A(n) of the power law series expansion. These two classes are separated by a novel ``critical'' point. Growth processes (DLA), rupture, earthquake and financial crashes seem to be characterized by oscillatory or bounded regular microscopic functions g(x) that lead to a slow power law decay of A(n), giving strong log-periodic amplitudes. In contrast, the regular function g(x) of statistical physics models with ``ferromagnetic''-type interactions at equibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables. These two classes of behavior can be traced back to the existence or abscence of ``antiferromagnetic'' or ``dipolar''-type interactions which, when present, make the Green functions non-monotonous oscillatory and favor spatial modulated patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new demonstration of the source of strong log-periodicity and of a justification of the general offered classification, update of reference lis

Comprehensive structural classification of ligand binding motifs in proteins

Comprehensive knowledge of protein-ligand interactions should provide a useful basis for annotating protein functions, studying protein evolution, engineering enzymatic activity, and designing drugs. To investigate the diversity and universality of ligand binding sites in protein structures, we conducted the all-against-all atomic-level structural comparison of over 180,000 ligand binding sites found in all the known structures in the Protein Data Bank by using a recently developed database search and alignment algorithm. By applying a hybrid top-down-bottom-up clustering analysis to the comparison results, we determined approximately 3000 well-defined structural motifs of ligand binding sites. Apart from a handful of exceptions, most structural motifs were found to be confined within single families or superfamilies, and to be associated with particular ligands. Furthermore, we analyzed the components of the similarity network and enumerated more than 4000 pairs of ligand binding sites that were shared across different protein folds.Comment: 13 pages, 8 figure

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

Universal Log-Periodic Correction to Renormalization Group Scaling for Rupture Stress Prediction From Acoustic Emissions

Based on the idea that the rupture of heterogenous systems is similar to a critical point, we show how to predict the failure stress with good reliability and precision ($\approx 5$) from acoustic emission measurements at constant stress rate up to a maximum load 15-20% below the failure stress. The basis of our approach is to fit the experimental signals to a mathematical expression deduced from a new scaling theory for rupture in terms of complex fractal exponents. The method is tested successfully on an industrial application, namely high pressure spherical tanks made of various fiber-matrix composites. As a by-product, our results constitute the first observation in a natural context of the universal periodic corrections to scaling in the renormalization-group framework. Our method could be applied usefully to other similar predicting problems in the natural sciences (earthquakes, volcanic eruptions, etc.)