Anomalous roughness with system size dependent local roughness exponent

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width \lambda L, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non universal global roughness exponent \alpha and the system size dependent spectrum of local roughness exponents,\xi_q, whereas the burning fronts possess conventional multi-affine scaling. The structure factor of turbulent flame fronts also exhibit unconventional scaling dependence on \lambda These results are expected to apply to a broad range of far from equilibrium systems, when the kinetic energy fluctuations exceed a certain critical value.Comment: 33 pages, 16 figure

Dynamic scaling approach to study time series fluctuations

We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.Comment: 25 pages, 7 figures, 1 tabl

Power law scaling of lateral deformations with universal Poissons index for randomly folded thin sheets

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poissons index nu = 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes, nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poissons ratio nu_e = 0.33 pm 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested

A continuum framework for mechanics of fractal materials II: elastic stress fields ahead of cracks in a fractal medium

This paper is devoted to the crack mechanics in heterogeneous materials with fractal (micro-)structures. Specifically, stress concentrations ahead of straight notches and self-affine cracks in fractal media are studied within a fractal continuum framework. A model of fractal continuum with fractal boundaries accounting for the metric, topological, and connectivity properties of the material microstructure and crack is employed for homogenization of crack problems in fractal media. It is found that the fractal nature of material heterogeneity can either delay or assist the crack initiation and propagation, depending on the interplay between metric and topological properties of the fractal domain

A continuum framework for mechanics of fractal materials I: from fractional space to continuum with fractal metric

This paper is devoted to the mechanics of fractally heterogeneous media. A model of fractal continuum with a fractional number of spatial degrees of freedom and a fractal metric is suggested. The Jacobian matrix of the fractal continuum deformation is defined and the kinematics of deformations is elucidated. The symmetry of the Cauchy stress tensor for continua with the fractal metric is established. A homogenization framework accounting for the connectivity, topological, and metric properties of fractal domains in heterogeneous materials is developed. The mapping of mechanical problems for fractal media into the corresponding problems for the fractal continuum is discussed. Stress and strain distributions in elastic fractal bars are analyzed. An approach to fractal bar optimization is proposed. Some features of acoustic wave propagation and localization in fractal media are briefly highlighted

Depinning and creeplike motion of wetting fronts in weakly vibrated granular media

We study the effect of weak vibrations on the imbibition of water in granular media. In our experiments, we have observed that as soon as the vibration is applied, an initially pinned wetting front advances in the direction of imbibition. We found that the front motion is governed by the avalanches of localized intermittent advances directed at 45 δ to the imbibition direction. When the rescaled gravitational acceleration of vertical vibrations is in the range of 0.81≤G≤0.95, we observed an almost steady motion of wetting front with a constant velocity v cr(G) exp-1/G during more than 20 min, whereas at lower accelerations (0.5≤G≤0.8) the front velocity decreases in time as vt -δ. We suggest that the steady motion of an imbibition front in a weakly vibrated granular medium can be treated as a creep motion associated with nonthermal temporal fluctuations of packing density in a weakly vibrated granular medium. © 2012 American Physical Society.This work was supported by the CSIC (España)– CONACYT(México) under Project No. J101.390, the FONCICYT (México–European Union) under Project No. 96095, and the Government of Mexico City under Grant No. PICCT08-64.Peer Reviewe