Analytical results for long-time behavior in anomalous diffusion.

We investigate through a generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor λ. We obtain as well an exact expression for λ for all kinds of diffusion. Moreover, we show that λ is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. The method is general and may be applied to many types of stochastic problem.

Crumpled states of a wire in a two-dimensional cavity with pins.

In this paper, we report an extensive experimental study of the configurations of a plastic wire injected into a two-dimensional planar cavity populated with fixed pins. The wire is not allowed to cross any pin, but it can move in a wormlike manner within the cavity until to become jammed in a crumpled state. The jammed packing fraction depends heavily on the topology of the cavity, which depends on the number of pins. The experiment reveals nontrivial entanglement effects and scaling laws which are largely independent of the details of the distribution of pins, the symmetry of the cavity or the type of the wire. A mean-field model for the process is presented and analogies with some basic aspects of statistical thermodynamics are discussed.

Condensation of elastic energy in two-dimensional packing of wires.

Forced packing of a long metallic wire injected into a two-dimensional cavity leads to crushed structures involving a hierarchical cascade of loops with varying curvature radii. We study the distribution of elastic energy stored in such systems from experiments, and high-resolution digital techniques. It is found that the set where the elastic energy of curvature is concentrated has dimension D(S) = 1.0 +/- 0.1, while the set where the mass is distributed has dimension D = 1.9 +/- 0.1.

Scaling properties in the packing of crumpled wires.

Statistical properties of configurations of a metallic wire injected into a transparent planar two-dimensional cavity for three different injection geometries are investigated with the aid of high-resolution digital imaging techniques. The observed patterns of folds are studied as a function of the packing fraction of the wire within the cavity. In particular, we have examined the dependence of the mass of wire within a circle of radius R, as well as the dependence of the number of contacts wire-wire with the packing fraction. The distribution function n(s) of connected loops with internal area s formed as a consequence of the folded structure of the wire, and the average coordination number for these loops are also examined. Several scaling laws connecting variables of physical interest are obtained and discussed and a relation of this problem with disordered two-dimensional foam and random packing of disks is examined.

Crumpled wires in two dimensions.

Geometric and statistical properties of wires injected into a two-dimensional cavity with three different injection geometries are investigated. Complex patterns of folds are observed and studied as a function of the length of the wire. The mass-size relation and the distribution function n(s) of loops with internal area s formed as a consequence of the folded structure of the wire are examined. Several scaling laws are found and a hierarchical model is introduced to explain the experimental behavior observed in this two-dimensional crumpling process.