No abstract

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.

Aspectos geométricos associados com o empacotamento hierárquico e heterogêneo de arames amassados são revistos. O fenômeno recentemente descoberto de condensação de energia elástica de curvatura nessas estruturas é discutido e novos resultados são apresentados, com ênfase em leis de escala robustas. Examina-se a possível relevância destas leis nas propriedades conformacionais de cadeias moleculares longas e densamente empacotadas em estado não-sólido como observado, por exemplo, para o DNA nos cromossomas ou nas cápsulas virais. Em particular, argumentos de campo médio são usados para estimar a dependência entre o número de laços e o comprimento dessas cadeias.Geometric aspects associated with the hierarchical and heterogeneous packing of crumpled wires are reviewed. The recently discovered phenomenon of condensation of elastic energy of curvature in these structures is discussed, and new results are presented with emphasis on robust scaling laws. It is examined the possible relevance of these laws in the conformational properties of long molecular chains densely packaged in a non-solid state, as e.g. in the packing of DNA strands in chromosomes, or in virus capsids. In particular, mean field arguments are used to estimate the dependence of the number of loops in the dense non-solid packed three-dimensional configurations of a very long polymer strand as a function of the number of monomers or the chain length.

An extensive Hurst analysis to quantify long-term statistical dependence is performed on time series associated with sliding of blocks on an inclined plane induced by small perturbations. The analysis reveals the existence of a fluctuation phenomenon exhibiting two phases, depending on the angle of inclination, both obeying a Hurst scaling . The first (second) phase has H = 0.70 (0.50) and refers to large (small) inclinations irrespective of the material of the block. These results indicate that sliding of blocks in the first regime exhibits persistence and indicate that there are long-term memory effects on the storage of shear stress at the block-plane interface. In the second regime, the long-term memory effects disappear and the sliding activity is intermittent; that is, it is distributed in bursts separated by variable periods of stasis.