Physical properties of a generalized model of multilayer adsorption of dimers.

We investigate the transport properties of a complex porous structure with branched fractal architectures formed due to the gradual deposition of dimers in a model of multilayer adsorption. We thoroughly study the interplay between the orientational anisotropy parameter p_{0} of deposited dimers and the formation of porous structures, as well as its impact on the conductivity of the system, through extensive numerical simulations. By systematically varying the value of p_{0}, several critical and off-critical scaling relations characterizing the behavior of the system are examined. The results demonstrate that the degree of orientational anisotropy of dimers plays a significant role in determining the structural and physical characteristics of the system. We find that the Einstein relation relating to the size scaling of the electrical conductance holds true only in the limiting case of p_{0}→1. Monitoring the fractal dimension of the interface of the multilayer formation for various p_{0} values, we reveal that in a wide range of p_{0}>0.2 interface shows the characteristic of a self-avoiding random walk, compared to the limiting case of p_{0}→0 where it is characterized by the fractal dimension of the backbone of ordinary percolation cluster at criticality. Our results thus can provide useful information about the fundamental mechanisms underlying the formation and behavior of wide varieties of amorphous and disordered systems that are of paramount importance both in science and technology as well as in environmental studies.

Unfolding of crumpled thin sheets.

Crumpled thin sheets are complex fractal structures whose physical properties are influenced by a hierarchy of ridges. In this paper, we report experiments that measure the stress-strain relation and show the coexistence of phases in the stretching of crumpled surfaces. The pull stress showed a change from a linear Hookean regime to a sublinear scaling with an exponent of 0.65±0.03, which is identified with the Hurst exponent of the crumpled sheets. The stress fluctuations are studied. The statistical distribution of force peaks is analyzed. It is shown that the unpacking of crumpled sheets is guided by a hierarchical order of ridges.

Transport properties in multilayer adsorption of dimers.

In this paper, we study the transport properties (percolation and conductivity) of a two-dimensional structure created by depositing dimers on a one-dimensional substrate where multilayer deposition is allowed. Specifically, we are interested in studying how the mentioned properties vary as a function of the height of the multilayer. The critical parameters of the percolation transition are calculated using finite-size scaling analysis, obtaining the scaling laws for the probability of percolation and the conductivity of the system. To calculate the electrical conductivity of the multilayer, we use the Frank-Lobb algorithm.

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.

Packing loops into annular cavities.

The continuous packing of a flexible rod in two-dimensional cavities yields a countable set of interacting domains that resembles nonequilibrium cellular systems and belongs to a new class of lightweight material. However, the link between the length of the rod and the number of domains requires investigation, especially in the case of non-simply connected cavities, where the number of avoided regions emulates an effective topological temperature. In the present article we report the results of an experiment of injection of a single flexible rod into annular cavities in order to find the total length needed to insert a given number of loops (domains of one vertex). Using an exponential model to describe the experimental data we quite minutely analyze the initial conditions, the intermediary behavior, and the tight packing limit. This method allows the observation of a new fluctuation phenomenon associated with instabilities in the dynamic evolution of the packing process. Furthermore, the fractal dimension of the global pattern enters the discussion under a novel point of view. A comparison with the classical problems of the random close packing of disks and jammed disk packings is made.

Scaling, crumpled wires, and genome packing in virions.

The packing of a genome in virions is a topic of intense current interest in biology and biological physics. The area is dominated by allometric scaling relations that connect, e.g., the length of the encapsulated genome and the size of the corresponding virion capsid. Here we report scaling laws obtained from extensive experiments of packing of a macroscopic wire within rigid three-dimensional spherical and nonspherical cavities that can shed light on the details of the genome packing in virions. We show that these results obtained with crumpled wires are comparable to those from a large compilation of biological data from several classes of virions.

Crumpling Damaged Graphene.

Through molecular mechanics we find that non-covalent interactions modify the fractality of crumpled damaged graphene. Pristine graphene membranes are damaged by adding random vacancies and carbon-hydrogen bonds. Crumpled membranes exhibit a fractal dimension of 2.71 ± 0.02 when all interactions between carbon atoms are considered, and 2.30 ± 0.05 when non-covalent interactions are suppressed. The transition between these two values, obtained by switching on/off the non-covalent interactions of equilibrium configurations, is shown to be reversible and independent on thermalisation. In order to explain this transition, we propose a theoretical model that is compatible with our numerical findings. Finally, we also compare damaged graphene membranes with other crumpled structures, as for instance polymerised membranes and paper sheets, that share similar scaling properties.

Nontrivial temporal scaling in a Galilean stick-slip dynamics.

We examine the stick-slip fluctuating response of a rough massive nonrotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The experiments presented here, which are reminiscent of Galileo's works with rolling objects on inclines, have brought in the last years important insights into the friction between surfaces in relative motion and are of relevance for earthquakes, differing from classical block-spring models by the mechanism of energy input in the system. Robust nontrivial temporal scaling laws appearing in the dynamics of this system are reported, and it is shown that the time-support where dissipation occurs approaches a statistical fractal set with a fixed value of dimension. The distribution of periods of inactivity in the intermittent motion of the cylinder is also studied and found to be closely related to the lacunarity of a random version of the classic triadic Cantor set on the line.

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.

Crumpled states of a wire in a cubic cavity with periodic obstacles.

In this paper, we study experimentally the configurations of a plastic wire injected into a cubic cavity containing periodic obstacles placed along a fixed direction. The wire moves in a wormlike manner within the cavity until it becomes jammed in a crumpled state. The maximum packing fraction of the wire depends on the topology of the cavity, which in turn depends on the number of obstacles. The experimental results exhibit scaling laws and display similarities as well as differences with a recently reported two-dimensional version of this complex packing problem. We discuss in detail several aspects of this problem that seem as intricate as the problem of a self-avoiding random walk. Analogies between the experiment reported and some statistical aspects of the bond-percolation problem, as well as of the interacting electron gas at finite temperature, and other physical issues are also discussed.

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.

A crumpled surface having transverse attractive interactions as a simplified model with biological significance.

Using extensive analogical simulations with square sheets of paper we investigate the influence of short-range transverse attractive interactions on the packing properties of a crumpled surface. These interactions are due to transverse connections or local bridges associated with a given number of binding sites localized on the two-dimensional surface and distributed in several patterns in the three-dimensional physical space. Geometrical relations and critical exponents describing the statistical properties of the crumpled surface are obtained as a function of the strength of the attractive interactions. Our model suggests how the presence of short-range interactions as, e.g. van der Waals forces can be important for the geometric plasticity of biological molecules, which in turn is important for biological function. The relevance of our results to the study of molecular conformation of proteins and membranes is discussed, and a comparison is also made between the behavior of the crumpled surface studied here and other important non-equilibrium fractal structures.