Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization, linguistic anomalous diffusion and mutation, and interaction among populations that occupy different regions. It is found that the dependence of the linguistic diversity on the area after colonization displays two power law regimes, both described by critical exponents which are dependent on the mutation probability. Most importantly for the future prospect of world's population, our results show that the linguistic diversity always decrease to an asymptotic very small value if large areas and sufficiently long times of interaction among populations are considered.
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.
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 surfaces (CS) obtained from random and irreversible compactification of aluminium foils are low-density fractal structures which become increasingly easy to deform as their size increases. The authors study the deformation of these objects when submitted to mechanical forces. In particular, they describe the behaviour of eight scaling relations which connect quantities such as stress, strain, surface roughness and geometrical variables for these CS. The critical exponents obtained from the scaling relations and some clues concerning the existence of universal behaviour in these processes are reported.
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