We consider the canonical Gibbs measure associated to a N-vortex system in a bounded domain Λ, at inverse temperature {Mathematical expression} and prove that, in the limit N→∞, {Mathematical expression}/N→β, αN→1, where β∈(-8π, + ∞) (here α denotes the vorticity intensity of each vortex), the one particle distribution function ρ{variant}N = ρ{variant}Nx, x∈Λ converges to a superposition of solutions ρ{variant}α of the following Mean Field Equation: {Mathematical expression} Moreover, we study the variational principles associated to Eq. (A.1) and prove thai, when β→-8π+, either ρ{variant}β → δx0 (weakly in the sense of measures) where x0 denotes and equilibrium point of a single point vortex in Λ, or ρ{variant}β converges to a smooth solution of (A.1) for β=-8π. Examples of both possibilities are given, although we are not able to solve the alternative for a given Λ. Finally, we discuss a possible connection of the present analysis with the 2-D turbulence. © 1992 Springer-Verlag

What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs usually propagate along an S-shaped curve with a rather sudden transition towards global agreement. It also helps to analyze and design new technologies that support or orchestrate self-organizing communication systems, such as recent social tagging systems for the web. The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. We show that the system undergoes a disorder/order transition, going trough a sharp symmetry breaking process to reach a shared set of conventions. Before the transition, the system builds up non-trivial scale-invariant correlations, for instance in the distribution of competing synonyms, which display a Zipf-like law. These correlations make the system ready for the transition towards shared conventions, which, observed on the time-scale of collective behaviors, becomes sharper and sharper with system size. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics.

In this letter we present a very general method to extract information from a generic string of characters, e.g. a text, a DNA sequence or a time series. Based on data-compression techniques, its key point is the computation of a suitable measure of the remoteness of two bodies of knowledge. We present the implementation of the method to linguistic motivated problems, featuring highly accurate results for language recognition, authorship attribution and language classification. (PACS: 89.70.+c,05.) Many systems and phenomena in nature are often represented in terms of sequences or strings of characters. In experimental investigations of physical processes, for instance, one typically has access to the system only through a measuring device which produces a time record of a certain observable, i.e. a sequence of data. On the other hand other systems are intrinsically described by string of characters, e.g. DNA and protein sequences, language.When analyzing a string of characters the main question is to extract the information it brings. For a DNA sequence this would correspond to the identification of the sub-sequences codifying the genes and their specific functions. On the other hand for a written text one is interested in understanding it, i.e. recognize the language in which the text is written, its author, the subject treated and eventually the historical background.The problem cast in such a way, one would be tempted to approach it from a very interesting point of view: that of information theory [1,2]. In this context the word information acquires a very precise meaning, namely that of the entropy of the string, a measure of the surprise the source emitting the sequences can reserve to us.As it is evident the word information is used with different meanings in different contexts. Suppose now for a while to be able to measure the entropy of a given sequence (e.g. a text). Is it possible to obtain from this measure the information (in the semantic sense) we were trying to extract from the sequence? This is the question we address in this paper.In particular we define in a very general way a concept of remoteness (or similarity) between pairs of sequences based on their relative informatic content. We devise, without loss of generality with respect to the nature of the strings of characters, a method to measure this distance based on data-compression techniques. The specific question we address is whether this informatic distance between pairs of sequences is representative of the real semantic difference between the sequences. It turns out that the answer is yes, at least in the framework of the examples on which we have implemented the method.

We propose a two-dimensional geometrical model, based on the concept of geometrical frustration, conceived for the study of compaction in granular media. The dynamics exhibits an interesting inverse logarithmic law that is well known from real experiments. Moreover, we present a simple dynamical model of N planes exchanging particles with excluded volume problems, which allows us to clarify the origin of the logarithmic relaxations and the stationary density distribution. A simple mapping allows us to cast this Tetris-like model in the form of an Ising-like spin system with vacancies.[S0031-9007(97)03818-0] PACS numbers: 81.05.Rm, 05.50. + q, 05.70.Ln A granular system may be in a number of different microscopic states at fixed macroscopic densities, and many unusual properties are linked to its nontrivial packing [1,2]. As pointed out by Edwards [2-4] the role that the concept of free energy plays in standard thermal systems as Ising models, in granular media seems to be played by the "effective volume," derived by a complex function of grain positions and orientations. In this way statistical mechanics provides theoretical concepts in the context of nonthermal systems.A recent experiment on the problem of density compaction in a dry granular system under tapping has shown [5] that density compaction follows an inverse logarithmic law with the tapping number.Several approaches have been proposed to explain this behavior [6][7][8][9][10][11], as geometrical models of "parking" [10,12] or simple free-volume theories [11] or the study of the dynamics of a frustrated lattice gas with quenched disorder subject to gravity and vibrations [9].In many seemingly different cases the logarithmic relaxation proposed in [5] to describe experimental data is reproduced. Moreover, the logarithmic law has turned out to be robust with respect to changes in the tapping procedure [9]. This suggests that such a relaxation behavior is extremely general and not linked to specific properties of definite realizations.Here we introduce a purely geometrical model of simple particles with several shapes on a lattice. We show that when subject to gravity and vibrations a logarithmic density relaxation [5] is found, due to the high entropic barriers (originated for geometrical reasons) to be passed by particles to improve global packing.We imagine a model similar to the computer game Tetris, in which neighboring grains can find different packing volumes according to their relative geometrical orientations. Although one could imagine a rich variety of shapes and dimensions, as in the real computer game, it is useful, without loss of generality for the main features, to think just of a system of elongated particles which occupy the sites of square lattice tilted by 45 ± (see Fig. 1, with periodic boundary conditions in the horizontal direction (cylindrical geometry) and a rigid plane at its bottom. In general, the only interactions between the particles are the geometrical ones. Particles cannot overlap, and this condition produces very strong ...

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