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[en] The dynamic critical exponent z is determined from numerical simulations for the three-dimensional (3D) lattice Coulomb gas (LCG) and the 3D XY models with relaxational dynamics. It is suggested that the dynamics is characterized by two distinct dynamic critical indices z0 and z related to the divergence of the relaxation time τ by τ∝ξz0 and τ∝k-z , where ξ is the correlation length and k the wave vector. The values determined are z0∼1.5 and z∼1 for the 3D LCG and z0∼1.5 and z∼2 for the 3D XY model. Comparisons with other results are discussed
[en] Vortices for 2D superfluids are introduced and are described in terms of a 2D Coulomb gas. The 2D classical JJ array is modeled by a 2D XY-model and a mapping between the XY-model and the Coulomb gas is given. The physical properties of a JJ array are then given in terms of the corresponding Coulomb gas properties. First aspects of the Kosterlitz-Thouless vortex unbinding transitions are reviewed. Consequences for the resistance as well as the frequency dependent conductivity are described. Next the vortex unbinding induced by an external current is considered with Consequencies for the non-linear IV-characteristics. Finally some some effects of a perpendicular magnetic field are discussed in terms of an interplay between free vortices and bound vortex pairs
[en] A random null model termed the blind-watchmaker network (BW) has been shown to reproduce the degree distribution found in metabolic networks. This might suggest that natural selection has had little influence on this particular network property. We investigate here the extent to which other structural network properties have evolved under selective pressure from the corresponding ones of the random null model: the clustering coefficient and the assortativity measures are chosen and it is found that these measures for the metabolic network structure are close enough to the BW network so as to fit inside its reachable random phase space. It is, furthermore, shown that the use of this null model indicates an evolutionary pressure towards low assortativity and that this pressure is stronger for larger networks. It is also shown that selecting for BW networks with low assortativity causes the BW degree distribution to deviate slightly from its power-law shape in the same way as the metabolic networks. This implies that an equilibrium model with fluctuating degree distribution is more suitable as a null model, when identifying selective pressures, than a randomized counterpart with fixed degree sequence, since the overall degree sequence itself can change under selective pressure on other global network properties.
[en] For certain hierarchical structures, one can study the percolation problem using the renormalization-group method in a very precise way. We show that the idea can also be applied to two-dimensional planar lattices by regarding them as hierarchical structures. Either a lower bound or an exact critical probability can be obtained using this method and the correlation-length critical exponent is approximately estimated as ν∼1.
[en] Evidence is presented for a systematic text-length dependence of the power-law index γ of a single book. The estimated γ values are consistent with a monotonic decrease from 2 to 1 with increasing text length. A direct connection to an extended Heap's law is explored. The infinite book limit is, as a consequence, proposed to be given by γ=1 instead of the value γ=2 expected if Zipf's law is universally applicable. In addition, we explore the idea that the systematic text-length dependence can be described by a meta book concept, which is an abstract representation reflecting the word-frequency structure of a text. According to this concept the word-frequency distribution of a text, with a certain length written by a single author, has the same characteristics as a text of the same length extracted from an imaginary complete infinite corpus written by the same author.
[en] In order to examine the uniqueness of the dynamic critical exponents and the exponent's dependence on dimensionality for XY models with time-dependent Ginzburg–Landau (TDGL) and resistively shunted junction (RSJ) dynamics we use two recently proposed methods to calculate the dynamic exponents in four dimensions. We discuss the relation to the dynamic universality classes and earlier works.
[en] Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups the unique words, or the elements could be inhabitants and the groups the cities in a country and so on. A random group formation (RGF) is presented from which a Bayesian estimate is obtained based on minimal information: it provides the best prediction for the number of groups with k elements, given the total number of elements, groups and the number of elements in the largest group. For each specification of these three values, the RGF predicts a unique group distribution N(k)∼exp(-bk)/kγ, where the power-law index γ is a unique function of the same three values. The universality of the result is made possible by the fact that no system-specific assumptions are made about the mechanism responsible for the group division. The direct relation between γ and the total number of elements, groups and the number of elements in the largest group is calculated. The predictive power of the RGF model is demonstrated by direct comparison with data from a variety of systems. It is shown that γ usually takes values in the interval 1≤γ≤2 and that the value for a given phenomenon depends in a systematic way on the total size of the dataset. The results are put in the context of earlier discussions on Zipf's and Gibrat's laws, N(k)∼k-2 and the connection between growth models and RGF is elucidated.
[en] The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds pc1 and pc2 with pc1 < pc2. Our Monte Carlo study implies that the second threshold pc2 is significantly lower than a recent claim by Nogawa and Hasegawa (2009 J. Phys. A: Math. Theor. 42 145001). This means that pc2 for the EBT does not obey the duality relation for the thresholds of dual graphs pc2+p-barc1=1 which is a property of a transitive, nonamenable, planar graph with one end. As in regular hyperbolic lattices, this relation instead becomes an inequality pc2+p-barc1<1. We also find that the critical behavior is well described by the scaling form previously found for regular hyperbolic lattices. (comments and replies)
[en] In Korean culture, the names of family members are recorded in special family books. This makes it possible to follow the distribution of Korean family names far back in history. It is shown here that these name distributions are well described by a simple null model, the random group formation (RGF) model. This model makes it possible to predict how the name distributions change and these predictions are shown to be borne out. In particular, the RGF model predicts that for married women entering a collection of family books in a certain year, the occurrence of the most common family name 'Kim' should be directly proportional to the total number of married women with the same proportionality constant for all the years. This prediction is also borne out to a high degree. We speculate that it reflects some inherent social stability in the Korean culture. In addition, we obtain an estimate of the total population of the Korean culture down to the year 500 AD, based on the RGF model, and find about ten thousand Kims.
[en] An allometric height–mass exponent γ gives an approximative power-law relation 〈M〉∝Hγ between the average mass 〈M〉 and the height H for a sample of individuals. The individuals in the present study are humans but could be any biological organism. The sampling can be for a specific age of the individuals or for an age interval. The body mass index is often used for practical purposes when characterizing humans and it is based on the allometric exponent γ = 2. It is shown here that the actual value of γ is to a large extent determined by the degree of correlation between mass and height within the sample studied: no correlation between mass and height means γ = 0, whereas if there was a precise relation between mass and height such that all individuals had the same shape and density then γ = 3. The connection is demonstrated by showing that the value of γ can be obtained directly from three numbers characterizing the spreads of the relevant random Gaussian statistical distributions: the spread of the height and mass distributions together with the spread of the mass distribution for the average height. Possible implications for allometric relations, in general, are discussed. (paper)