Results 1 - 10 of 12765
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[en] A canonical finite-temperature mean-field approximation and a higher-order approach, which includes particular two-body correlations, are developed and compared with the exact (canonical) and the usual mean-field (grand-canonical) results within the context of an exactly solvable fermion model. Special projected statistics in a particular canonical subspace are also discussed
[en] The solution of the spin glasses in the Mean Field approximation gives some interesting characteristics such as the existence of an infinite number of pure states organized in an ultrametric way (like in Taxonomy). These properties raise the spin glasses to a paradigm of the complex systems. (Author) 7 refs
[en] We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary and tricritical percolation transitions is governed by specific composite operators of the field-theoretic representation of this process. We calculate corresponding critical exponents for tricritical percolation in mean-field theory and for ordinary percolation to 1-loop order. Our results agree well with the available numerical data. (paper)
[en] The isoscaling parameter usually denoted by α depends upon both the symmetry energy coefficient and the isotopic contents of the dissociating systems. We compute α in theoretical models: first in a simple mean field model and then in thermodynamic models using both grand canonical and canonical ensembles. For finite systems the canonical ensemble is much more appropriate. The model values of α are compared with a much used standard formula. Next we turn to cases where in experiments, there are significant deviations from isoscaling. We show that in such cases, although the grand canonical model fails, the canonical model is capable of explaining the data
[en] We introduce a stochastic model in which adjacent planar regions A, B merge stochastically at some rate λ(A, B) and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite regions appear in finite time? We give a simple condition on λ for this hegemony property to hold, and another simple condition for it to not hold, but there is a large gap between these conditions, which includes the case λ(A, B) ≡ 1. For this case, a non-rigorous analytic argument and simulations suggest hegemony.
[en] We investigate the formulation of mean-field (MF) approaches for co-evolving dynamic model systems, focusing on the accuracy and validity of different schemes in closing MF equations. Within the context of a recently introduced co-evolutionary snowdrift game in which rational adaptive actions are driven by dissatisfaction in the payoff, we introduce a method to test the validity of closure schemes and analyse the shortcomings of previous schemes. A previous scheme suitable for adaptive epidemic models is shown to be invalid for the model studied here. A binomial-style closure scheme that significantly improves upon the previous schemes is introduced. Fixed-point analysis of the MF equations not only explains the numerical observed transition between a connected state with suppressed cooperation and a highly cooperative disconnected state, but also reveals a previously undetected connected state that exhibits the unusual behaviour of decreasing cooperation as the temptation for uncooperative action drops. We proposed a procedure for selecting proper initial conditions to realize the unusual state in numerical simulations. The effects of the mean number of connections that an agent carries are also studied.
[en] Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the mean-field theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model. We verify this theory with GPU-accelerated simulations on very large networks (N ∼ 10"6) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f → 0, we show that this behavior is far more likely to occur naturally than was previously believed.