[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] Canards, special trajectories that follow invariant repelling slow manifolds for long time intervals, have been frequently observed in slow-fast systems of either biological, chemical and physical nature. Here, collective canard explosions are demonstrated in a population of globally-coupled phase-rotators subject to adaptive coupling. In particular, we consider a bimodal Kuramoto model displaying coexistence of asynchronous and partially synchronized dynamics subject to a linear global feedback. A detailed geometric singular perturbation analysis of the associated mean-field model allows us to explain the emergence of collective canards in terms of the stability properties of the one-dimensional critical manifold, near which the slow macroscopic dynamics takes place. We finally show how collective canards and related manifolds gradually emerge in the globally-coupled system for increasing system sizes, in spite of the trivial dynamics of the uncoupled rotators.

[en] As a continuation of the study of the herding model proposed in (Bae et al. in arXiv:1712.01085 , 2017), we consider in this paper the derivation of the kinetic version of the herding model, the existence of the measure-valued solution and the corresponding herding behavior at the kinetic level. We first consider the mean-field limit of the particle herding model and derive the existence of the measure-valued solutions for the kinetic herding model. We then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals. First, we derive a herding phenomena of the measure-valued solutions under virtually no restrictions on the parameter sets using the Barbalat’s lemma. We, however, don’t get any herding rate in this case. On the other hand, we also establish a Grönwall type estimate for another herding functional, leading to the exponential herding rate, under comparatively strict conditions. These results are then extended to smooth solutions.

[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] Highlights: • We study a two-scale kinematic dynamo by the multiscale stability theory methods. • For mirror-antisymmetric flow, alpha-effect and eddy diffusivity act jointly. • Due to the action of alpha-effect magnetic field experiences oscillations in time. • Anisotropic magnetic eddy diffusivity becomes negative due to its singular behaviour. • Large-scale magnetic field is generated for any value of molecular diffusivity -- Abstract: We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the multiscale stability theory. It turns out that, due to the magnetic $\alpha$-effect in such flows, the large-scale mean field experiences harmonic oscillations in time on the scale O($\epsilon t$) without growth or decay. Here $\epsilon$ is the spatial scale ratio and $t$ is the fast time of the order of the flow turnover time. The interaction of the accompanying fluctuating magnetic field with the flow gives rise to an anisotropic magnetic eddy diffusivity, whose dependence on the direction of the large-scale wave vector generically exhibits a singular behaviour, and thus to negative eddy diffusivity for whichever molecular magnetic diffusivity. Consequently, such flows always act as kinematic dynamos on the time scale O(${\epsilon }^{2}t$); for the directions at which eddy diffusivity is infinite, the large-scale mean-field growth rate is finite on the scale O(${\epsilon }^{3∕2}t$). We investigate numerically this dynamo mechanism for two sample flows.

[en] Published in summary form only

[en] The nuclear collective motion is described as the variation of the non-Hermitian mean field, and the corresponding collective Hamiltonian is obtained

[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.