Fundamental domains of cluster categories inside module categories

Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field, and let $\mathcal{C}_{H}$ be the corresponding cluster category. We give a description of the (standard) fundamental domain of $\mathcal{C}_{H}$ in the bounded derived category $\mathcal{D}^{b}(H)$, and of the cluster-tilting objects, in terms of the category $\mod\Gamma$\ of finitely generated modules over a suitable tilted algebra $$ Furthermore, we apply this description to obtain (the quiver of) an arbitrary cluster-tilted algebra.Comment: 20 pages, 9 figure

An expanded merger-tree description of cluster evolution

We model the formation and evolution of galaxy clusters in the framework of an extended dark matter halo merger-tree algorithm that includes baryons and incorporates basic physical considerations. Our modified treatment is employed to calculate the probability density functions of the halo concentration parameter, intracluster gas temperature, and the integrated Comptonization parameter for different cluster masses and observation redshifts. Scaling relations between cluster mass and these observables are deduced that are somewhat different than previous results. Modeling uncertainties in the predicted probability density functions are estimated. Our treatment and the insight gained from the results presented in this paper can simplify the comparison of theoretical predictions with results from ongoing and future cluster surveys.Comment: 11 pages, 9 figures, submitted to MNRA

A theoretical study of the cluster glass-Kondo-magnetic disordered alloys

The physics of disordered alloys, such as typically the well known case of CeNi1-xCux alloys, showing an interplay among the Kondo effect, the spin glass state and a magnetic order, has been studied firstly within an average description like in the Sherrington-Kirkpatrick model. Recently, a theoretical model (PRB 74, 014427 (2006)) involving a more local description of the intersite interaction has been proposed to describe the phase diagram of CeNi1-xCux. This alloy is an example of the complex interplay between Kondo effect and frustration in which there is in particular the onset of a cluster-glass state. Although the model given in Ref. PRB 74, 014427 (2006) has reproduced the different phases relatively well, it is not able to describe the cluster-glass state. We study here the competition between the Kondo effect and a cluster glass phase within a Kondo Lattice model with an inter-cluster random Gaussian interaction. The inter-cluster term is treated within the cluster mean-field theory for spin glasses, while, inside the cluster, an exact diagonalisation is performed including inter-site ferromagnetic and intra-site Kondo interactions. The cluster glass order parameters and the Kondo correlation function are obtained for different values of the cluster size, the intra-cluster ferromagnetic coupling and the Kondo intra-site coupling. We obtain, for instance, that the increase of the Kondo coupling tends to destroy the cluster glass phase.Comment: 6 pages, 2 figures, Accepted for publication in Physica

Thermo-kinetic approach of single-particles and clusters involving anomalous diffusion under viscoelastic response

We present a thermo-kinetic description of anomalous diffusion of single-particles and clusters in a viscoelastic medium in terms of a non-Markovian diffusion equation involving memory functions. The scaling behaviour of these functions is analyzed by considering hydrodynamics and cluster-size space random walk arguments. We explain experimental results on diffusion of Brownian particles in the cytoskeleton, in cluster-cluster aggregation and in a suspension of micelles.Comment: To be published in the Journal of Physical Chemistry