Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field

The fluctuation-dissipation theorem and the linear Glauber model

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.Comment: Accepted for publication (Physical Review E

The curious case of the companion: evidence for cold accretion onto a dwarf satellite near the isolated elliptical NGC 7796

The isolated elliptical (IE) NGC 7796 is accompanied by an interesting early-type dwarf galaxy, named NGC7796-DW1. It exhibits a tidal tail, very boxy isophotes, and multiple nuclei or regions (A, B, and C) that are bluer than the bulk population of the galaxy, indicating a younger age. These properties are suggestive of a dwarf-dwarf merger remnant. We use the Multi-Unit Spectroscopic Explorer (MUSE) at the VLT to investigate NGC 7796-DW1. We extract characteristic spectra to which we apply the STARLIGHT population synthesis software to obtain ages and metallicities of the various population components of the galaxy. The galaxy's main body is old and metal-poor. A surprising result is the extended line emission in the galaxy, forming a ring-like structure with a projected diameter of 2.2 kpc. The line ratios fall into the regime of HII-regions, although OB-stellar populations cannot be identified by spectral signatures. Nucleus A is a relatively old (7 Gyr or older) and metal-poor super star cluster, most probably the nucleus of the dwarf, now displaced. The star-forming regions B and C show younger and distinctly more metal-rich components. The emission line ratios of regions B and C indicate an almost solar oxygen abundance, if compared with radiation models of HII regions. NGC7796-DW1 occupies a particular role in the group of transition-type galaxies with respect to its origin and current evolutionary state, being the companion of an IE. The dwarf-dwarf merger scenario is excluded because of the missing metal-rich merger component. A viable alternative is gas accretion from a reservoir of cold, metal-rich gas. NGC7796 has to provide this gas within its X-ray bright halo. As illustrated by NGC7796-DW1, cold accretion may be a general solution to the problem of extended star formation histories in transition dwarf galaxies. (abridged)Comment: comments: 13 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

Polydispersity Effects in the Dynamics and Stability of Bubbling Flows

The occurrence of swarms of small bubbles in a variety of industrial systems enhances their performance. However, the effects that size polydispersity may produce on the stability of kinematic waves, the gain factor, mean bubble velocity, kinematic and dynamic wave velocities is, to our knowledge, not yet well established. We found that size polydispersity enhances the stability of a bubble column by a factor of about 23% as a function of frequency and for a particular type of bubble column. In this way our model predicts effects that might be verified experimentally but this, however, remain to be assessed. Our results reinforce the point of view advocated in this work in the sense that a description of a bubble column based on the concept of randomness of a bubble cloud and average properties of the fluid motion, may be a useful approach that has not been exploited in engineering systems.Comment: 11 pages, 2 figures, presented at the 3rd NEXT-SigmaPhi International Conference, 13-18 August, 2005, Kolymbari, Cret

Double coherence resonance in neuron models driven by discrete correlated noise

We study the influence of correlations among discrete stochastic excitatory or inhibitory inputs on the response of the FitzHugh-Nagumo neuron model. For any level of correlation the emitted signal exhibits at some finite noise intensity a maximal degree of regularity, i.e., a coherence resonance. Furthermore, for either inhibitory or excitatory correlated stimuli a {\it Double Coherence Resonance} (DCR) is observable. DCR refers to a (absolute) maximum coherence in the output occurring for an optimal combination of noise variance and correlation. All these effects can be explained by taking advantage of the discrete nature of the correlated inputs.Comment: 4 pages, 3 figures in eps, to appear in Physical Review Letter

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results