Condensation for a fixed number of independent random variables

A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal density \rho_c<\infty. The distribution of particles conditioned on the total number of particles equal to n does not depend on \phi (canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density \rho_c; the remaining particles concentrate (condensate) on a single site.Comment: 6 page

Phase Transition in the ABC Model

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.Comment: 18 pages, 3 figure

Condensation Transitions in Two Species Zero-Range Process

We study condensation transitions in the steady state of a zero-range process with two species of particles. The steady state is exactly soluble -- it is given by a factorised form provided the dynamics satisfy certain constraints -- and we exploit this to derive the phase diagram for a quite general choice of dynamics. This phase diagram contains a variety of new mechanisms of condensate formation, and a novel phase in which the condensate of one of the particle species is sustained by a `weak' condensate of particles of the other species. We also demonstrate how a single particle of one of the species (which plays the role of a defect particle) can induce Bose-Einstein condensation above a critical density of particles of the other species.Comment: 17 pages, 4 Postscript figure

Extracting predictive models from marked-p free-text documents at the Royal Botanic Gardens, Kew, London

In this paper we explore the combination of text-mining, un-supervised and supervised learning to extract predictive models from a corpus of digitised historical floras. These documents deal with the nomenclature, geographical distribution, ecology and comparative morphology of the species of a region. Here we exploit the fact that portions of text in the floras are marked up as different types of trait and habitat. We infer models from these different texts that can predict different habitat-types based upon the traits of plant species. We also integrate plant taxonomy data in order to assist in the validation of our models. We have shown that by clustering text describing the habitat of different floras we can identify a number of important and distinct habitats that are associated with particular families of species along with statistical significance scores. We have also shown that by using these discovered habitat-types as labels for supervised learning we can predict them based upon a subset of traits, identified using wrapper feature selection

Phase fluctuations in the ABC model

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of $L$ sites, the steady state profiles move on a microscopic time scale of order $L^3$. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations

Phase diagram of a generalized ABC model on the interval

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site $i=1,...,N$ is occupied by a particle of type \a=A,B,C, with the average density of each particle species N_\a/N=r_\a fixed. These particles interact via a mean field non-reflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N\rw\infty, i/N\rw x\in[0,1] has a unique density profile \p_\a(x) except for some special values of the r_\a for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature $T_c=3\sqrt{r_A r_B r_C}/2\pi$.Comment: 25 pages, 6 figure

UV Spectroscopy of Metal-Poor Massive Stars in the Small Magellanic Cloud

The Hubble Space Telescope has provided the first clear evidence for weaker winds of metal-poor massive stars in the Small Magellanic Cloud, confirming theoretical predictions of the metallicity dependence of mass-loss rates and wind terminal velocities. For lower luminosity O-type stars however, derived mass-loss rates are orders of magnitude lower than predicted, and are at present unexplained.Comment: 4 pages, 3 figures. To appear in 'The Impact of HST on European Astronomy', Eds., G. De Marchi & F.D. Macchetto, Astrophysics & Space Science, Springe

Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting from an empty initial lattice, the system enters a symmetry broken state after some time T_1 through an amplification loop of initial fluctuations. It remains in the symmetry broken state for a time T_2 through a traffic jam effect. Applying a simple martingale argument, we obtain rigorous asymptotic estimates for the expected times ~ L ln(L) and ln() ~ L, where L is the system size. The actual value of T_1 depends strongly on the initial fluctuation in the amplification loop. Numerical simulations suggest that T_2 is exponentially distributed with a mean that grows exponentially in system size. For the phase transition line we argue and confirm by simulations that the flipping time between sign changes of the difference of particle numbers approaches an algebraic distribution as the system size tends to infinity.Comment: 23 pages, 7 figure

An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update

Within the formalism of matrix product ansatz, we study a two-species asymmetric exclusion process with backward and forward site-ordered sequential update. This model, which was originally introduced with the random sequential update, describes a two-way traffic flow with a dynamic impurity and shows a phase transition between the free flow and traffic jam. We investigate the characteristics of this jamming and examine similarities and differences between our results and those with random sequential update.Comment: 25 pages, Revtex, 7 ps file