Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata

We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of Toom. They are defined as stochastic perturbations of cellular automata belonging to the category of monotonic binary tessellations and possessing a property of erosion. We prove, for a set of initial conditions, exponential convergence of the induced processes toward an extremal invariant measure with a highly predominant spin value. We also show that this invariant measure presents exponential decay of correlations in space and in time and is therefore strongly mixing.Comment: 21 pages, 0 figure, revised version including a generalization to a larger class of models, structure of the arguments unchanged, minor changes suggested by reviewers, added reference

Influence of transport and ocean ice extent on biogenic aerosol sulfur in the Arctic atmosphere

The recent decline in sea ice cover in the Arctic Ocean could affect the regional radiative forcing via changes in sea ice-atmosphere exchange of dimethyl sulfide (DMS) and biogenic aerosols formed from its atmospheric oxidation, such as methanesulfonic acid (MSA). This study examines relationships between changes in total sea ice extent north of 70 degrees N and atmospheric MSA measurement at Alert, Nunavut, during 1980-2009; at Barrow, Alaska, during 1997-2008; and at Ny-Alesund, Svalbard, for 1991-2004. During the 1980-1989 and 1990-1997 periods, summer (July-August) and June MSA concentrations at Alert decreased. In general, MSA concentrations increased at all locations since 2000 with respect to 1990 values, specifically during June and summer at Alert and in summer at Barrow and Ny-Alesund. Our results show variability in MSA at all sites is related to changes in the source strengths of DMS, possibly linked to changes in sea ice extent as well as to changes in atmospheric transport patterns. Since 2000, a late spring increase in atmospheric MSA at the three sites coincides with the northward migration of the marginal ice edge zone where high DMS emissions from ocean to atmosphere have previously been reported. Significant negative correlations are found between sea ice extent and MSA concentrations at the three sites during the spring and June. These results suggest that a decrease in seasonal ice cover influencing other mechanisms of DMS production could lead to higher atmospheric MSA concentrations

Stochastic theory of non-equilibrium wetting

We study a Langevin equation describing non-equilibrium depinning and wetting transitions. Attention is focused on short-ranged attractive substrate-interface potentials. We confirm the existence of first order depinning transitions, in the temperature-chemical potential diagram, and a tricritical point beyond which the transition becomes a non-equilibrium complete wetting transition. The coexistence of pinned and depinned interfaces occurs over a finite area, in line with other non-equilibrium systems that exhibit first order transitions. In addition, we find two types of phase coexistence, one of which is characterized by spatio-temporal intermittency (STI). A finite size analysis of the depinning time is used to characterize the different coexisting regimes. Finally, a stationary distribution of characteristic triangles or facets was shown to be responsible for the structure of the STI phase.Comment: To appear in Europhys. Lett. // 3 figure

First order phase transition in a 1+1-dimensional nonequilibrium wetting process

A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics which generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the non-wet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters which define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the transition line.Comment: 4 pages, RevTeX, including 4 eps figure

The effect of organic compounds on the growth rate of cloud droplets in marine and forest settings

International audienceOrganic matter represents an important fraction of the fine particle aerosol, yet our knowledge of the roles of organics in the activation of aerosol particles into cloud droplets is poor. A cloud condensation nucleus (CCN) counter is used to examine the relative growth rates of cloud droplets for case studies from field measurements on the North Pacific Ocean and in a coniferous forest. A model of the condensational growth of water droplets, on particles dissolving according to their solubility in water, is used to simulate the initial scattering of the droplets as they grow in the CCN counter. Simulations of the growth rates of fine particles sampled in the marine boundary layer of the North Pacific Ocean indicate that the main influence of the marine organic material on the water uptake rate is from its effect on the size distribution of the sulphate. Simulations of the observations of water uptake on biogenic organic aerosol particles sampled in a coniferous forest indicate an impact of the organic on the water uptake rates, but one that is still smaller than that of pure sulphate. The solubility of the organic becomes an important factor in determining the water uptake as the organic mass increases relative to sulphate. The values of the organic component of the hygroscopicity parameter ? that describes the CCN activity were found to be negligible for the marine particles and 0.02?0.05 for the forest particles

Generic two-phase coexistence in nonequilibrium systems

Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperature-magnetic-field phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite (n-dimensional) region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model [Toom,Geoff,GG], that exhibits generic bistability, i.e. two-phase coexistence over a finite region of its two-dimensional parameter space (see Section 1). In addition to its interest as a genuine nonequilibrium property, generic multistability, defined as a generalization of bistability, is both of practical and theoretical relevance. In particular, it has been used recently to argue that some complex structures appearing in nature could be truly stable rather than metastable (with important applications in theoretical biology), and as the theoretical basis for an error-correction method in computer science (see [GG,Gacs] for an illuminating and pedagogical discussion of these ideas).Comment: 7 pages, 6 figures, to appear in Eur. Phys. J. B, svjour.cls and svepj.clo neede

Multicomponent dynamical systems: SRB measures and phase transitions

We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various definitions of SRB measures are considered as well.Comment: 13 pages, LaTeX 2

Characterization of the Humoral Immune Response during Staphylococcus aureus Bacteremia and Global Gene Expression by Staphylococcus aureus in Human Blood

Attempts to develop an efficient anti-staphylococcal vaccine in humans have so far been unsuccessful. Therefore, more knowledge of the antigens that are expressed by Staphylococcus aureus in human blood and induce an immune response in patients is required. In this study we further characterize the serial levels of IgG and IgA antibodies against 56 staphylococcal antigens in multiple serum samples of 21 patients with a S. aureus bacteremia, compare peak IgG levels between patients and 30 non-infected controls, and analyze the expression of 3626 genes by two genetically distinct isolates in human blood. The serum antibody levels were measured using a bead-based flow cytometry technique (xMAP®, Luminex corporation). Gene expression levels were analyzed using a microarray (BμG@s microarray). The initial levels and time taken to reach peak IgG and IgA antibody levels were heterogeneous in bacteremia patients. The antigen SA0688 was associated with the highest median initial-to-peak antibody fold-increase for IgG (5.05-fold) and the second highest increase for IgA (2.07-fold). Peak IgG levels against 27 antigens, including the antigen SA0688, were significantly elevated in bacteremia patients versus controls (P≤0.05). Expression of diverse genes, including SA0688, was ubiquitously high in both isolates at all time points during incubation in blood. However, only a limited number of genes were specifically up- or downregulated in both isolates when cultured in blood, compared to the start of incubation in blood or during incubation in BHI broth. In conclusion, most staphylococcal antigens tested in this study, including many known virulence factors, do not induce uniform increases in the antibody levels in bacteremia patients. In addition, the expression of these antigens by S. aureus is not significantly altered by incubation in human blood over time. One immunogenic and ubiquitously expressed antigen is the putative iron-regulated ABC transporter SA0688

Novel non-equilibrium critical behavior in unidirectionally coupled stochastic processes

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A -> A + A, A + A -> A, and A -> \emptyset. We study a hierarchy of such DP processes for particle species A, B,..., unidirectionally coupled via the reactions A -> B, ... (with rates \mu_{AB}, ...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents \beta_i which are markedly reduced at each hierarchy level i >= 2. This scenario can be understood on the basis of the mean-field rate equations, which yield \beta_i = 1/2^{i-1} at the multicritical point. We then include fluctuations by using field-theoretic renormalization group techniques in d = 4-\epsilon dimensions. In the active phase, we calculate the fluctuation correction to the density exponent for the second hierarchy level, \beta_2 = 1/2 - \epsilon/8 + O(\epsilon^2). Monte Carlo simulations are then employed to determine the values for the new scaling exponents in dimensions d<= 3, including the critical initial slip exponent. Our theory is connected to certain classes of growth processes and to certain cellular automata, as well as to unidirectionally coupled pair annihilation processes. We also discuss some technical and conceptual problems of the loop expansion and their possible interpretation.Comment: 29 pages, 19 figures, revtex, 2 columns, revised Jan 1995: minor changes and additions; accepted for publication in Phys. Rev.

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.