Aspects of stochastic resonance in reaction-diffusion systems: The nonequilibrium-potential approach

We analyze several aspects of the phenomenon of stochastic resonance in reaction-diffusion systems, exploiting the nonequilibrium potential's framework. The generalization of this formalism (sketched in the appendix) to extended systems is first carried out in the context of a simplified scalar model, for which stationary patterns can be found analytically. We first show how system-size stochastic resonance arises naturally in this framework, and then how the phenomenon of array-enhanced stochastic resonance can be further enhanced by letting the diffusion coefficient depend on the field. A yet less trivial generalization is exemplified by a stylized version of the FitzHugh-Nagumo system, a paradigm of the activator-inhibitor class. After discussing for this system the second aspect enumerated above, we derive from it -through an adiabatic-like elimination of the inhibitor field- an effective scalar model that includes a nonlocal contribution. Studying the role played by the range of the nonlocal kernel and its effect on stochastic resonance, we find an optimal range that maximizes the system's response.Comment: 16 pages, 15 figures, uses svjour.cls and svepj-spec.clo. Minireview to appear in The European Physical Journal Special Topics (issue in memory of Carlos P\'erez-Garc\'{\i}a, edited by H. Mancini

Critical exponents for the long-range Ising chain using a transfer matrix approach

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance $r^\alpha$, $1<\alpha<2$, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and the number of interaction constants can be independently increased. Systems with interactions between spins up to 18 sites apart and up to 2500 spins in the chain are considered. We obtain data for the critical exponents $\nu$ associated with the correlation length based on the Finite Range Scaling (FRS) hypothesis. FRS expressions require the evaluation of derivatives of the thermodynamical properties, which are obtained with the help of analytical recurrence expressions obtained within the TM framework. The Van den Broeck extrapolation procedure is applied in order to estimate the convergence of the exponents. The TM procedure reduces the dimension of the matrices and circumvents several numerical matrix operations.Comment: 10 pages, 2 figures, Conference NEXT Sigma Ph

Noise-induced phase transitions: Effects of the noises' statistics and spectrum

The local, uncorrelated multiplicative noises driving a second-order, purely noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The potential scientific and technological interest of this phenomenon calls for a study of the effects of the noises' statistics and spectrum. This task is facilitated if these noises are dynamically generated by means of stochastic differential equations (SDE) driven by white noises. One such case is that of Ornstein--Uhlenbeck noises which are stationary, with Gaussian pdf and a variance reduced by the self-correlation time (\tau), and whose effect on the NIPT phase diagram has been studied some time ago. Another such case is when the stationary pdf is a (colored) Tsallis' (q)--\emph{Gaussian} which, being a \emph{fat-tail} distribution for (q>1) and a \emph{compact-support} one for (q<1), allows for a controlled exploration of the effects of the departure from Gaussian statistics. As done before with stochastic resonance and other phenomena, we now exploit this tool to study--within a simple mean-field approximation and with an emphasis on the \emph{order parameter} and the ``\emph{susceptibility}''--the combined effect on NIPT of the noises' statistics and spectrum. Even for relatively small (\tau), it is shown that whereas fat-tail noise distributions ((q>1)) counteract the effect of self-correlation, compact-support ones ((q<1)) enhance it. Also, an interesting effect on the susceptibility is seen in the last case.Comment: 6 pages, 10 figures, uses aipproc.cls, aip-8s.clo and aipxfm.sty. To appear in AIP Conference Proceedings. Invited talk at MEDYFINOL'06 (XV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics

Bulk shape of brane-world black holes

We propose a method to extend into the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parameterized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat ``pancake'' for astrophysical sources.Comment: 10 pages, MPLA style, 5 figures, accepted for publication in MPL

The K-selected Butcher-Oemler Effect

[abridged] We investigate the Butcher-Oemler effect in a sample of K-selected galaxies in 33 clusters at 0.15 < z < 0.92. We attempt to duplicate the original Butcher-Oemler analysis as closely as possible given the characteristics of our data. We find that the infrared selected blue fractions are lower than those measured in the optical and that the trend with redshift is much weaker. Comparison with optical data in clusters in common with Butcher & Oemler (1984) shows that infrared selection is the primary difference between our study and optically selected samples. We suggest that the Butcher-Oemler effect is in large part due to a population of star-forming low mass galaxies which will evolve into dwarf galaxies. These early results point to the need for larger and deeper infrared samples of cluster galaxies to address this issueComment: 37 pages, 19 figures, ApJ accepted (vol 598 n1

Invited review: KPZ. Recent developments via a variational formulation

Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits. Such expansion becomes naturally truncated at third order, giving rise to a nonlinear stochastic partial differential equation to be regarded as a gradient-flow counterpart to the KPZ equation. A dynamic renormalization group analysis at one-loop order of this new mesoscopic model yields the KPZ scaling relation alpha+z=2, as a consequence of the exact cancelation of the different contributions to vertex renormalization. This result is quite remarkable, considering the lower degree of symmetry of this equation, which is in particular not Galilean invariant. In addition, this scheme is exploited to inquire about the dynamical behavior of the KPZ equation through a path-integral approach. Each of these aspects offers novel points of view and sheds light on particular aspects of the dynamics of the KPZ equation.Comment: 16 pages, 2 figure

Echocardiography combined with cardiopulmonary exercise testing for the prediction of outcome in idiopathic pulmonary arterial hypertension

BACKGROUND: Right ventricular (RV) function is a major determinant of exercise intolerance and outcome in idiopathic pulmonary arterial hypertension (IPAH). The aim of the study was to evaluate the incremental prognostic value of echocardiography of the RV and cardiopulmonary exercise testing (CPET) on long-term prognosis in these patients. METHODS: One hundred-thirty treatment-naïve IPAH patients were enrolled and prospectively followed. Clinical worsening (CW) was defined by a reduction in 6-minute walk distance plus an increase in functional class, or non elective hospitalization for PAH, or death. Baseline evaluation included clinical, hemodynamic, echocardiographic and CPET variables. Cox regression modeling with c-statistic and bootstrapping validation methods were done. RESULTS: During a mean period of 528 ± 304 days, 54 patients experienced CW (53%). Among demographic, clinical and hemodynamic variables at catheterization, functional class and cardiac index were independent predictors of CW (Model-1). With addition of echocardiographic and CPET variables (Model-2), peak O2 pulse (peak VO2/heart rate) and RV fractional area change (RVFAC) independently improved the power of the prognostic model (AUC: 0.81 vs 0.66, respectively; p=0.005). Patients with low RVFAC and low O2 pulse (low RVFAC + low O2 pulse) and high RVFAC+low O2 pulse showed 99.8 and 29.4 increase in the hazard ratio, respectively (relative risk -RR- of 41.1 and 25.3, respectively), compared with high RVFAC+high O2 pulse (p=0.0001). CONCLUSIONS: Echocardiography combined with CPET provides relevant clinical and prognostic information. A combination of low RVFAC and low O2 pulse identifies patients at a particularly high risk of clinical deterioration

Strong Correlations in Actinide Redox Reactions

Reduction-oxidation (redox) reactions of the redox couples An(VI)/An(V), An(V)/An(IV), and An(IV)/An(III), where An is an element in the family of early actinides (U, Np, and Pu), as well as Am(VI)/Am(V) and Am(V)/Am(III), are modeled by combining density functional theory with a generalized Anderson impurity model that accounts for the strong correlations between the 5f electrons. Diagonalization of the Anderson impurity model yields improved estimates for the redox potentials and the propensity of the actinide complexes to disproportionate.Comment: 17 pages, 10 figure, 3 tables. Corrections and clarifications; this version has been accepted for publication in The Journal of Chemical Physic