Diffusion in Fluctuating Media: The Resonant Activation Problem

We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic deterministic and the other stochastic. We study the dynamics of a system of particles moving in that medium, and characterize the problem from different points of view: mean first passage time (MFPT), probability of return to a given site ($P_{s_0}$), and the total length displacement or number of visited lattice sites ($\Lambda$). We observe a double {\it resonant activation}-like phenomenon when we plot the MFPT and $P_{s_0}$ as functions of the intensity of the transition rate stochastic component.Comment: RevTex, 15 pgs, 8 figures, submitted to Eur.Phys.J.

Bulk Mediated Surface Diffusion: Non Markovian Desorption with Finite First Moment

Here we address a fundamental issue in surface physics: the dynamics of adsorbed molecules. We study this problem when the particle's desorption is characterized by a non Markovian process, while the particle's adsorption and its motion in the bulk are governed by a Markovian dynamics. We study the diffusion of particles in a semi-infinite cubic lattice, and focus on the effective diffusion process at the interface $z = 1$. We calculate analytically the conditional probability to find the particle on the $z=1$ plane as well as the surface dispersion as functions of time. The comparison of these results with Monte Carlo simulations show an excellent agreement.Comment: 16 pages, 7 figs. European Physical Journal B (in press

Bulk Mediated Surface Diffusion: The Infinite System Case

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.Comment: 15 pages, 7 figure

Bulk Mediated Surface Diffusion: Finite System Case

We address the dynamics of adsorbed molecules (a fundamental issue in surface physics) within the framework of a Master Equation scheme, and study the diffusion of particles in a finite cubic lattice whose boundaries are at the $z=1$ and the $z=L$ planes where $L = 2,3,4,...$, while the $x$ and $y$ directions are unbounded. As we are interested in the effective diffusion process at the interface $z = 1$, we calculate analytically the conditional probability for finding the system on the $z=1$ plane as well as the surface dispersion as a function of time and compare these results with Monte Carlo simulations finding an excellent agreement.Comment: 19 pages, 8 figure

Variational Formulation for the KPZ and Related Kinetic Equations

We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. The procedure used for KPZ was extended in order to derive more general forms of such a functional leading to other nonlinear kinetic equations, as well as cases with density dependent surface tension.Comment: RevTex, 8pgs, double colum

The Use of Rank Histograms and MVL Diagrams to Characterize Ensemble Evolution in Weather Forecasting

13 páginas, 9 figuras.-- El pdf del artículo es la versión pre-print.Rank Histograms are suitable tools to assess the quality of ensembles within an ensemble prediction system or framework. By counting the rank of a given variable in the ensemble, we are basically making a sample analysis, which does not allow us to distinguish if the origin of its variability is external noise or comes from chaotic sources. The recently introduced Mean to Variance Logarithmic (MVL) Diagram accounts for the spatial variability, being very sensitive to the spatial localization produced by infinitesimal perturbations of spatiotemporal chaotic systems. By using as a benchmark a simple model subject to noise, we show the distinct information given by Rank Histograms and MVL Diagrams. Hence, the main effects of the external noise can be visualized in a graphic. From the MVL diagram we clearly observe a reduction of the amplitude growth rate and of the spatial localization (chaos suppression), while from the Rank Histogram we observe changes in the reliability of the ensemble. We conclude that in a complex framework including spatiotemporal chaos and noise, both provide a more complete forecasting picture.We acknowledge financial support from MEC, Spain, through Grant No. CGL2007- 64387/CLI, and also thank the AECID, Spain, for support through projects A/013666/07 and A/018685/08. JAR thanks the MEC, Spain, for the award of a Juan de la Cierva fellowship. HSW thanks to the European Commission for the award of a Marie Curie Chair during part of the development of this work.Peer reviewe

Probabilistic cost-effectiveness analysis of controlled ovarian stimulation with recombinant FSH plus recombinant LH vs. human menopausal gonadotropin for women undergoing IVF

Background The association of recombinant FSH plus recombinant LH in 2:1 ratio may be used not only to induce ovulation in anovulatory women with hypogonadotropic hypogonadism but also to achieve multiple follicular developments in human IVF. The aim of this analysis was to estimate the cost-effectiveness of Controlled Ovarian Stimulation (COS) with recombinant FSH (rFSH) plus recombinant LH (rLH) in comparison with highly purified human menopausal gonadotropin (HP-hMG) in the woman undergoing in vitro fertilization (IVF) in Italy. Methods A probabilistic decision tree was developed to simulate patients undergoing IVF, either using r-FSH + r-LH or HP-hMG to obtain COS. The model considers the National Health System (NHS) perspective and a time horizon equal to two years. Simulations were reported considering the number of retrieved oocytes (5–9, 10–15 and > 15) and transition probabilities were estimated through specific analyses carried out on the population of 848 women enrolled in the real-life. Results The model estimated that patients undertaking therapeutic protocol with r-FSH + r-LH increase the general success rate (+ 6.6% for pregnancy). The incremental cost-effectiveness ratio (ICER) per quality-adjusted life year (QALY) of r-FSH + r-LH was below the willingness to pay set at €20,000 for all the considered scenarios. Conclusions The cost-utility analysis demonstrated that the r-FSH + r-LH is a cost-effective option for the Italian National Health System (NHS)