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

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

Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation

In order to perform numerical simulations of the KPZ equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf--Cole transformation applied to a diffusion equation (with \emph{multiplicative} noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen. On the other hand, since the discretization is an operation performed on \emph{space} and the Hopf--Cole transformation is \emph{local} both in space and time, the former should be the same regardless of the field to which it is applied. It is shown that whereas some discretization schemes pass both consistency tests, known examples in the literature do not. The requirement of consistency for the discretization of Lyapunov functionals is argued to be a natural and safe starting point in choosing spatial discretization schemes. We also analyze the relation between real-space and pseudo-spectral discrete representations. In addition we discuss the relevance of the Galilean invariance violation in these consistent discretization schemes, and the alleged conflict of standard discretization with the fluctuation--dissipation theorem, peculiar of 1D.Comment: RevTex, 23pgs, 2 figures, submitted to Phys. Rev.

Modelling investigation of HF CW response to sudden and sustained organic and hydraulic overloads

INTRODUCTION Constructed wetlands (CWs) are typically designed assuming idealized steady-state influent loads. However, CWs might face sporadic periods of overloading during their lifespan, due to an increase either in the volume of wastewater to treat or in the pollutant concentrations in wastewater (or both). Although this technology is well known for its buffering capacity, the mechanisms behind it are not well understood. In this study we aim to improve the understanding of the internal processes that make horizontal flow constructed wetlands (HF CWs) able to cope with sudden contaminant and/or hydraulic overloads, and also to investigate if and how sustained overloading affects the long-term performance of these systems. METHODS In this study, we employ the BIO_PORE model (Samsó and García, 2013a), which simulates the hydraulics (Darcian flow), biochemistry (CWM1 biokinetic model, Langergraber et al., 2009), plant effects (nutrient uptake and oxygen release) and the interactions between bacteria and accumulated solids in HF CWs. The effect of organic overloads is studied using the same HF CW configuration and influent pollutant loads as those considered by Samsó and García (2013b) (10.3 m long and 5.3 m wide CW – COD and TN effluent concentrations validated by Samsó and García (2013a)). The final state of the simulation carried out by Samsó and García (2013b), which corresponds to the end of the 3rd year of operation of the wetland, is used as initial condition of the simulations developed in this work, which are one year long and reproduce the functioning of the HF CW subject to overloads. These overloads are simulated by increasing inflow COD concentrations, hydraulic loads, or both at the same time. For the increases in organic loads, three overloading scenarios are tested: +10%, +30% and +50% of influent COD concentration while keeping influent N-NH4 concentrations constant. Additionally, the effect of the HRT is tested by comparing simulations with +30% increase in the organic load, +30% increase in the hydraulic load, and combined +15% increase in both hydraulic and organic loads. RESULTS AND DISCUSSION Both the increase in influent COD concentration and different HRT promote a change in bacterial community distribution, which exhibits the same zonation shown by Samsó and García (2013b), but with differences in the relative amount of biomass of each bacterial group with respect to the total biomass. Comparison of simulations with similar total biomass reveals how variations in COD removal efficiency for different hydraulic and organic loads are controlled by changes in HRTs and influent concentrations, respectively.Increasing influent COD concentrations stimulates bacterial growth, with total biomass (TB) that tends be more abundant and to occupy more CW space towards the CW outlet (Figure 1, top). Moreover, the portion of TB near the inlet shifts towards the outlet as well due to the higher inert material that is accumulated near the inlet (Figure 1, bottom). HF CW shows a good buffer capacity for organic overloads, with COD removal efficiencies even higher at the end of the simulated year compared to the beginning of the simulation (not shown). However, the response time is long due to the low growth rate of anaerobic bacteria. This results in a long transition phase (almost six months) in which COD removal efficiency is lower (from 91.3% at normal loadings to 80% for +50% organic overloading) (not shown). Additionally, feeding HF CW with higher organic loads reduces their lifespan due to higher accumulation of inert material (Figure 1). COD removal efficiencies are also influenced by HRT. COD removal efficiency is higher in the first four months when only hydraulic loads are increased, while higher concentrations promote a higher removal efficiency in the last 8 months of the simulation. Fig. 1. Spatial distribution of total microbial biomass (upper panels) and accumulated solids (lower panels) at the 360th day of simulation (end of the fourth year of HF-CW functioning) for different organic overloads. Values are expressed in kg m−3. CONCLUSIONS HF CWs guarantee a good but slow buffering capacity of COD removal in response to organic overloads. This buffering capacity is achieved through changes on the total biomass and on the relative concentration of the different bacterial groups within the granular media. Moreover, we demonstrate that organic and/or hydraulic overloads reduce HF CW’s lifespan

Construction of an evidence-based integrated morphology cleavage embryo score for implantation potential of embryos scored and transferred on day 2 after oocyte retrieval

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Economic evaluation of Medically Assisted Reproduction: An educational overview of methods and applications for healthcare professionals

Economic evaluations of the value-for-money of Medically Assisted Reproduction (MAR) interventions are increasingly important due to growing pressure on healthcare budgets. Although such evaluations are commonplace in the published literature, the number/methodological complexity of different evaluations available, and the challenges specific to MAR interventions, can complicate the interpretation of such analyses for fertility treatments. This article aims to serve as an educational resource and provide context on the design/interpretation of economic analyses for MAR interventions. Several areas are relevant for first-line providers and decision makers: scope of analysis, comparator used, perspective/time horizon considered, outcomes used to measure success, and how results from cost-effectiveness studies can be summarised and used in clinical practice. We aim to help clinicians better understand the strengths/weaknesses of economic analyses, to enable the best use of the evidence in practice, so resources available for MAR interventions can provide maximum value to patients and society

Resonant phenomena in extended chaotic systems subject to external noise: the Lorenz'96 model case

We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of "toy" model used for climate studies. Through the analysis of the system's time evolution and its time and space correlations, we have obtained numerical evidence for two stochastic resonance-like behavior. Such behavior is seen when both, the usual and a generalized signal-to-noise ratio function are depicted as a function of the external noise intensity or the system size. The underlying mechanism seems to be associated to a "noise-induced chaos reduction". The possible relevance of these and other findings for an "optimal" climate prediction are discussed.Comment: Submitted to Europhysics Letters (LaTex, 12 pgs, 5 figures

A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Fingerprints of Kitaev physics in the magnetic excitations of honeycomb iridates

In the quest for realizations of quantum spin liquids, the exploration of Kitaev materials - spin-orbit entangled Mott insulators with strong bond-directional exchanges - has taken center stage. However, in these materials the local spin-orbital j=1/2 moments typically show long-range magnetic order at low temperature, thus defying the formation of a spin-liquid ground state. Using resonant inelastic x-ray scattering (RIXS), we here report on a proximate spin liquid regime with clear fingerprints of Kitaev physics in the magnetic excitations of the honeycomb iridates alpha-Li2IrO3 and Na2IrO3. We observe a broad continuum of magnetic excitations that persists up to at least 300K, more than an order of magnitude larger than the magnetic ordering temperatures. We prove the magnetic character of this continuum by an analysis of the resonance behavior. RIXS measurements of the dynamical structure factor for energies within the continuum show that dynamical spin-spin correlations are restricted to nearest neighbors. Notably, these spectroscopic observations are also present in the magnetically ordered state for excitation energies above the conventional magnon excitations. Phenomenologically, our data agree with inelastic neutron scattering results on the related honeycomb compound RuCl3, establishing a common ground for a proximate Kitaev spin-liquid regime in these materials.Comment: 13 pages, 14 figure