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.

PROGETTO PER UN ECOMUSEO MULTIMEDIALE NELLA BORGATA PARALOUP

Descrizione del progetto di "ecomuseo multimediale per la Borgata Paraloup" un museo, essenzialmente multimediale, che sarà diffuso sul erritorio circostante, sotto forma di stimoli sensoriali e di segnalazioni, ma saprà anche porsi in connessione con luoghi più distanti e significativi, nell’idea di costituire Paraloup quale ganglio di una rete di memoria più ampia e sald

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

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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Yardstick Competition in German Municipalities

Does increasing transparency improve fiscal policy behavior of local governments? One way this could take place is via Yardstick Competition between incumbents of neighboring municipalities. This paper contributes to the literature by introducing a simple model which employs probabilistic voting to show the effect of Yardstick Competition on the amount of political rents diverted from the tax revenue. Since additional rents lower the probability of being reelected, the incumbent will reduce equilibrium rents if voters use information on fiscal performance in similar municipalities to evaluate the incumbent's quality. I test this hypothesis on a panel dataset of municipal budget and electoral data in the german state of Northrine-Westphalia. I show evidence for Yardstick Competition in the local business and property tax rates.Kann zunehmende Transparenz im kommunalen Budgetprozess die fiskalpolitische Disziplin der politischen Entscheidungsträger verbessern? In dieser Arbeit wird ein positiver Modellrahmen entwickelt, anhand dessen die Wirkungsweise von steigen - der Transparenz auf das Entscheidungsverhalten von Kommunalpolitikern durch den Yardstick Competition Effekt dargestellt werden kann. Politiker reduzieren die Veruntreuung finanzieller Mittel, wenn ihr Verhalten von den Wählern relativ zur Leistung von Politikern in benachbarten Kommunen bewertet wird. Unter Anwendung von Methoden der räumlichen Ökonometrie auf kommunale Haushalts- und Wahldaten der Jahre 1989 bis 2004 wird gezeigt, dass die räumliche Korrelation in den Gewerbe- und Grundsteuerhebesätzen in Nordrhein-Westfalen auf die Existenz von Yardstick Competition zurückzuführen ist