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

Transport–diffusion models with nonlinear boundary conditions and solution by generalized collocation methods

AbstractThis paper deals with the derivation of a class of nonlinear transport and diffusion models implemented with nonlinear boundary conditions. Mathematical tools to treat the initial-boundary value problems are developed, based on generalized collocation methods, focused on the treatment of nonlinear boundary conditions in one space dimension. Applications refer to a problem of interest in applied sciences

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

Rainwater harvesting for home-garden irrigation: a case study in Italy

In residential buildings, drinking water is often used for tasks that do not necessarily require high quality water, such as home-garden irrigation. Our research focuses on the idea of harvesting rainwater to promote sustainable management of low-quality water resources on a building scale for irrigation purposes. The effectiveness of a collection system depends on the weather conditions, which determine also the water need of the plants, on the size of the cultivated area and on the collection surfaces. In this research, a rainwater harvesting system (RWH) for the irrigation of home-gardens in the city of Celano (L'Aquila - Italy) has been analysed. The obtained results show that to maximize water savings a great investment is necessary, i.e. not refundable in a reasonable period due to the low cost of drinking water. On the contrary, to maximize the economic return, it is required a smaller and cheaper tank, but the maximum water savings efficiency decrease to about 60%. In the latter case the RWH system can be cheaper than an irrigation plant supplied by the aqueduct. In the work graphs are provided for practical design use for realizing a RWH system in areas with meteorological conditions similar to those of the survey area, according both the highest water savings efficiency or the highest economic return

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

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.

Additional ecological services of CSO-CW besides water treatment: modelling CSO-CW behaviour for urban runoff management

INTRODUCTION Combined sewer overflows (CSOs) have been recognized as a dangerous pollutant source for receiving water bodies, and CSO treatment is hence very important to promote a sustainable development. Constructed wetlands (CWs) are starting to be considered as a viable and eco-sustainable technology to treat CSOs (Meyer et al., 2013). However, CSO-CW provides other ecological services beside to water treatment: (i) urban runoff management, (ii) biodiversity increase, (iii) social services (e.g., recreation). Here we have developed a mathematical model of a real case study to highlight the functioning of CSO-CW as also a flood mitigation system, which promotes an urban runoff management from a post-development (high peak, short duration) back again to a pre-development (low peak, high duration) hydrograph influent to the river (Fletcher et al., 2013). METHODS The experimental case study is located in Gorla Maggiore, Italy (46°N, 9°E). The CSO-CW is composed of: (i) grid and sedimentation tank as first flush primary treatment; (ii) four French-type vertical subsurface flow (VF) CW beds as secondary stage (3840 m2) designed to treat the first flush (up to 640 l s-1); (iii) a free water surface flow (FWS) wetland with multiple roles of tertiary treatment of first flush and also second flush treatment (3174 m2), biodiversity increasing, recreational area, and hydraulic buffer (with a floodable surface area up to 7200 m2). The theoretical hydraulic retention time (HRT) is equal to 36 h. A sampling campaign has been done in 2014 in order to characterise temporal variations of CSO quality and quantity and to assess CW removal performances. The data about water quantity (CSO flow rates continuously registered by an automatic sensor with a sampling frequency of 15 minutes) are here used as input of the mathematical model. The mathematical model simulates the unsaturated water flow in VF beds (Richards equation) and the depth of the ponding layer above the VF surface and in the FWS (mass balance equations). In this way, water outflows from each stage of the CW plant are estimated, and the flood mitigation efficiency of the CW is evaluated for different type of CSO events (i.e., single or multiple average CSO events, high return time CSO event). RESULTS AND DISCUSSION The model results show the good performance of the CSO-CW as flood mitigation system. The single CSO average event (883 m3 over 2.4 hours, with a maximum flow rate of 250 l/s) is satisfactorily laminated: (i) the peak flow is reduced by 95%; (ii) the outflow duration is 21 times longer than the one of the CSO event; (iii) the CW is able to store 95% of the influent volume during the CSO event.The CSO-CW exhibits also performs well for CSO mitigation when a sequence of consecutive CSO average events (up to 5, i.e. the maximum number of consecutive CSO events registered) is considered as shown in Figure 1. In this case, the peak flow is reduced by 53%, the outflow is prolonged 5.7 times compared to the CSO event duration, and 38% of the influent volume is stored during the CSO event. Flood mitigation performances remain high also for events with high return time (equal to 10 years – maximum flow rate: 3.4 m3 s−1, volume: 11497 m3, duration: 4.8 h), for which the FWS behaves as a buffer system storing 71% of the influent volume, in addition to the lower (11%) but not negligible mitigation effect provided by the VF beds. Moreover, the peak flow (86% reduction) and the outflow duration (27 times longer than the CSO event duration) are satisfactorily improved for such 10 year return time events. Fig. 1. Influent and simulated effluent flow rate from CSO-CW treatment for a sequence of 5 consecutive CSO mean events: influent CSO (gray line), VF outflow (dotted line), VF overflow (dashed line), and FWS outflow (continuous line). CONCLUSIONS The results of this modelling study confirm the potential of CWs to behave as flood mitigation systems providing the additional ecological service of sustainable urban runoff management. The selected case study demonstrates how CSO-CW promotes a shift from a post-development (high peak, short duration) to a pre-development (low peak, high duration) hydrograph influent to the river water body

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)

The impacts of increasing current velocity on the drift of Simulium monticola (Diptera: Simuliidae): a laboratory approach

Current velocity and associated physical forces are among the most important factors shaping lotic benthic communities. The recent increase in the frequency and intensity of flow alterations, especially related to hydroelectric use or irrigation, represents a key element of riverine environment deterioration. Numerous studies have investigated the effect of current velocity increases on macrobenthic fauna, underlining that, in most cases, these increases enhance the drift, i.e. the abandonment of the substrate by macroinvertebrates. The purpose of this study is to examine the drift propensity of Simulium monticola (Diptera: Simuliidae) under different water velocities. Simuliidae are one of the most characteristic components of fast-flowing environments in rivers. Experiments were conducted in an artificial stream in the laboratories of Politecnico di Torino, analysing the drift of organisms at different current velocities. The observed variability of drift appears to be related to velocity increases: interestingly, we evidenced an inverse relationship between velocity and drift propensity, with low amounts of drifting organisms at higher velocities. This tendency was not related to the size of Simuliidae larvae: when comparing the size of drifting organisms with velocity, no significant correlations were detected. We hypothesized that the tendency to drift was mainly behavioural rather than catastrophic, and related to the preference for high water velocities. Our findings support the hypothesis that increases in water velocity can cause complex changes in the drift of the macrobenthic community, increasing the propensity for some species to leave the substrate and decreasing it for other