Iacopo Borsi

BIOMASS GROWTH IN UNSATURATED POROUS MEDIA: HYDRAULIC PROPERTIES CHANGES

We present a model to describe the biomass growth process taking place in an unsaturated porous medium during a bioremediation process. We focus on the so-called column experiment. At the initial time biomass and polluted water is inoculated in the column. The subsequent changes of hydraulic properties are analyzed. We also show some preliminary simulations.

Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media

In this paper we consider the PDE describing the fluid flow in a porous medium, focusing on the solution’s dependence upon the choice of the saturation curve and the hydraulic conductivity. Basically, we consider two different saturation curves (say θ1 and θ2) and two different hydraulic conductivities (K1 and K2) which are both “close” in the Lloc-norm. Then we find estimates to prove a constitutive stability for the solutions of the corresponding problems with the same boundary and initial conditions.

FREEWAT: FREE and open source software tools for WATer resource management

FREEWAT is an HORIZON 2020 project financed by the EU Commission under the call WATER INNOVATION: BOOSTING ITS VALUE FOR EUROPE. FREEWAT main result will be an open source and public domain GIS integrated modelling environment for the simulation of water quantity and quality in surface water and groundwater with an integrated water management and planning module. FREEWAT aims at promoting water resource management by simplifying the application of the Water Framework Directive and other EU water related Directives. Specific objectives of the FREEWAT project are: to coordinate previous EU and national funded research to integrate existing software modules for water management in a single environment into the GIS based FREEWAT; to support the FREEWAT application in an innovative participatory approach gathering technical staff and relevant stakeholders (in primis policy and decision makers) in designing scenarios for the proper application of water policies.The open source characteristics of the platform allow to consider this an initiative ad includendum (looking for inclusion of other entities), as further research institutions, private developers etc. may contribute to the platform development.Through creating a common environment among water research/professionals, policy makers and implementers, FREEWAT main impact will be on enhancing science- and participatory approach and evidence-based decision making in water resource management, hence producing relevant and appropriate outcomes for policy implementation. The Consortium is constituted by partners from various water sectors from 10 EU countries, plus Turkey and Ukraine. Synergies with the UNESCO HOPE initiative on free and open source software in water management greatly boost the value of the project. Large stakeholders involvement is thought to guarantee results dissemination and exploitation.

A non-local model for cancer stem cells and the tumour growth paradox

The tumour growth paradox refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSCs) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumour selects for CSC, thereby increasing the fitness of the tumour. In this paper, we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumour growth and tumour spread. Such a model has never been analysed, and we prove results on local and global existence of solutions, their uniqueness and their boundedness. We show numerically that this model exhibits the tumour growth paradox for all parameters tested. This effect becomes more relevant for small renewal rate of the CSC.

Software tools for sustainable water resources management: the GIS-integrated FREEWAT platform

This paper aims at presenting the open source and public domain FREEWAT platform capabilities for water resource management, including: (i) pre-processing modules to facilitate the preparation of input data, (ii) modelling tools for the analysis of several processes aimed at supporting water resource management, and (iii) post-processing tools to present results.The FREEWAT platform is based on open source solutions to perform an integrated coupling between the QGIS desktop software, surface and subsurface model engines, mostly based on fully distributed and numerically-based codes developed by the USGS, and other software applications, and the SpatiaLite spatial database. The development of the FREEWAT platform was supported by the main needs and priorities expressed by relevant stakeholders from the water sector involved in the early stage of the project.Extensive testing on the platform is still going on and training material and six User Manuals were prepared to disseminate its use as a standard software for managing surface/sub-surface water quantity and quality dynamics under demand-driven and supply-constrained conditions. The testing phase also includes demonstration of the platform capabilities on 14 case studies at European scale and beyond, to address specific water management issues. Nine of them are devoted to the application of EU water-related Directives, while the others address water management issues in the rural environment under the requirements of EU and/or national/local regulations. Beyond software testing, this demonstration is thought as an experiment on involving stakeholders in the formation of water plans yet during the technical phase of the analysis.

FREEWAT, a Free and Open Source, GIS-Integrated, Hydrological Modeling Platform: L. Foglia et al. Groundwater XX, no. X: XX-XX

Author(s): Foglia, Laura; Borsi, Iacopo; Mehl, Steffen; De Filippis, Giovanna; Cannata, Massimiliano; Vasquez-SuA±e, Enric; Criollo, Rotman; Rossetto, Rudy

Modeling blood filtration in hollow fibers dialyzers coupled with patient’s body dynamics

— We develop a mathematical model for cross filtration in a hollow fibers dialyzer, taking into account not only the phenomena occurring within the machine, but also the redistribution of chemicals between intraand extracellular compartments in the patient’s body. The scheme for the cross flow is derived with reference to a single fiber, starting from the basic laws of fluid dynamics and exploiting the smallness of the ratio between the fiber radius and the fiber length to obtain significant simplifications. We end up with a system of integral and partial di¤erential equations in which the input data are in principle unknown. Indeed, the blood composition is considerably altered while going through the fiber and the body reacts redistributing urea, sodium ions, etc. between intraand extracellular compartments with its own dynamics, thus updating the various concentrations at the dialyzer inlet. Such a coupling is an essential feature of the model. We present numerical simulations, showing a reasonable agreement with the data for a specific patient taken from the literature.

L’impianto di ricarica riverbank filtration di S. Alessio (Lucca): attività di monitoraggio e modellistica nel progetto EU FP7 MARSOL@@@The riverbank filtration plant in S. Alessio (Lucca): monitoring and modeling activity within EU the FP7 MARSOL project

The riverbank filtration (RBF) scheme along the Serchio River, Lucca (Tuscany – Italy) allows abstraction of an overall amount of about 1 m3/s groundwater providing drinking water for about 300000 people of the coastal Tuscany (town of Lucca, Pisa and Livorno). Water is derived by means of an RBF scheme by a set of ten vertical wells inducing riverbank filtration into a high yield (10-2 m2/s transmissivity) sand and gravel aquifer including a downstream weir to raise river head and increasing water storage in the aquifer along the river reach. Within the framework of the MARSOL FPVII-ENV-2013 project, the Sant’Alessio well field will be used to demonstrate the sustainability, by a technical, social and market point of view, and the benefits of RBF managing versus the unmanaged option. The Serchio experimental site will involve merging existing and proved technologies, including continuous monitoring of several parameters and analytes and the development of dedicated software tools, to produce a Decision Support System (DSS) based on remote data acquisition and transmission and GIS physically-based fully distributed numerical modeling to continuously monitor and manage the well field, reducing also, prone to error, human operated activities. A set of sensors will be installed to monitor by a quantitative and qualitative point of view hydrologic variables in the river water, in the aquifer, the unsaturated zone and the wells. Data will be continuously acquired and remotely transmitted to a server where they will first be checked for consistency and then sent to a database for processing in a dedicated modelling environment included in the DSS and equipped with an alert system to inform water managers about the scheme performance and reaching limits of infiltration rates or water quality indices. The DSS along with the installed sensors, data transmission and storage tools will constitute a prototype whose potential market exploitation will be tested.

Social-economical mobility and redistribution policy

We present and discuss an integro-differential equation that models economic dynamics in a closed population. An “economic inequality index” is introduced and some examples are provided showing how changes in social mobility can produce increasing (or decreasing) social equity.

Glow discharge in low pressure plasma PVD: mathematical model and numerical simulations

In this paper we analyze the problem of glow discharge in low pressure plasma in industrial plant, for chambers of different shapes and various working parameters, like pressure and electric potential. The model described is based upon a static approximation of the AC configuration with two electrodes and a drift diffusion approximation for the current density of positive ions and electrons. A detailed discussion of the boundary conditions imposed is given, as well as the full description of the mathematical model.Numerical simulations were performed for a simple 1D model and two different 2D models, corresponding to two different settings of the industrial plant. The simpler case consists of a radially symmetric chamber, with one central electrode (cathode), based upon a DC generator. In this case, the steel chamber acts as the anode. The second model concerns a two dimensional horizontal cut of the most common plant configuration, with two electrodes connected to an AC generator. The case is treated in a “quasi-static” approximation. The three models show some common behaviours, particularly including the main expected features, such as dark spaces, glow regions and a wide “plasma region”. Furthermore, the three shown models show some similarities with previously published results concerning 1D and simplified 2D models, as well as with some preliminary results of the full 3D case.