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A data-driven Reduced Order Model (ROM) based on a Proper Orthogonal Decomposition - Radial Basis Function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of Atrial Fibrillation (AF). The Full Order Model (FOM) is represented by incompressible Navier-Stokes equations, discretized with a Finite Volume (FV) approach. Both the Newtonian and the Casson's constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up., Comment: 21 pages, 14 figures

In this paper we propose a multiscale traffic model, based on the family of Generic Second Order Models, which integrates multiple trajectory data into the velocity function. This combination of a second order macroscopic model with microscopic information allows us to reproduce significant variations in speed and acceleration that strongly influence traffic emissions. We obtain accurate approximations even with a few trajectory data. The proposed approach is therefore a computationally efficient and highly accurate tool for calculating macroscopic traffic quantities and estimating emissions.

We consider an optimal flow control problem in a patient-specific coronary artery bypass graft with the aim of matching the blood flow velocity with given measurements as the Reynolds number varies in a physiological range. Blood flow is modelled with the steady incompressible Navier-Stokes equations. The geometry consists in a stenosed left anterior descending artery where a single bypass is performed with the right internal thoracic artery. The control variable is the unknown value of the normal stress at the outlet boundary, which is need for a correct set-up of the outlet boundary condition. For the numerical solution of the parametric optimal flow control problem, we develop a data-driven reduced order method that combines proper orthogonal decomposition (POD) with neural networks. We present numerical results showing that our data-driven approach leads to a substantial speed-up with respect to a more classical POD-Galerkin strategy proposed in [59], while having comparable accuracy.

We study epidemic Susceptible-Infected-Susceptible models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on Caputo derivative, for which we establish existence results of the solutions. Also, we investigate a model based on Caputo-Fabrizio operator, for which we provide existence of solutions and a study of the equilibria. Numerical simulations for both models and a direct numerical comparison are also provided.

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [20], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present a Lax-Friedrichs type discretization scheme recovering the theoretical results by means of numerical tests. We calibrate the multi-class model with real data and compare the fitted model to the real trajectories. Finally, we test the ability of the model to simulate the overtaking of vehicles., Comment: 21 pages, 14 figures

In this paper we consider the fractional SIS epidemic model ($\alpha$-SIS model) in the case of constant population size. We provide a representation of the explicit solution to the fractional model and we illustrate the results by numerical schemes. A comparison with the limit case when the fractional order $\alpha \uparrow 1$ (the SIS model) is also given. We analyse the effects of the fractional derivatives by comparing the SIS and the $\alpha$-SIS models., Comment: 17 pages, 6 figures

In this paper we consider the problem of estimating emissions due to vehicular traffic on complex networks, and minimizing their effect by regulating traffic at junctions. For the traffic evolution, we consider a Generic Second Order Model, which encompasses the majority of two-equations (i.e. second-order) models available in the literature, and extend it to road networks with merge and diverge junctions. The dynamics on the whole network is determined by selecting a solution to the Riemann Problems at junctions, i.e. the Cauchy problems with constant initial data on each incident road. The latter are solved assuming the maximization of the flow and assigning a traffic distribution coefficient for outgoing roads of diverges, and a priority rule for incoming roads of merges. A general emission model is considered and its parameters are tuned to the NOx emission rate. The minimization of emissions is then formulated in terms of the traffic distribution and priority parameters, taking into account travel times. A comparison is provided between roundabouts with optimized parameters and traffic lights, which correspond to time-varying traffic priorities. Our approach can be adapted to manage traffic in complex networks in order to reduce emissions while keeping travel time at acceptable levels., Comment: 24 pages, 11 figures

The societal impact of traffic is a long-standing and complex problem. We focus on the estimation of ozone production due to vehicular traffic. For this, we couple a system of conservation laws for vehicular traffic, an emission model, and a system of partial differential equations for the main reactions leading to ozone production and diffusion. The second-order model for traffic is obtained by choosing a special velocity function for a Collapsed Generalized Aw-Rascle-Zhang model and is tuned on NGSIM data. On the other side, the system of partial differential equations describes the main chemical reactions of $\mathrm{NO_x}$ gases with a source term provided by a general emission model applied to the output of the traffic model. We analyze the ozone impact of various traffic scenarios and describe the effect of traffic light timing. The numerical tests show the negative effect of vehicles restarts on $\mathrm{NO_x}$ emissions, suggesting to increase the length of the green phase of traffic lights to reduce them., Comment: 27 pages, 13 figures

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by partial differential equations (PDEs), which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement. To this aim, we put in place an algorithm based on the combination of two methods: first, we use the Dynamic Mode Decomposition to create a mathematical model describing the mass transfer; second, we use the notion of Wasserstein distance (also known as earth mover's distance) to reconstruct the underlying velocity field that is responsible for the displacement. Finally, we consider a real-life application: the algorithm is employed to study the travel flows of people in large populated areas using, as input data, density profiles (i.e. the spatial distribution) of people in given areas at different time instances. This kind of data are provided by the Italian telecommunication company TIM and are derived by mobile phone usage., Comment: 19 pages, 10 figures

In this paper we deal with the study of travel flows and patterns of people in large populated areas. Information about the movements of people is extracted from coarse-grained aggregated cellular network data without tracking mobile devices individually. Mobile phone data are provided by the Italian telecommunication company TIM and consist of density profiles (i.e. the spatial distribution) of people in a given area at various instants of time. By computing a suitable approximation of the Wasserstein distance between two consecutive density profiles, we are able to extract the main directions followed by people, i.e. to understand how the mass of people distribute in space and time. The main applications of the proposed technique are the monitoring of daily flows of commuters, the organization of large events, and, more in general, the traffic management and control., Comment: 6 pages, 14 figures