Generalized Wasserstein distance and its application to transport equations with source

In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized Wasserstein distance to study a transport equation with source, in which both the vector field and the source depend on the measure itself. We prove existence and uniqueness of the solution to the Cauchy problem when the vector field and the source are Lipschitzian with respect to the generalized Wasserstein distance

Existence and approximation of probability measure solutions to models of collective behaviors

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown, expressed in terms of a probability measure evolving in time. We develop an existence and approximation theory of the solutions to such models and we show that some recently proposed models of crowd and swarm dynamics fit our theoretic paradigm.Comment: 31 pages, 1 figur

Time-evolving measures and macroscopic modeling of pedestrian flow

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, analysis and numerical approximation of the resulting mathematical structures, which is the main target of this work, follow more easily and straightforwardly than in case of standard hyperbolic conservation laws, also used in the specialized literature by some Authors to address analogous problems.Comment: 27 pages, 6 figures -- Accepted for publication in Arch. Ration. Mech. Anal., 201

Design of a Test Setup for the Characterization of the Dynamic Transfer Matrix of Cavitating Inducers

The paper describes a reduced-order analytical model for the characterization of the dynamic transfer matrix of complex test setups including cavitating pumps. The model, even if based on several simplifying assumptions (quasi 1-dimensional flow, small oscillations, incompressible working fluid, quasi-static response of all the components of the system), is able of providing good indications about the order of magnitude of the expected pressure and flow rate oscillations in the system under given flow conditions and, more in general, about the experiment design. The model has been applied to Alta’s Cavitating Pump Rotordynamic Test Facility with the custom-designed DAPAMITO3 axial inducer, in order to start the design process of an experiment for the characterization of the inducer dynamic matrix. It has been found that a good mechanism for providing an external excitation to the facility can be represented by a device able of mechanically vibrating the water tank in a ver..