Vincenzo Coscia

Bio: Vincenzo Coscia is an academic researcher from University of Ferrara. The author has contributed to research in topics: Mathematical theory & Lipschitz domain. The author has an hindex of 12, co-authored 37 publications receiving 774 citations.

On the mathematical theory of vehicular traffic flow i: fluid dynamic and kinetic modelling

Abstract: This review reports the existing literature on traffic flow modelling in the framework of a critical overview which aims to indicate research perspectives The contents mainly refer to modelling by fluid dynamic and kinetic equations and are arranged in three parts The first part refers to methodological aspects of mathematical modelling and to the interpretation of experimental results The second part is devoted to modelling and deals both with methodological aspects and with the description of some specific models The third part reports about an overview on applications and research perspectives

First-order macroscopic modelling of human crowd dynamics

Abstract: This paper deals with the mathematical modelling of crowd dynamics within the framework of continuum mechanics. The method uses the mass conservation equation closed by phenomenological models linking the local velocity to density and density gradients. The closures take into account movement in more than one space dimension, presence of obstacles, pedestrian strategies, and modelling of panic conditions. Numerical simulations of the initial-boundary value problems visualize the ability of the models to predict several interesting phenomena related to the complex system under consideration.

On the mathematical theory of vehicular traffic flow II: Discrete velocity kinetic models

Abstract: This paper deals with the modelling of vehicular traffic flow by methods of the discrete mathematical kinetic theory. The discretization is developed in the velocity space by a grid adapted to the local density. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale, while the adaptative grid allows an improved description of various phenomena related to vehicular traffic flow. Specific models are proposed and a qualitative and computational analysis is developed to show the properties of the model and their ability to describe real flow conditions. A critical analysis, proposed in the last part of the paper, outlines suitable research perspectives.

Haemodynamic enhancement in perforator flaps: the inversion phenomenon and its clinical significance. A study of the relation of blood velocity and flow between pedicle and perforator vessels in perforator flaps.

Abstract: Perforator flaps are perfused through a long vessel whose calibre decreases from its origin to the skin, because all branches have been sealed, resulting in a conduit with resistances in series, rather than a tree with resistances in parallel, as in the normal systemic circulation. This study was planned to assess whether the differences between perforator flap and normal systemic vasculature have an impact on haemodynamic parameters in perforator flaps and on their clinical significance. The study was performed on 10 patients. Echo-colour-Doppler measurement of diameters, velocity of flow and calculations of flow rate were made at the level of flap pedicle artery and skin perforator artery, pre- and post-operatively in each patient. Statistical analysis used the Wilcoxon matched pairs signed sum rank test. Our data show that in the donor area pre-operatively, blood velocity in skin artery perforator is lower that in the corresponding pedicle artery, whereas post-operatively, in perforator flaps, blood velocity in the perforator is higher than in the pedicle. The difference was statistically significant (P<0.01). There is an inversion of the gradient of blood velocity between pedicle artery and perforator artery compared to normal circulation. Furthermore, in normal circulation flow through the perforator was found smaller than that at the pedicle, whereas in perforator flaps, flow through the perforator is smaller but is a greater proportion of the flow through the pedicle and the difference is statistically significant (P<0.01). Therefore, the velocity of blood and the rate of flow reaching the skin are higher in perforator flaps than in normal circulation.

Existence, uniqueness and stability of regular steady motions of a second-grade fluid

Abstract: In this paper we study the well-posedness of the steady motions problem for a second-grade fluid in a bounded domain, with adherence conditions at the boundary. We prove the existence and uniqueness of steady classical solutions for any value of the normal stress moduli α1 and α2, thus showing that the thermodynamical restrictions are not needed for the mathematical problem being well-set. Moreover, we find that such steady motions are exponentially non-linearly stable, provided α1 > 0.

On the Navier-Stokes equations

Abstract: A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam

Abstract: A traffic jam on a highway is a very familiar phenomenon. From the physical viewpoint, the system of vehicular flow is a non-equilibrium system of interacting particles (vehicles). The collective effect of the many-particle system induces the instability of a free flow state caused by the enhancement of fluctuations, and the transition to a jamming state occurs spontaneously if the average vehicle density exceeds a certain critical value. Thus, a bottleneck is only a trigger and not the essential origin of a traffic jam. In this paper, we present the first experimental evidence that the emergence of a traffic jam is a collective phenomenon like 'dynamical' phase transitions and pattern formation

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

Abstract: This paper presents a review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena. The survey of models deals with the representation scales and the mathematical frameworks that are used for the modeling approach. The paper also considers the challenging objective of modeling complex systems consisting of large systems of individuals interacting in a nonlinear manner, where one of the modeling difficulties is the fact that these systems are difficult to model at a global level when based only on the description of the dynamics of individual elements. The review is concluded with a critical analysis focused on research perspectives that consider the development of a unified modeling strategy.