93 citations · 104 across the 12 of their papers we have counts for
16 papers
The Follow-the-Leader scheme with non-monotone velocity
Marco Di Francesco
This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity ma…
A system of continuity equations with nonlocal interactions of Morse type
Marco Di Francesco, Valeria Iorio
We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest i…
Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux
M. Di Francesco, S. Fagioli, E. Radici
We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for…
The approximation of the quadratic porous medium equation via nonlocal interacting particles subject to repulsive Morse potential
Marco Di Francesco, Valeria Iorio, Markus Schmidtchen
We propose a deterministic particle method for a one-dimensional nonlocal equation with interactions through the repulsive Morse potential. We show that the particle method converg…
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
CDO calibration via Magnus Expansion and Deep Learning
Marco Di Francesco, Kevin Kamm
In this paper, we improve the performance of the large basket approximation developed by Reisinger et al. to calibrate Collateralized Debt Obligations (CDO) to iTraxx market data.…
Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion
Marco Di Francesco, Yahya Jaafra
In this paper we consider a one-dimensional nonlocal interaction equation with quadratic porous-medium type diffusion in which the interaction kernels are attractive, nonnegative,…
Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species
Martin Burger, Marco Di Francesco, Simone Fagioli +1
Macroscopic models for systems involving diffusion, short-range repulsion, and long-range attraction have been studied extensively in the last decades. In this paper we extend the…
A deterministic particle approximation for non-linear conservation laws
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini +1
We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely,…
Follow-the-leader approximations of macroscopic models for vehicular and pedestrian flows
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini +1
We review recent results and present new ones on a deterministic follow-the-leader particle approximation of first and second order models for traffic flow and pedestrian movements…
Deterministic particle approximation of the Hughes model in one space dimension
M. Di Francesco, S. Fagioli, M. D. Rosini +1
In this paper we present a new approach to the solution to a generalized version of Hughes' models for pedestrian movements based on a follow-the-leader many particle approximation…
Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic
M. Di Francesco, S. Fagioli, M. D. Rosini
We consider the Follow-The-Leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi-population formulation. We prove rigorous convergence to weak solutio…
Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
Marco Di Francesco, Massimiliano D. Rosini
We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the…
Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension
Marco Di Francesco, Massimo Fornasier, Jan-Christian Hütter +1
We study the long time behavior of the Wasserstein gradient flow for an energy functional consisting of two components: particles are attracted to a fixed profile by means of a…
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
Giovanni A. Bonaschi, José A. Carrillo, Marco Di Francesco +1
We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and…
Condensation phenomena in nonlinear drift equations
Jose' A. Carrillo, Marco Di Francesco, Giuseppe Toscani
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we…