In this work we discuss an Mean Field Games approach to traffic management on multi-lane roads. Such approach is particularly indicated to model self driven vehicles with perfect information of the domain. The mathematical interest of the problem is related to the fact that the system of partial differential equations obtained in this case is not in the classic form, but it consists of two continuity equations (one for each lane) and a variational inequality, coming from the Hamilton-Jacobi theory of the hybrid control.

Adriano Festa Simone Göttlich

We introduce a macroscopic model for a network of conveyor belts with various speeds and capacities. In a different way from traffic flow models, the product densities are forced to move with a constant velocity unless they reach a maximal capacity and start to queue. This kind of dynamics is governed by scalar conservation laws consisting of a discontinuous flux function. We define appropriate coupling conditions to get well-posed solutions at intersections and provide a detailed description of the solution. Some numerical simulations are presented to illustrate and confirm the theoretical results for different network configurations.

Adriano Festa Simone Göttlich Marion Pfirsching

We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical conditions. We prove a convergence theorem and some error estimates. Additionally, the theoretical results are validated by numerical tests. Finally, we apply the scheme to simulate traffic flows modeling problems.

Elisabetta Carlini Adriano Festa Nicolas Forcadel

We discuss the general framework of a stochastic two-player, hybrid differential game, and we apply it to the modelling of a "match race" between two sailing boats, namely a competition in which the goal of both players is to proceed in the windward direction, while trying to slow down the other player. We provide a convergent approximation scheme for the computation of the value function of the game, and we validate the approach on some typical racing scenarios.

Simone Cacace Roberto Ferretti Adriano Festa

Black-body radiation, omnipresent at room temperature, couples nearby Rydberg states. The resulting state mixture features strong dipolar interactions, which may induce dephasing in a Rydberg many-body system. Here we report on a single atom resolved study of this state contamination and the emerging pairwise interactions in optical tweezers. For near-resonant laser detuning we observe characteristic correlations with a length scale set by the dipolar interaction. Our study reveals the microscopic origin of avalanche excitation observed in previous experiments.

Lorenzo Festa Nikolaus Lorenz Lea-Marina Steinert Zaijun Chen Philip Osterholz Robin Eberhard Christian Gross

We introduce a class of systems of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e. tessellations of domains with respect to geodesic distances where generators and centroids coincide. Typical examples are given by geodesic centroidal Voronoi tessellations and geodesic centroidal power diagrams. An appropriate version of the Fast Marching method on unstructured grids allows computing the solution of the Hamilton-Jacobi system and therefore the associated tessellations. We propose various numerical examples to illustrate the features of the technique.

Fabio Camilli Adriano Festa

The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent viscosity solution and, respectively, duality solution. We supplement our theoretical analysis with various numerical examples to illustrate the features of the schemes.

Fabio Camilli Adriano Festa Luciano Marzufero

We have implemented C like Continuation based programming language. Continuation based C, CbC was implemented using micro-C on various architecture, and we have tried several CbC programming experiments. Here we report new implementation of CbC compiler based on GCC 4.2.3. Since it contains full C capability, we can use CbC and C in a mixture.

Shinji Kono Kento Yogi

The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are used to calculate a few mechanical quantities pertinent to the periodic motions of celestial bodies. Several values have been obtained which result in reasonable agreement with the corresponding experimental data. A gravitational dimensionless structure constant has been determined, using the data relative to the solar sistem, which allows to quantitatively account for phenomena on a much wider scale. In particular, some information is acquired about the recently discovered extrasolar planetary systems and about the general empirical law which connects the spin of a celestial body with the square of its mass.

A. G. Agnese R. Festa

The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the superlinear convergence which, in presence of a finite number of controls, is reached in finite time. Performances of the method can be significantly improved by using parallel computing; how to build a parallel version of method is not a trivial point, the difficulties come from the strict relation between various values of the solution, even related to distant points of the domain. In this contribution we propose a parallel version of the Howard's algorithm driven by an idea of domain decomposition. This permits to derive some important properties and to prove the convergence under quite standard assumptions. The good features of the algorithm will be shown through some tests and examples.

Adriano Festa