Laboratoire Jean-Alexandre Dieudonné

We address the problem of estimating the drift parameter in a system of N interacting particles driven by additive fractional Brownian motion of Hurst index H ≥ 1/2. Considering continuous observation of the interacting particles over a fixed interval [0, T ], we examine the asymptotic regime as N → ∞. Our main tool is a random variable reminiscent of the least squares estimator but unobservable due to its reliance on the Skorohod integral. We demonstrate that this object is consistent and asymptotically normal by establishing a quantitative propagation of chaos for Malliavin derivatives, which holds for any H ∈ (0, 1). Leveraging a connection between the divergence integral and the Young integral, we construct computable estimators of the drift parameter. These estimators are shown to be consistent and asymptotically Gaussian. Finally, a numerical study highlights the strong performance of the proposed estimators.

• Reformulate the incompressible magneto-hydro-dynamics in terms of differential forms • Underline how the fluid velocity shows up in the magnetic compartment thanks to the Lie’s derivative • Underline how the magnetic induction acts on the fluid compartment thanks to the Laplace’s force Magnetohydrodynamic offers examples of non-scalar advection-diffusion problems which are relevant for applications. We consider its formulation in terms of differential forms, with the presence of operators such as the exterior derivative and Lie’s derivative, being aware of the underneath analogy between electromagnetic dynamic and incompressible fluid dynamic. We analyze the intrinsic structure of the magnetic and fluid coupling, with a special attention to the Laplace’s force. Taking the cue from [11] we focus on the density of virtual power associated with each of the involved forces.

In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized by a different reaction time and interaction range. We construct approximate solutions using a Hilliges-Weidlich scheme and we provide uniform L $\infty$ and BV estimates which ensure the convergence of the scheme, thus obtaining existence of entropy weak solutions of bounded variation. Uniqueness follows from an L 1 stability result derived from the entropy condition. Additionally, we provide numerical simulations to illustrate applications to mixed autonomous / human-driven traffic flow modeling. In particular, we show that the presence of autonomous vehicles improves overall traffic flow and stability.

Context. Dynamical friction is an important phenomenon in stellar dynamics (and plasma physics) resulting in the slowing down of a massive test particle upon many two-body scatters with background particles. Chandrasekhar’s original formulation, developed for idealized infinite and homogeneous systems, has been found to be sufficiently accurate even in models of finite extent and radially dependent density profiles. However, in some cases N-body simulations have evidenced a breakdown of Chandrasekhar’s formalism. In particular, in the case of cored stellar systems, the analytical predictions underestimate the rate of in-fall of the test particle. Moreover, the orbital decay appears to stop at a critical radius where in principle the effect of dynamical friction should still be non-negligible. Aims. Several explanations for such discrepancy have been proposed so far. In spite of this, it remains unclear whether the origin is a finite N effect or an effect arising from the resonance (or near-resonance) of the orbits of the test and field particles, which is independent of N, such as dynamical buoyancy. Here we aim to shed some light on this issue with tailored numerical experiments. Methods. We performed ad hoc simulations of a massive tracer initially placed on a low-eccentricity orbit in spherical equilibrium models with increasing resolution. We used an N-body code for which the self-consistent interaction among the background particles can be substituted with the effect of the static smooth potential of the system’s continuum limit, so that the higher-order contributions to the dynamical friction arising from the formation of a wake can be neglected if needed. Results. We find that, contrary to what has been reported in previous literature, a suppression of dynamical friction happens in both cuspy and cored models. When neglecting the interaction among field particles, we observe in both cases a clear N−1/2 scaling of the radius at which dynamical friction ceases to be effective. This hints at a granularity-induced origin of the so-called core-stalling of the massive tracer in cored models.

Cultural heritage generative management systems (CH-GeMS) are systems supporting the management of the actor and process interactions through the continuous production and adaptation of value through self-organization, learning, and coevolution of such interactions. CH-GeMS are an improvement of cultural heritage management systems based on AI-driven generative models.

In this paper, we propose three control strategies, based on different levels of cooperation (centralized, decentralized and quasi-decentralized), to improve density dependent traffic performance indexes, such as fuel consumption, by acting on a small number of Connected and Automated Vehicles (CAVs) operating as moving bottlenecks on the surrounding flow. We rely on a multi-scale approach to model mixed traffic of CAVs in the bulk flow. In particular, CAVs are individually tracked and they are allowed to overtake (if on distinct lanes) or queuing (if on the same lane). Controlling CAVs desired speeds allows to act on the system to minimize the selected cost function. For the proposed control strategies, we apply both global optimization and a Model Predictive Control approach. In particular, we perform numerical tests to investigate how the CAVs number and positions impact the result, showing that few, optimally chosen vehicles are sufficient to significantly improve the selected performance indexes, even using a decentralized control policy. Simulation results support the attractive perspective of exploiting a very small number of vehicles as endogenous control actuators to regulate traffic flow on road networks, providing a flexible alternative to traditional control methods.