arXiv subjects

Matteo Piu

Publications and source records attributed to Matteo Piu.

5 recordsLinked to original sources

arXiv2025

Control of kinetic opinion dynamics in popularity-adaptive social networks

This paper presents a mathematical model for opinion dynamics in popularity-adaptive social networks, where both opinion spreading and the evolution of social media contacts depend on agents' popularity and the prominence of their views. While previous approaches accounted for the influence of popularity on opinion dynamics, we introduce a novel feedback mechanism in which opinion affects the formation of contacts. Within a kinetic modeling framework, we describe the evolution of the coupled dynamics of opinions and network structure, incorporating a class of control laws in order to promote interactions with popular individuals and amplify dominant opinions. Such control strategies are introduced to influence both opinion formation and connectivity, representing interventions such as awareness campaigns or moderation policies. Numerical results show how control strategies can mitigate polarization, foster consensus, or guide opinion distributions in dynamically evolving networks.

math.OC↗

arXiv2025

Second-order multilane traffic flow models: from the microscopic to the macroscopic scale

This study addresses multilane vehicular traffic modelling, focusing on the rigorous transition from microscopic (individual vehicle-based) to macroscopic (aggregate flow-based) descriptions. While previous research on multilane traffic has largely focused on first-order models, we derive two novel multilane second-order macroscopic models by applying a microscopic-to-macroscopic limit to the multilane Bando-Follow-the-Leader model. These two models diverge fundamentally in their closure relations during the scaling limit: Model 1 directly projects the velocity dynamics, whereas Model 2 is built upon the heuristic conservation of the generalized momentum across lanes. Both models incorporate lane-changing dynamics through source terms in a hyperbolic system of balance laws, yet their structural differences lead to distinct relaxation limits, with Model 2 naturally relaxing to the first-order macroscopic multilane model recently derived by the authors, and Model 1 yielding a novel, non-standard first-order system. We propose several numerical experiments showing that the models can reproduce complex traffic phenomena, including congestion propagation, non-equilibrium effects, capacity drops, and asymmetric lane usage. Leveraging experimental datasets from real-world highways, we further construct lane-specific empirical fundamental diagrams and compare them with their simulated counterparts. The results demonstrate that the structural assumptions of Model 2 provide a superior quantitative fit with empirical data, faithfully capturing critical density values, traffic scattering, and characteristic lane-dependent patterns, thus offering a robust and generalizable tool for realistic traffic flow analysis.

physics.soc-ph↗

arXiv2025

Micro-macro and macro-macro limits for controlled leader-follower systems

We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a fully continuum macro-macro system. For each limiting procedure, we establish quantitative stability and convergence estimates based on modulated energy methods and Wasserstein distances. These results provide a rigorous foundation for the hierarchical reduction of controlled multi-agent systems. Numerical simulations are presented, including examples with interaction potentials beyond the analytical class considered, to demonstrate the dynamics and support the theoretical results.

math.AP↗

arXiv2022

Derivation and stability analysis of macroscopic multi-lane models for vehicular traffic flow

The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of hyperbolic balance laws. The macroscopic limit is derived without assuming ad hoc space and time scalings. The analysis of the stability of the equilibria of the model is discussed. The proposed numerical tests confirm the theoretical findings between the macroscopic and microscopic modeling, and the results of the stability analysis.

math.AP↗

arXiv2022

Stability analysis of microscopic models for traffic flow with lane changing

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the stability of the steady states starting from the model in the one-lane case and extending the results to the generic multi-lane case with the careful design of the lane changing rules. We compare the results with numerical tests, that confirm the predictions of the linear stability analysis and also show that the model is able to reproduce stop & go waves, a typical feature of congested traffic.

math.CA↗