Benedetto Piccoli - Böcker

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow.

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow.

The book contains the lecture notes of a graduate level course, cross-listed for advanced undergraduate students, on the mathematical tools used in biomathematics and systems biology. The book contains general introductory material on: linear algebra, graph theory, network flows, probability and Markov chains, difference and differential equations, control theory. Later chapters focus on specific applications, such as epidemiological models, social dynamics, bionetworks, and quantitative systems pharmacology.

This volume presents a coherent and high-quality collection of contributions addressing key challenges in traffic modeling and control. The chapters showcase a blend of theoretical rigor and practical relevance, with diverse methodologies ranging from PDE control to game theory and data-driven modeling. One chapter presents a retrospective on PDE backstepping techniques for stabilizing stop-and-go waves, extending from single-lane models to more complex multi-lane and multi-class systems. Another introduces a second-order time-to-collision metric that accounts for non-static acceleration and turning, improving predictive accuracy in safety analysis. The CGARZ model simplifies second-order traffic dynamics by collapsing free-flow regimes while preserving detail in congestion, striking a balance between realism and tractability. A multi-population mean field game framework is proposed to model the interaction between human-driven and autonomous vehicles, with a detailed stability analysis that sheds light on the benefits of CAV integration. Another contribution develops a multi-lane model where autonomous vehicles act as mobile bottlenecks, coupling macroscopic flow dynamics with controlled microscopic agents. The volume also includes a rigorous analysis of the Hughes model for pedestrian flow with affine cost functions, exploring uniqueness and sensitivity with respect to both initial data and model parameters.

This book presents mathematical models and numerical simulations of crowd dynamics. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one.

This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.