Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications: Classical and Non–Classical Advanced Mathematics for Real Life Applications

✍ Scribed by Massimiliano Daniele Rosini (auth.)

• Publisher: Springer International Publishing
• Year: 2013
• Tongue: English
• Leaves: 243
• Series: Understanding Complex Systems
• Edition: 1
• Category: Library

✦ Synopsis

This monograph presents a systematic treatment of the theory for hyperbolic conservation laws and their applications to vehicular traffics and crowd dynamics. In the first part of the book, the author presents very basic considerations and gradually introduces the mathematical tools necessary to describe and understand the mathematical models developed in the following parts focusing on vehicular and pedestrian traffic. The book is a self-contained valuable resource for advanced courses in mathematical modeling, physics and civil engineering. A number of examples and figures facilitate a better understanding of the underlying concepts and motivations for the students. Important new techniques are presented, in particular the wave front tracking algorithm, the operator splitting approach, the non-classical theory of conservation laws and the constrained problems. This book is the first to present a comprehensive account of these fundamental new mathematical advances.

✦ Table of Contents

Front Matter....Pages 1-10
Introduction....Pages 1-7
Front Matter....Pages 9-9
Mathematical Preliminaries....Pages 11-21
One-Dimensional Scalar Conservation Laws....Pages 23-42
The Riemann Problem....Pages 43-50
The Cauchy Problem....Pages 51-62
The Initial-Boundary Value Problem and the Constraint....Pages 63-91
One-Dimensional Systems of Conservation Laws....Pages 93-110
One-Dimensional Systems of Balance Laws (Weakly Coupled)....Pages 111-120
Front Matter....Pages 121-121
Vehicular Traffic....Pages 123-138
Equilibrium Traffic Models....Pages 139-148
Generalizations of Equilibrium Traffic Models....Pages 149-160
Cost Functionals....Pages 161-166
Numerical Applications....Pages 167-173
Non-equilibrium Traffic Models....Pages 175-190
Front Matter....Pages 191-191
General Concepts....Pages 193-201
The CR Model....Pages 203-226
Applications....Pages 227-237
Back Matter....Pages 239-242

✦ Subjects

Astrophysics and Astroparticles; Particle Acceleration and Detection, Beam Physics; Quantum Field Theories, String Theory; Mathematical Physics