Modelling and Optimisation of Flows on Networks: Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle

by Luigi Ambrosio, Alberto Bressan, Dirk Helbing, Axel Klar, Enrique Zuazua

Overview

In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.

Product Details

ISBN-13:	9783642321597
Publisher:	Springer Berlin Heidelberg
Publication date:	12/14/2012
Series:	Lecture Notes in Mathematics , #2062
Edition description:	2013
Pages:	497
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

A User’s Guide to Optimal Transport.- Hyperbolic Conservation Laws: an Illustrated Tutorial.- Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models.- On the Controversy around Daganzo’s Requiem for and Aw-Rascle’s Resurrection of Second-Order Traffic Flow Models.- Theoretical vs. Empirical Classification and Prediction of Congested Traffic States.- Self-Organized Network Flows.- Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections.- Modeling and Optimization of Scalar Flows on Networks.- The Wave Equation: Control and Numerics