Optimal Transport for Applied Mathematicians

Optimal Transport for Applied Mathematicians
Author: Filippo Santambrogio
Publisher: Birkhäuser
Total Pages: 376
Release: 2015-10-17
Genre: Mathematics
ISBN: 3319208284

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.

Transportation Systems Engineering

Transportation Systems Engineering
Author: Ennio Cascetta
Publisher: Springer Science & Business Media
Total Pages: 723
Release: 2013-03-09
Genre: Technology & Engineering
ISBN: 1475768737

"This book provides a rigorous and comprehensive coverage of transportation models and planning methods and is a must-have to anyone in the transportation community, including students, teachers, and practitioners." Moshe Ben-Akiva, Massachusetts Institute of Technology.

Advanced Transport Phenomena

Advanced Transport Phenomena
Author: L. Gary Leal
Publisher: Cambridge University Press
Total Pages: 7
Release: 2007-06-18
Genre: Technology & Engineering
ISBN: 1139462067

Advanced Transport Phenomena is ideal as a graduate textbook. It contains a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems, focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory. Also covered are unidirectional flows, lubrication and thin-film theory, creeping flows, boundary layer theory, and convective heat and mass transport at high and low Reynolds numbers. The emphasis is on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain solutions that are due either to geometric simplifications, or large or small values of dimensionless parameters. The author emphasizes setting up problems and extracting as much information as possible short of obtaining detailed solutions of differential equations. The book also focuses on the solutions of representative problems. This reflects the book's goal of teaching readers to think about the solution of transport problems.

Transportation for Livable Cities

Transportation for Livable Cities
Author: Vukan Vuchic
Publisher: Routledge
Total Pages: 562
Release: 2017-09-08
Genre: Social Science
ISBN: 1351318144

The twenty-first century finds civilization heavily based in cities that have grown into large metropolitan areas. Many of these focal points of human activity face problems of economic inefficiency, environmental deterioration, and an unsatisfactory quality of life—problems that go far in determining whether a city is "livable." A large share of these problems stems from the inefficiencies and other impacts of urban transportation systems. The era of projects aimed at maximizing vehicular travel is being replaced by the broader goal of achieving livable cities: economically efficient, socially sound, and environmentally friendly. This book explores the complex relationship between transportation and the character of cities and metropolitan regions. Vukan Vuchic applies his experience in urban transportation systems and policies to present a systematic review of transportation modes and their characteristics. Transportation for Livable Cities dispels the myths and emotional advocacies for or against freeways, rail transit, bicycles,and other modes of transportation. The author discusses the consequences of excessive automobile dependence and shows that the most livable cities worldwide have intermodal systems that balance highway and public transit modes while providing for pedestrians, bicyclists, and paratransit. Vuchic defines the policies necessary for achieving livable cities: the effective implementation of integrated intermodal transportation systems.