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.

Homeland security, transportation, and city planning depend upon well-designed evacuation routes. You can’t wait until the day of to realize your plan won’t work. Designing successful evacuation plans requires an in-depth understanding of models and control designs for the problems of traffic flow, construction and road closures, and the intangible human factors. Pedestrian Dynamics: Mathematical Theory and Evacuation Control clearly delineates the derivation of mathematical models for pedestrian dynamics and how to use them to design feedback controls for evacuations. The book includes: Mathematical models derived from basic principles Mathematical analysis of the model Details of past work MATLAB® code 65 figures and 400 equations Unlike most works on traffic flow, this book examines the development of optimal methods to effectively control and improve pedestrian traffic flow. The work of a leading expert, it examines the differential equations applied to conservation laws encountered in the study of pedestrian dynamics and evacuation control problem. The author presents new pedestrian traffic models for multi-directional flow in two dimensions. He considers a range of control models in various simulations, including relaxed models and those concerned with direction and magnitude velocity commands. He also addresses questions of time, cost, and scalability. The book clearly demonstrates what the future challenges are and provides the tools to meet them.

Effective evacuations can save lives. This book provides mathematical models of pedestrian movements that can be used specifically for designing feedback control laws for effective evacuation. The book also provides various feedback control laws to accomplish the effective evacuation. It book uses the hydrodynamic hyperbolic PDE macroscopic pedestrian models since they are amenable to feedback control design. The control designs are obtained through different nonlinear techniques.

An aging population, increasing obesity and more people with mobility impairments are bringing new challenges to the management of routine and emergency people movement in many countries. These population challenges, coupled with the innovative designs being suggested for both the built environment and other commonly used structures (e.g., transportation systems) and the increasingly complex incident scenarios of fire, terrorism, and large-scale community disasters, provide even greater challenges to population management and safety. Pedestrian and Evacuation Dynamics, an edited volume, is based on the Pedestrian and Evacuation Dynamics (PED) 5th International 2010 conference, March 8th-10th 2010, located at the National Institute of Standards and Technology, Gaithersburg, MD, USA. This volume addresses both pedestrian and evacuation dynamics and associated human behavior to provide answers for policy makers, designers, and emergency management to help solve real world problems in this rapidly developing field. Data collection, analysis, and model development of people movement and behavior during nonemergency and emergency situations will be covered as well.

Due to an increasing number of reported catastrophes all over the world, the safety especially of pedestrians today, is a dramatically growing field of interest, both for practitioners as well as scientists from various disciplines. The questions arising mainly address the dynamics of evacuating people and possible optimisations of the process by changing the architecture and /or the procedure.

The 6th International Conference on Pedestrian and Evacuation Dynamics (PED2012) showcased research on human locomotion. This book presents the proceedings of PED2012. Humans have walked for eons; our drive to settle the globe began with a walk out of Africa. However, much remains to discover. As the world moves toward sustainability while racing to assess and accommodate climate change, research must provide insight on the physical requirements of walking, the dynamics of pedestrians on the move and more. We must understand, predict and simulate pedestrian behaviour, to avoid dangerous situations, to plan for emergencies, and not least, to make walking more attractive and enjoyable. PED2012 offered 70 presentations and keynote talks as well as 70 poster presentations covering new and improved mathematical models, describing new insights on pedestrian behaviour in normal and emergency cases and presenting research based on sensors and advanced observation methods. These papers offer a starting point for innovative new research, building a strong foundation for the next conference and for future research.

Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.