Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.
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Takashi Suzuki
Mean Field Theories and Dual Variation Mathematical Structures of the Mesoscopic Model Second Edition
Atlantis Studies in Mathematics for Engineering and Science Volume 11
Series editor Prof. Charles K. Chui, Department of Statistics, Stanford University, Stanford, CA, USA
Aims and scope of the series The series ‘Atlantis Studies in Mathematics for Engineering and Science’ (AMES) publishes high quality monographs in applied mathematics, computational mathematics, and statistics that have the potential to make a significant impact on the advancement of engineering and science on the one hand, and economics and commerce on the other. We welcome submission of book proposals and manuscripts from mathematical scientists worldwide who share our vision of mathematics as the engine of progress in the disciplines mentioned above. For more information on this series and our other book series, please visit our website at: www.atlantis-press.com/publications/books. Atlantis Press 8, square des Bouleaux 75019 Paris, France
More information about this series at http://www.atlantis-press.com
Takashi Suzuki
Mean Field Theories and Dual Variation Mathematical Structures of the Mesoscopic Model Second Edition
Takashi Suzuki Graduate School of Engineering Science Osaka University Toyonaka, Osaka Japan
ISSN 1875-7642 ISSN 2467-9631 (electronic) Atlantis Studies in Mathematics for Engineering and Science ISBN 978-94-6239-153-6 ISBN 978-94-6239-154-3 (eBook) DOI 10.2991/978-94-6239-154-3 Library of Congress Control Number: 2015954602 © Atlantis Press and the author(s) 2008, 2015 This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. Printed on acid-free paper
Preface to the Second Edition
Seven years have past since the first edition of this book is published. This new edition is composed of 13 chapters. Actually, we have broken two chapters of the first edition into several ones, providing with additional sections. We also added new chapters, following fundamental concepts of the first edition. Thus we deal with several models in physics, chemistry and biology, taking regarding two mathematical structures, that is the duality and scaling. In this new edition, we added several topics in physics, particularly the theory of perfect fluids and that of static magnetic fields. Some parts, particularly, the chapters of chemotaxis and time realization are also modified according to the study after the first edition. Below we record the descriptions at the beginning of the chapters of the first edition.
Duality-Sealed Variation Self-organization is a phenomenon widely observed in physics, chemistry, and biology. Usually, it is mentioned in the context of far-from-equilibrium of dissipative open systems describing the discharge of entropy, but the other aspect, formation of self-assembly, is sea
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