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The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.
In the past ten years there has been a rapid growth of the research and application area known as Lab-on-a-Chip. After an initial focus on electrokinetic separation techniques on chip, the scope of the field has widened to include topics like microfluidics, DNA analysis, cell analysis, microreactors and mass spectrometer interfacing. As well as the analytical chemistry community, synthetic chemists, chemical engineers, biochemists and biomedical engineers are now also becoming more and more interested in using new micro- and nanotechnological techniques. This first Lab-on-a-Chip book contains a broad collection of papers on microtechnology, microfluidics, analytical methods and applications. All contributions are written by leading researchers in their respective fields, and provide new scientists with an overview of the field, to make him/her aware of the enormous opportunities offered by modern technology. The work presented in this book will definitely stimulate readers to new ideas and concepts, and lead to further innovations in this area. - Provides a quick introduction into the different aspects of this field - Describes technology that has already revolutionized the world of chemical and biochemical analysis and synthesis - All contributions are written by leading researchers in their respective fields
This collection of fully peer-reviewed papers were presented at the 26th Leeds-Lyon Tribology Symposium which was held in Leeds, UK, 14-17 September, 1999. The Leeds-Lyon Symposia on Tribology were launched in 1974, and the large number of references to original work published in the Proceedings over many years confirms the quality of the published papers. It also indicates that the volumes have served their purpose and become a recognised feature of the tribological literature. This year's title is 'Thinning Films and Tribological Interfaces', and the papers cover practical applications of tribological solutions in a wide range of situations. The evolution of a full peer review process has been evident for a number of years. An important feature of the Leeds-Lyon Symposia is the presentation of current research findings. This remains an essential feature of the meetings, but for the 26th Symposium authors were invited to submit their papers for review a few weeks in advance of the Symposium. This provided an opportunity to discuss recommendations for modifications with the authors.
HereOCOs a groundbreaking book that introduces and discusses the important aspects of lab-on-a-chip, including the practical techniques, circuits, microsystems, and key applications in the biomedical, biology, and life science fields. Moreover, this volume covers ongoing research in lab-on-a-chip integration and electric field imaging. Presented in a clear and logical manner, the book provides you with the fundamental underpinnings of lab-on-a-chip, presents practical results, and brings you up to date with state-of-the-art research in the field. This unique resource is supported with over 160 illustrations that clarify important topics throughout.