Dynamics In Models Of Coarsening Coagulation Condensation And Quantization

The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on Nanoscale Material Interfaces: Experiment, Theory and Simulation'' from November 2004 to January 2005. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field. This invaluable volume collects the expanded lecture notes of four of those self-contained tutorials. The topics covered include dynamics in different models of domain coarsening and coagulation and their mathematical analysis in material sciences; a mathematical and computational study for quantized vortices in the celebrated GinzburgOCoLandau models of superconductivity and the mean field GrossOCoPitaevskii equations of superfluidity; the nonlinear SchrAdinger equation and applications in BoseOCoEinstein condensation and plasma physics as well as their efficient and accurate computation; and finally, an introduction to constitutive modeling of macromolecular fluids within the framework of the kinetic theory. This volume serves to inspire graduate students and researchers who will embark upon original research work in these fields."

The focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing planetary problems and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global challenges. Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has increased to the point where it influences the global climate, impacts the ability of the planet to feed itself and threatens the stability of these systems. Issues such as climate change, sustainability, man-made disasters, control of diseases and epidemics, management of resources, risk analysis and global integration have come to the fore. Written by specialists in several fields of mathematics and applied sciences, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Mathematics of Energy and Climate Change held in Lisbon, Portugal, in March 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book presents the state of the art in advanced research and ultimate techniques in modeling natural, economical and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences.

This book presents the current views of leading physicists on the bizarre property of quantum theory: nonlocality. Einstein viewed this theory as “spooky action at a distance” which, together with randomness, resulted in him being unable to accept quantum theory. The contributions in the book describe, in detail, the bizarre aspects of nonlocality, such as Einstein–Podolsky–Rosen steering and quantum teleportation—a phenomenon which cannot be explained in the framework of classical physics, due its foundations in quantum entanglement. The contributions describe the role of nonlocality in the rapidly developing field of quantum information. Nonlocal quantum effects in various systems, from solid-state quantum devices to organic molecules in proteins, are discussed. The most surprising papers in this book challenge the concept of the nonlocality of Nature, and look for possible modifications, extensions, and new formulations—from retrocausality to novel types of multiple-world theories. These attempts have not yet been fully successful, but they provide hope for modifying quantum theory according to Einstein’s vision.

Based on the analytical methods and the computer programs presented in this book, all that may be needed to perform MRI tissue diagnosis is the availability of relaxometric data and simple computer program proficiency. These programs are easy to use, highly interactive and the data processing is fast and unambiguous. Laboratories (with or without sophisticated facilities) can perform computational magnetic resonance diagnosis with only T1 and T2 relaxation data. The results have motivated the use of data to produce data-driven predictions required for machine learning, artificial intelligence (AI) and deep learning for multidisciplinary and interdisciplinary research. Consequently, this book is intended to be very useful for students, scientists, engineers, the medical personnel and researchers who are interested in developing new concepts for deeper appreciation of computational magnetic resonance imaging for medical diagnosis, prognosis, therapy and management of tissue diseases.

This book is an indispensable guide for anyone seeking to familarize themselves with research in braid groups, configuration spaces and their applications. Starting at the beginning, and assuming only basic topology and group theory, the volume's noted expositors take the reader through the fundamental theory and on to current research and applications in fields as varied as astrophysics, cryptography and robotics. As leading researchers themselves, the authors write enthusiastically about their topics, and include many striking illustrations. The chapters have their origins in tutorials given at a Summer School on Braids, at the National University of Singapore's Institute for Mathematical Sciences in June 2007, to an audience of more than thirty international graduate students.

This volume showcases lecture notes collected from tutorials presented at the Workshop on Moving Interface Problems and Applications in Fluid Dynamics that was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences, National University of Singapore. As part of the program, these tutorials were conducted by specialists within their respective areas such as Robert Dillon, Zhilin Li, John Lowengrub, Frank Lu and Gretar Tryggvason. The topics in the program encompass modeling and simulations of biological flow coupled to deformable tissue/elastic structure, shock wave and bubble dynamics and various applications like biological treatments with experimental verification, multi-medium flow or multiphase flow and various applications including cavitation/supercavitation, detonation problems, Newtonian and non-Newtonian fluid, and many other areas. This volume benefits graduate students and researchers keen in the field of interfacial flows for application to physical and biological systems. Even beginners will find this volume a very useful starting point with many relevant references applicable.