Space Time Yang Mills Gravity And Dynamics Of Cosmic Expansion How Quantum Yang Mills Gravity In The Super Macroscopic Limit Leads To An Effective G V T And New Perspectives On Hubble S Law The Cosmic Redshift And Dark Energy

This volume offers a valuable insight into various aspects of the ongoing work directed at measuring neutrino mass. It took twenty years to refute the assertions of Bethe and Peierls that neutrinos were not observable, but it has since been realised that much can be learnt from these particles. The moral is, as Fiorini argues here, that the study of neutrinos was and remains demanding but rewarding. Subjects addressed in this volume include; clarifying the meaning of the Klapdor-Kleingrothaus results, probing the Majorana nature of neutrinos, observing lepton number violating effects for the first time, studying the end point of the spectrum in the search for neutrino masses and speculating whether it is possible to measure neutrino masses in cosmology. Lectures are enriched with rich historical overviews and valuable introductory material. Attention is also given to theoretical topics such as the evolution of the concept of mass in particle physics, a status report on neutrino oscillations and current discussion on neutrino masses. The reader is further reminded that neutrino masses may also have some bearing on the very origin of the matter among us, and have many deep links with other important lines of current physics research.

This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). The first part of the book studies the role of noise in finite ensembles of nanomagnetic particles: we show geometric ergodicity of a unique invariant measure of Gibbs type and study related properties of approximations of the SLLG, including time discretization and Ginzburg-Landau type penalization. In the second part we propose an implementable space-time discretization using random walks to construct a weak martingale solution of the corresponding stochastic partial differential equation which describes the magnetization process of infinite spin ensembles. The last part of the book is concerned with a macroscopic deterministic equation which describes temperature effects on macro-spins, i.e. expectations of the solutions to the SLLG. Furthermore, comparative computational studies with the stochastic model are included. We use constructive tools such as e.g. finite element methods to derive the theoretical results, which are then used for computational studies. The numerical experiments motivate an interesting interplay between inherent geometric and stochastic effects of the SLLG which still lack a rigorous analytical understanding: the role of space-time white noise, possible finite time blow-up behavior of solutions, long-time asymptotics, and effective dynamics.

Geodesy is the science of accurately measuring and understanding three fundamental properties of Earth: its geometric shape, its orientation in space, and its gravity field, as well as the changes of these properties with time. Over the past half century, the United States, in cooperation with international partners, has led the development of geodetic techniques and instrumentation. Geodetic observing systems provide a significant benefit to society in a wide array of military, research, civil, and commercial areas, including sea level change monitoring, autonomous navigation, tighter low flying routes for strategic aircraft, precision agriculture, civil surveying, earthquake monitoring, forest structural mapping and biomass estimation, and improved floodplain mapping. Recognizing the growing reliance of a wide range of scientific and societal endeavors on infrastructure for precise geodesy, and recognizing geodetic infrastructure as a shared national resource, this book provides an independent assessment of the benefits provided by geodetic observations and networks, as well as a plan for the future development and support of the infrastructure needed to meet the demand for increasingly greater precision. Precise Geodetic Infrastructure makes a series of focused recommendations for upgrading and improving specific elements of the infrastructure, for enhancing the role of the United States in international geodetic services, for evaluating the requirements for a geodetic workforce for the coming decades, and for providing national coordination and advocacy for the various agencies and organizations that contribute to the geodetic infrastructure.

The book is based on research presentations at the international conference, “Emerging Trends in Applied Mathematics: In the Memory of Sir Asutosh Mookerjee, S.N. Bose, M.N. Saha and N.R. Sen”, held at the Department of Applied Mathematics, University of Calcutta, during 12–14 February 2014. It focuses on various emerging and challenging topics in the field of applied mathematics and theoretical physics. The book will be a valuable resource for postgraduate students at higher levels and researchers in applied mathematics and theoretical physics. Researchers presented a wide variety of themes in applied mathematics and theoretical physics—such as emergent periodicity in a field of chaos; Ricci flow equation and Poincare conjecture; Bose–Einstein condensation; geometry of local scale invariance and turbulence; statistical mechanics of human resource allocation: mathematical modelling of job-matching in labour markets; contact problem in elasticity; the Saha equation; computational fluid dynamics with applications in aerospace problems; an introduction to data assimilation, stochastic analysis and bounds on noise for Holling type-II model, graph theoretical invariants of chemical and biological systems; strongly correlated phases and quantum phase transitions of ultra cold bosons; and the mathematical modelling of breast cancer treatment.

A pedagogical introduction to the physics of black holes. The membrane paradigm represents the four-dimensional spacetime of the black hole's "event horizon" as a two-dimensional membrane in three-dimensional space, allowing the reader to understand and compute the behavior of black holes in complex astrophysical environments.

Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.