Tag: Topological

Free Download Anomalous and Topological Hall Effects in Itinerant Magnets By Yuki Shiomi (auth.)
2013 | 89 Pages | ISBN: 4431543600 | PDF | 4 MB
This book presents an investigation of the anomalous and topological Hall effects in some itinerant ferromagnets and helimagnets by measurements of Hall effects driven by electrical or heat current. New clarifications are provided for spin-dependent Hall effects induced by the Berry phase, skew scattering, and scalar spin chirality.The author reveals the scattering-free nature of the Berry-phase-induced anomalous Hall current by conducting the first comparative study of electrical and thermal Hall effects. The impurity-element dependence of the anomalous Hall effect caused by skew scattering is systematically investigated in the low-resistivity region for Fe. Two new examples showing a topological Hall effect are found in helimagnets, in which nonzero scalar spin chirality arises from the modulation of spin structure through Dzyaloshinsky-Moriya (DM) interaction. Such a DM-interaction-mediated topological Hall effect is a new type of topological Hall effect. Also the temperature dependence of topological Hall terms in the thermal Hall effect and Nernst-Ettingshausen effect is found to be totally different from that in the electrical Hall effect.These results will be useful for applications of spin current to devices with low power consumption.

Free Download Formation and Interactions of Topological Defects: Proceedings of a NATO Advanced Study Institute on Formation and Interactions of Topological Defects, held August 22-September 2, 1994, in Cambridge, England By T. W. B. Kibble (auth.), Anne-Christine Davis, Robert Brandenberger (eds.)
1995 | 397 Pages | ISBN: 1461357675 | PDF | 27 MB
Topological defects have recently become of great interest in condensed matter physics, particle physics and cosmology. They are the unavoidable remnants of many symmetry breaking phase transitions. Topological defects can play an important role in describing the properties of many condensed matter systems (e.g. superfluids and superconduc tors); they can catalyze many unusual effects in particle physics models and they may be responsible for seeding the density perturbations in the early Universe which de velop into galaxies and the large-scale structure of the Universe. Topological defects are also of great interest in mathematics as nontrivial solutions of nonlinear differential equations stabilized by topological effects. The purpose of the Advanced Study Institute "Formation and Interactions of Topo logical Defects" was to bring together students and practitioners in condensed matter physics, particle physics and cosmology, to give a detailed exposition of the role of topo logical defects in these fields; to explore similarities and differences in the approaches; and to provide a common basis for discussion and future collaborative research on common problems.

Free Download Topological Methods in Differential Equations and Inclusions By Annamaria Canino, Marco Degiovanni (auth.), Andrzej Granas, Marlène Frigon, Gert Sabidussi (eds.)
1995 | 522 Pages | ISBN: 9401041504 | PDF | 18 MB
The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.

Free Download Topological Nonlinear Analysis II: Degree, Singularity and Variations By Gianfausto Dell’ Antonio (auth.), Michele Matzeu, Alfonso Vignoli (eds.)
1996 | 605 Pages | ISBN: 1461286654 | PDF | 15 MB
The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell ‘A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, … mN, described in cartesian co ordinates by the system of equations (0.1) where f) V’k,m == -£l–‘ m = 1, 2, 3.

Free Download Pablo Amster, "Topological Methods in the Study of Boundary Value Problems "
English | ISBN: 1461488923 | 2014 | 242 pages | EPUB | 4 MB
This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.

Free Download Vladimir M. Fomin, "Self-rolled Micro- and Nanoarchitectures: Topological and Geometrical Effects"
English | ISBN: 3110574101 | 2020 | 148 pages | PDF | 4 MB
The work shows the fascination of topology- and geometry-governed properties of self-rolled micro- and nanoarchitectures. The author provides an in-depth representation of the advanced theoretical and numerical models for analyzing key effects, which underlie engineering of transport, superconducting and optical properties of micro- and nanoarchitectures.

Free Download Vladimir M. Fomin, "Self-rolled Micro- and Nanoarchitectures: Topological and Geometrical Effects"
English | ISBN: 3110574101 | 2020 | 148 pages | PDF | 4 MB
The work shows the fascination of topology- and geometry-governed properties of self-rolled micro- and nanoarchitectures. The author provides an in-depth representation of the advanced theoretical and numerical models for analyzing key effects, which underlie engineering of transport, superconducting and optical properties of micro- and nanoarchitectures.

Free Download Topology: An Introduction with Application to Topological Groups By George McCarty, Mathematics
2011 | 304 Pages | ISBN: 0486656330 | PDF | 22 MB
This superb text offers a thorough background in elementary point set topology. Topics includesets and functions, groups, metric spaces, topologies, topological groups, compactness and connectedness, function spaces, the fundamental group, the fundamental group of the circle, locally isomorphic groups, and more. Exercises and problems appear throughout the text. 1967 edition.

Free Download Topological Methods for Delay and Ordinary Differential Equations:
With Applications to Continuum Mechanics
English | 2024 | ISBN: 3031613368 | 227 Pages | PDF EPUB (True) | 25 MB

Free Download Topological Model Theory by Jörg Flum , Martin Ziegler
English | PDF | 1980 | 161 Pages | ISBN : 3540097325 | 5.9 MB
The task of model theory is to investigate mathematical structures with the aid of formal languages. Classical model theory deals with algebraic struc- tures. Topological model theory investigates topological structures. A to- pological structure is a pair (=,a) consisting of an algebraic structure ~ and a topology ~ on A. Topological groups and topological vector spaces are examples. The formal language in the study of topological structures is L t- This is the fragment of the (monadic) second-order language (the set variab- les ranging over the topology ~) obtained by allowing quantification over set variables in the form 3X(t e X ^ ~), wheret is a term and the second- order variable X occurs only negatively in ~ (and dually for the universal quantifier). Intuitively, L t allows only quantifications over sufficiently small neighborhoods of a point.