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Nonlinear Analysis - Theory and Methods
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
Flowing Matter
This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena. Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents. Depending on the microscopic interactions, an assembly of molecules or of mes...
Computational Methods for Physicists
This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.
Diamond and Related Nanostructures
Over the past twenty years, the field of carbon structures has been invigorated by the discovery of fullerenes and carbon nanotubes. These nano-structured carbons have attracted a tremendous interest in the fundamental properties of discrete carbon molecules, leading to the discovery of novel complex crystalline and quasi-crystalline materials. As a consequence, a variety of applications have been developed, including technical and bio-medical materials and miniaturized tools. Diamond and Related Nanostructures focuses on the advances in the area of diamond-like carbon nanostructures (hyper-structures built from fullerenes and/or carbon nanotube junctions) and other related carbon nanostructures. Each chapter contributes to the topic from different fields, ranging from theory to synthesis and properties investigation of these new materials. This volume brings together the major findings in the field and provides a source of inspiration and understanding to advanced undergraduates, graduates, and researchers in the fields of Physics, Graph Theory, Crystallography, Computational and Synthetic Chemistry.
Time-Resolved Spectroscopy in Complex Liquids
Time-Resolved Spectroscopy in Complex Liquids is intended to introduce the experimental researchers to state-of-the-art techniques in the study of the dynamics of complex liquids. The contributors concentrate on time-resolved optical spectroscopy, which recently produced many relevant results and new information about complex liquids. This is an emerging topic of soft-matter science and this book provides the most up-to-date account of new development.
Complex Geometry and Dynamics
This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading experts in their respective fields. This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.
Complex Analysis
This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.
Surfaces and Interfaces of Liquid Crystals
This book describes the state of the art of our understanding of liquid-crystal interfaces on a molecular level. The interactions of liquid crystal molecules with a surface play an essential role in the operation of liquid crystal displays (LCD's) and other LC devices that are based on the controllable anchoring of LC molecules on polymer coated surfaces. This book addresses the microscopic interaction between a macromolecule (liquid crystal, polymer) and a wall, using state of the art surface and interface-sensitive experimental techniques, such as Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), Linear and Nonlinear Optical Microscopy and (Dynamic) Light Scattering (DLS). These experimental techniques were complemented with computer simulations and supra molecular chemistry methods to develop controllable polymeric surfaces.
Recent Advances in Mathematical Analysis
This book collects selected peer reviewed papers on the topics of Nonlinear Analysis, Functional Analysis, (Korovkin-Type) Approximation Theory, and Partial Differential Equations. The aim of the volume is, in fact, to promote the connection among those different fields in Mathematical Analysis. The book celebrates Francesco Altomare, on the occasion of his 70th anniversary.
