Complex liquids constitute a basic element in modern materials science; their significant features include self-assembly, mesoscale structures, complex dynamics, unusual phases and enormous sensitivity to perturbations. Understanding their nature and properties are a great challenge to modern materials science that demands novel approaches. This book focuses on nonlinear dielectric phenomena, particularly on nonlinear dielectric spectroscopy (NDS), which may be considered a possible successor to broadband dielectric spectroscopy (BDS). NDS phenomena directly coupled to mesoscale heterogeneity fluctuations, so information obtained in this way is basically complementary to BDS tests. The book also discusses the application of NDS in a set of complex liquid systems: glassy liquids, liquid crystals, liquids with critical point phenomena, and bio-relevant liquids. The complementary application of NDS and BDS may allow the discovery of universal patterns for the whole category of complex liquids. Written by specialists in the field of nonlinear dielectric studies, theoreticians and experimentalists, ranging from solid state physics to biophysics, the book is organized so that it can serve as a basic textbook for a non-experienced reader.

This book is unique in supplying a comprehensive presentation of high pressures, negative pressures, random constraints and strong electric field exogenic (external) impacts on various soft matter systems. The book is an excellent guide in this novel and still puzzling research area. The book comes as a result from the ARW NATO brainstorming discussion in Odessa, Ukraine (8-12 Oct. 2005). It contains 31 papers prepared by key specialists in the field.

This book introduces the ideas and concepts of nonlinear dielectric spectroscopy, outlines its history, and provides insight into the present state of the art of the experimental technology and understanding of nonlinear dielectric effects. Emphasis is on what can be learned from nonlinear experiments that could not be derived from the linear counterparts. The book explains that nonlinear dielectric spectroscopy can be used as a tool to measure structural recovery or physical aging, as well as connections between dynamics and thermodynamic variables such as enthalpy and entropy. Supercooled liquids in their viscous regime are ideal candidates for investigating nonlinear effects, because they are particularly sensitive to changes in temperature, and thus also to changes in the electric field. Other interesting materials covered are plastic crystals and complex liquids near criticality. The book also points out that, compared with other techniques such as mechanical shear experiments, the nonlinear regime of dielectric spectroscopy is special in the sense that the energies involved always remain small compared with thermal energies. To demonstrate this, nonlinear features of mechanical experiments are discussed. Theoretical approaches to nonlinear effects are particularly complicated because the tools available for the linear regime no longer apply. As a result, there is no single generally accepted theory to nonlinear dielectric responses of real liquids. Various approaches to nonlinear dielectric features have been reported, and the different aspects are communicated in several chapters. The book communicates recent progress most effectively through individual contributions from specialists in their respective fields. Chapter 'Third and Fifth Harmonic Responses in Viscous Liquids' is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles.

This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis, material characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, and finally, the biological effects and medical applications of electromagnetic fields.

Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker-Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.