Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.

Beyond the world of atoms, at scales smaller than the smallest nuclei, a new world comes into view, populated by an array of colorful elementary particles: strange and charmed quarks, muons and neutrinos, gluons and photons, and many others, all interacting in beautifully intricate patterns. Beyond the Nanoworld tells the story of how this new real

Analysis and dissociation have proved to be useful tools to understand the basic functions of the brain and the mind, which therefore have been decomposed to a multitude of ever smaller subsystems and pieces by most scientific approaches. However, the understanding of complex functions such as consciousness will not succeed without a more global consideration of the ways the mind-brain works. This implies that synthesis rather than analysis should be applied to the brain. The present book offers a collection of contributions ranging from sensory and motor cognitive neuroscience to mood management and thought, which all focus on the dissociation between conscious (explicit) and nonconscious (implicit) processing in different cognitive situations. The contributions in this book clearly demonstrate that conscious and nonconscious processes typically interact in complex ways. The central message of this collection of papers is: In order to understand how the brain operates as one integrated whole that generates cognition and behaviour, we need to reassemble the brain and mind and put all the conscious and nonconscious pieces back together again. (Series B)

What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n

Computational Physics. Selected Methods, Simple Exercises, Serious Applications is an overview written by leading researchers of a variety of fields and developments. Selected Methods introduce the reader to current fields, including molecular dynamics, hybrid Monte-Carlo algorithms, and neural networks. Simple Exercises give hands-on advice for effective program solutions from a small number of lines to demonstration programs with elaborate graphics. Serious Applications show how questions concerning, for example, aging, many-minima optimisation, or phase transitions can be treated by appropriate tools. The source code and demonstration graphics are included on a 3.5" MS-DOS diskette.

Addressing the need for an up-to-date reference on silicon devices and heterostructures, Beyond the Desert 99 reviews the technology used to grow and characterize Goup IV alloy films. It covers the theory, device design, and simulation of heterojunction transistors, emphasizing their relevance in developing the technologies involving strained layer

The most recent LEP data is included in the lectures. The subjects include Higgs physics, KM angles, weak CP violation, neutron electric dipole moment, SUSY phenomenology, radiative corrections, and e+e- experiments.

In recent years very active research has been going on to understand the physics and chemistry of clusters, an intermediate state of matter between atoms and solids. Great excitement has been added to these efforts with the recent discovery of a new form of carbon, the fullerene and its aggregates, and subsequent observations of superconductivity with alkali doping. This volume critically reviews the recent progress made in the area of clusters and discusses the new problems opened up with the ongoing developments in fullerenes.

Optic flow provides all the information necessary to guide a walking human or a mobile robot to its target. Over the past 50 years, a body of research on optic flow spanning the disciplines of neurophysiology, psychophysics, experimental psychology, brain imaging and computational modelling has accumulated. Today, when we survey the field, we find independent lines of research have now converged and many arguments have been resolved; simultaneously the underpinning assumptions of flow theory are being questioned and alternative accounts of the visual guidance of locomotion proposed. At this critical juncture, this volume offers a timely review of what has been learnt and pointers to where the field is going.