Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species).
This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is [...]
This book is volume 1 of a two-volume set which describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state. Volume 2 will describe dynamical scaling in far-from-equilibrium relaxation behaviour and ageing.
The book begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the [...]
This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems.
In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology and bio-informatics – can be expressed as counting problems, in which specified graphs, or shapes, are counted.
One very [...]
Mary Sommerville (1780-1872), after whom Sommerville College Oxford was named, was the first woman scientist to win an international reputation entirely in her own right, rather than through association with a scientific brother or father.
She was active in astronomy, one of the most demanding areas of science of the day, and flourished in the unique [...]
This book provides an interdisciplinary overview of a new and broad class of materials under the unified name nanostructured soft matter. It covers materials ranging from short amphiphile molecules to block copolymers, proteins, colloids and their composites, microemulsions and bio-inspired systems, like vesicles. The book shines light on the fundamental question: how self-assembly of various [...]
Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO – developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since – plays [...]
Polarons in Advanced Materials will lead the reader from single-polaron problems to multi-polaron systems and finally to a description of many interesting phenomena in high-temperature superconductors, ferromagnetic oxides, conducting polymers and molecular nanowires. The book divides naturally into four parts. Part I introduces a single polaron and describes recent achievements in analytical and numerical studies [...]
