A collection of review talks and popular science papers by Lev Okun. The talks were given at major international conferences on elementary particle physics during the 1980s. The papers discuss experimental tests of fundamental physical principles and the concept of mass in relativity theory.

The interest in membranes and higher dimensional extended geometrical objects was inspired by the great successes of the string and superstring, first in 1968-73 as a theory of hadrons and then since 1984 as a “theory of everything” — a unified theory of all interactions, including quantum gravity. In particular, membranes, “supermembranes” and “spinning membranes” have been studied since 1985; an unexpected connection with supergravity opened in 1988 some new prospects for a quantized theory. General theorems about higher dimensional...

Gauge theory, which underlies modern particle physics as well as the theory of gravity, and hence all of physics as we know it today, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. Unfortunately, in view of the pressure to cover aspects of the theory that are necessary for its many important applications, very little space is usually devoted in textbooks and graduate courses to the treatment of these concepts. The present small volume is an attempt to help in some degree to redress this imbalance in the literature. The topics...

This is a series of lecture notes on nonlinear dynamics for physicists. The level is that of an advanced undergraduate or beginning graduate student. The main aim of these lectures is to present a balance of qualitative and quantitative material. The book also aims to address three main questions about nonlinear dynamics: what is nonlinear dynamics all about and what makes it differ from linear dynamics which permeate all familiar textbooks?; from the physicist's point of view, why should we study nonlinear systems and leave the comfortable territory of linearity?; and how can one progress in...

This book considers molecular structural information, statistical methods and thermodynamic measurements, and the ways in which the relative role of each differs from another. By putting together selected papers in a single publication, the book highlights the cohesive aspects of certain advances through time and development, and can aid historical studies. Several papers from journals not widely circulated can also be found in this selection of papers.

This work presents a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This edition contains three new surveys covering geometric constraint solving, computational geometry and the Exact Computation Paradigm.

This text introduces a rapidly growing new research area - the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behaviour of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our universe shortly after the Big Bang. In particular, chaos is rediscovered in a new appearance in these...

The phase structure of particle physics shows up in matter at extremely high densities and/or temperatures as they were reached in the early universe, or in heavy-ion collisions, as they are performed in laboratory. This work covers a variety of analytical and numerical tools that are needed to study the phase structure of particle physics.