Boltzmann''s formula S = In[ W (E) ] defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay OCo for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann''s original definition of the microcanonical ensemble. Starting from Boltzmann''s formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phase transitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E, N) . Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum. The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum. Contents: The Mechanical Basis of Thermodynamics; Micro-Canonical Thermodynamics of Phase Transitions Studied in the Potts Model; Liquid-Gas Transition and Surface Tension Under Constant Pressure; Statistical Fragmentation Under Repulsive Forces of Long Range; The Collapse Transition in Self-Gravitating Systems First Model-Studies; Appendices: On the Historical Development of Statistical Nuclear Multifragmentation Models; The Micro-Canonical Ensemble of Na-Clusters; Some General Technical Aspects of Micro-Canonical Monte Carlo Simulation on a Lattice. Readership: Advanced level graduate students, lecturers and researchers in statistical and condensed matter physics."

Boltzmann's formula S = In(W(E) defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay -- for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble. Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phasetransitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E, N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum. The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. New insights into the many facets of the many-body physics of the critical point are presented. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum.

This Book Emphasises The Development Of Problem Solving Skills In Undergraduate Science And Engineering Students.The Book Provides More Than 350 Solved Examples With Complete Step-By-Step Solutions As Well As Around 100 Practice Problems With Answers.Also Explains The Basic Theory, Principles, Equations And Formulae For A Quick Understanding And Review. Can Serve Both As A Useful Text And Companion Book To Those Pre-Paring For Various Examinations In Physics.

Scientists and engineers are increasingly making use of simulation methods to solve problems which are insoluble by analytical techniques. Monte Carlo methods which make use of probabilistic simulations are frequently used in areas such as numerical integration, complex scheduling, queueing networks, and large-dimensional simulations. This collection of papers arises from a conference held at the University of Nevada, Las Vegas, in 1994. The conference brought together researchers across a range of disciplines whose interests include the theory and application of these methods. This volume provides a timely survey of this field and the new directions in which the field is moving.

Nucleation of Water: From Fundamental Science to Atmospheric and Additional Applications provides a comprehensive accounting of the current state-of-the-art regarding the nucleation of water. It covers vapor-liquid, liquid-vapor, liquid-ice and vapor-ice transitions and describes basic kinetic and thermodynamic concepts in a manner understandable to researchers working on specific applications. The main focus of the book lies in atmospheric phenomena, but it also describes engineering and biological applications. Bubble nucleation, although not of major atmospheric relevance, is included for completeness. This book presents a single, go-to resource that will help readers understand the breadth and depth of nucleation, both in theory and in real-world examples. - Offers a single, comprehensive work on water nucleation, including cutting- edge research on ice, cloud and bubble nucleation - Written primarily for atmospheric scientists, but it also presents the theories in such a way that researchers in other disciplines will find it useful - Written by one of the world's foremost experts on ice nucleation

CRIS (Catania Relativistic Ion Studies) is a new series of Topical Conferences to be held at regular intervals in Catania or in its environs. Aim of the CRIS Conferences is to gather active researchers from several countries to discuss specific hot topics in the field of heavy ion physics.The first CRIS Conference, CRIS '96, has been devoted to “Critical Phenomena and Collective Observables”, a quite hot topic after the recent experimental evidences of a liquid-gas phase transition in finite nuclei found by the EOS and ALADiN Collaborations and the progress made in the understanding of the relevance of collective observables, like flow and balance energy for the study of the Nuclear Equation of State.

The workshop was about the developments of the thermodynamical and dynamical behavior of many-body systems in which the interactions decay very slowly with the distance: they present very strange properties, not found in the other systems. The possibility of testing the theoretical ideas in laboratory systems was the most innovative issue.

Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose--Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student.

Provides a critical elaboration of thermodynamics as applied to phase transition, discusses the relationship between the ensemble theory of classical and quantum statistics and thermodynamics, and then obtains Maxwell-Boltzmann, Fermi-Dirac and the Bose-Einstein distributions.