Library of Congress Cataloging-in-PublicationAll rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. PrefaceIt is hard to find a field in theoretical physics which can compete with the theory of phase transitions and critical phenomena with respect to the number of written textbooks, reviews and monographs. In our opinion, writing a new book can be justified only by treating in a different manner new trends existing in the area. What do we have in mind in our case? There are just a few books on critical phenomena in systems with confined geometry: a collection of reprints [Cardy, ed. (1988)], a collection of reviews [Privman, ed. (1990)], and the monograph [Krech (1994)] on the Casimir effect. Indeed, in some modern texbooks on critical phenomena one can find special chapters devoted to this topic, see, e.g., [Cardy (1996)], [Domb (1996)], [Zinn-Justin (1996)], [Henkel (1999)]. Against the background of the numerous papers that appear annually, the gap in the monographic literature on the subject is obvious. The present book attempts to partially fill up this gap. We hope also to give our modest contribution in spreading the scaling ideas for fruitful interpretation and analysis of phase transitions in classical and quantum systems of finite volume. It is a well known fact that the volume is an irrelevant parameter for the local properties of a macroscopic system and, therefore, can be chosen arbi trary large. The conventional statistical mechanical theory studies abstract systems, consisting of infinitely many particles in an infinite volume, due to the essential simplifications that occur in their description. Moreover, it becomes possible to describe phase transitions mathematically in terms of discontinuous or singular behavior of some thermodynamic functions. In constructing the above, so called thermodynamic limit [Van Hove (1949) VU1Preface tities. For example, in the canonical Gibbs ensemble the increase in the number of particles N has to be accompanied by a proportional increase in the volume V, so that the density p = N/V be constant. Any intensive quantity ay of a finite system can be written in the form ay = a,oo + Say, where a^ is the bulk value and Say is a finite-size correction which tends to zero as V -► oo. The finite-size correction Say contains a more detailed information about the shape of the system and the boundary conditions. Usually, the correction term becomes essential under rather special condi tions, e.g., in the vicinity of a second-order phase transition. When the relevant thermodynamic parameters approach a critical point, t...

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By means of differential scanning calorimetry and from a review of published data we demonstrate in this work that low-molecular weight kosmotropic substances (water-structure makers) of different chemical structure such as disaccharides, proline, and glycerol have identical effects on the phase behavior of several kinds of phospholipids and glycolipids. These substances favor formation of the high-temperature inverted hexagonal phase (H(II)) and the low-temperature lamellar crystalline (L(c)) and gel (L( β )) phases at the expense of the intermediate lamellar liquid-crystalline phase (L( α )). The latter phase may completely disappear from the phase diagram at high enough solute concentration. By contrast, chaotropic substances (water-structure breakers) such as sodium thiocyanate and guanidine hydrochloride expand the existence range of L( α ) at the expense of the adjacent L( β ) and H(II) phases. Moreover, chaotropes are able to induce the appearance of missing intermediate liquid-crystalline phases in lipids displaying direct L( β )→H(II) transitions in pure water. In previous publications we have considered the influence of chaotropic and kosmotropic substances on the lipid phase behavior as a manifestation of their indirect (Hofmeister) interactions with the lipid aggregates. For a quantitative characterization of this effect, here we derive a general thermodynamic equation between lipid phase transition temperature and solute concentration, analogous to the Clapeyron-Clausius equation between transition temperature and pressure. It provides a clear description in physical quantities of the disparate effects of kosmotropic and chaotropic substances on the relative stability of the lipid-water phases. According to this equation, the magnitude of the solute effect is proportional to the hydration difference of the adjacent lipid phases and inversely proportional to the transition latent heat. The sign and magnitude of the transition shifts depend also on the degree of solute depletion (for kosmotropes) or enrichment (for chaotropes) at the interfaces, in comparison to the solute concentration in bulk water.

Computer simulations of the totally asymmetric simple-exclusion process on chains with a double-chain section in the middle are performed in the case of random-sequential update. The outer ends of the chain segments connected to the middle double-chain section are open, so that particles are injected at the left end with rate alpha and removed at the right end with rate beta. At the branching point of the graph (the left end of the middle section) the particles choose with equal probability 1/2 which branch to take and then simultaneous motion of the particles along the two branches is simulated. With the aid of a simple theory, neglecting correlations at the junctions of the chain segments, the possible phase structures of the model are clarified. Density profiles and nearest-neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained and discussed. Cross correlations are found to exist between equivalent sites of the branches of the middle section whenever they are in a coexistence phase.

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We consider the discrete-time evolution of a finite number of particles obeying the totally asymmetric exclusion process with backward-ordered update on an infinite chain. Our first result is a determinant expression for the conditional probability of finding the particles at given initial and final positions, provided that they start and finish simultaneously. The expression has the same form as the one obtained by J. Stat. Phys. 88, 427 (1997)] for the continuous-time process. Next we prove that under some sufficient conditions the determinant expression can be generalized to the case when the particles start and finish at their own times. The latter result is used to solve a nonstationary zero-range process on a finite chain with open boundaries.

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