Mean-field theory of temperature cycling experiments in spin-glasses

We study analytically the effect of temperature cyclings in mean-field spin-glasses. In accordance with real experiments, we obtain a strong reinitialization of the dynamics on decreasing the temperature combined with memory effects when the original high temperature is restored. The same calculation applied to mean-field models of structural glasses shows no such reinitialization, again in accordance with experiments. In this context, we derive some relations between experimentally accessible quantities and propose new experimental protocols. Finally, we briefly discuss the effect of field cyclings during isothermal aging.Comment: Some misprints corrected, references updated, final version to apper in PR

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

Static and dynamic typing for the termination of mobile processes

A process terminates if all its reduction sequences are finite. We propose two type systems that ensure termination of pi-calculus processes. Our first type system is purely static. It refines previous type systems by Deng and Sangiorgi by taking into account certain partial order information on names so to enhance the techniques from term rewriting (based on lexicographic and multiset orderings) that underpin the proof of termination. The second system is mixed, in that it combines a static and a dynamic analysis. During the static analysis, processes are annotated with assertions. These are then used at run time to monitor the execution of processes. An exception may be raised if certain conditions that may lead to divergence are met. We illustrate the expressiveness of the solutions proposed with a few examples of programming idioms that were beyond reach for previous type systems

Termination in higher-order concurrent calculi

We study termination of programs in concurrent higher-order languages. A higher-order concurrent calculus combines features of the \u3bb-calculus and of the message-passing concurrent calculi. However, in contrast with the \u3bb-calculus, a simply-typed discipline need not guarantee termination and, in contrast with message-passing calculi such as the \u3c0\u3c0-calculus, divergence can be obtained even without a recursion (or replication) construct. We first consider a higher-order calculus where only processes can be communicated. We propose a type system for termination that borrows ideas from termination in rewriting systems (and following the approach to termination in the \u3c0-calculus in [3]). We then show how this type system can be adapted to accommodate higher-order functions in messages. Finally, we address termination in a richer calculus that includes localities and a passivation construct, as well as name-passing communication. We illustrate the expressiveness of the type systems on a few examples

Towards \u2018up to context\u2019 reasoning about higher-order processes

Proving behavioural equivalences in higher-order languages is a difficult task, because interactions involve complex values, namely terms of the language. In coinductive (i.e., bisimulation-like) techniques for these languages, a useful enhancement is the \u2018up-to context\u2019 reasoning, whereby common pieces of context in related terms are factorised out and erased. In higher-order process languages, however, such techniques are rare, as their soundness is usually delicate and difficult to establish. In this paper we adapt the technique of unique solution of equations, that implicitly captures \u2018up-to context\u2019 reasoning, to the setting of the Higher-order \u3c0-calculus. Equations are written and solved with respect to normal bisimilarity, chosen both because of its efficiency \u2014 its clauses do not require universal quantifications on terms supplied by the external observer \u2014 and because of the challenges it poses on the \u2018up-to context\u2019 reasoning and that already show up when proving its congruence properties

Termination in Higher-Order Concurrent Calculi

We study termination of programs in concurrent higher-order languages. A higher-order concurrent calculus combines features of the $lambda$-calculus and of the message-passing concurrent calculi. However, in contrast with the $lambda$-calculus, a simply-typed discipline need not guarantee termination; and, in contrast with message-passing calculi such as the $pi$-calculus, termination can be obtained even without a recursion (or replication) construct. We first consider a higher-order calculus where only processes can be communicated. We propose a type system for termination that borrows ideas from termination in Rewriting Systems. We then show how this type system can be adapted to accommodate higher-order functions in messages. Finally, we address termination in a richer calculus, that includes localities and a passivation construct, as well as name-passing communication. We illustrate the expressiveness of the type systems on a few examples

Minimality results for the spatial logics

1 Introduction Over the last 15 years, a lot of research has gone into calculi of mobile processes.Among these, the ss-calculus is the best known. A number of other calculi, how-ever, have been put forward to study aspects of mobility not directly covere

On the representation of references in the Pi-Calculus

The \u3c0-calculus has been advocated as a model to interpret, and give semantics to, languages with higher-order features. Often these languages make use of forms of references (and hence viewing a store as set of references). While translations of references in \u3c0-calculi (and CCS) have appeared, the precision of such translations has not been fully investigated. In this paper we address this issue. We focus on the asynchronous \u3c0-calculus (A\u3c0), where translations of references are simpler. We first define \u3c0ref, an extension of A\u3c0 with references and operators to manipulate them, and illustrate examples of the subtleties of behavioural equivalence in \u3c0ref. We then consider a translation of \u3c0ref into A\u3c0. References of \u3c0ref are mapped onto names of A\u3c0 belonging to a dedicated \u201creference\u201d type. We show how the presence of reference names affects the definition of barbed congruence. We establish full abstraction of the translation w.r.t. barbed congruence and barbed equivalence in the two calculi. We investigate proof techniques for barbed equivalence in A\u3c0, based on two forms of labelled bisimilarities. For one bisimilarity we derive both soundness and completeness; for another, more efficient and involving an inductive \u201cgame\u201d on reference names, we derive soundness, leaving completeness open. Finally, we discuss examples of uses of the bisimilarities

Separability, Expressiveness, and Decidability in the Ambient Logic

The Amient Logic (AL) has been proposed for expressing properties of process mobility in the calculs of Mobile Ambients (MA) and a basis for query languages on, semistructured data.We study some basic questions concerning the descriptivend discriminant power of AL, focusing on the equivalence on processess induced by logic (=L). We consider MAa, and two Tuing complete subsets of it, MAIF and MA SYNIF, respectively defined by imposing a semantic and a syntactic constraint on process prefixes. The main contributions include : conductive and inductive operational characterisations of =L; An axiomatisation of +L on MA SYNIF, the construction of characteristics formulas for the processes in MAIF with respect to =L; the decidability of +L on MAIF and on MA SYN IF and its undecidability on MALa logique des Ambients (AL) a été introduite pour expérimenter des propriétés ayant trait à la mobilité des processus dans le calcul des Ambients Mobiles(MA), ainsi qu'en tant que fondement pour des langages de requêtes pour des données semi-structurées.Nous étudions un certain nombre de questions fondamentales ayant trait au pouvoir expressif de cette logique, en bous intéressant à l'équivalence sur les processus induite par la loqique (=L). nous considérons AM, Ainsi que deux sous-ensemble Turing complets de ce calcul, MAIF et MA SYNIF, définis par les biais de restrictions syntaxique et sémantique sur les termes préfixés..Parmi nos principales contributions, nous pouvons mentionner : deux caractérisations, coinductive et inductive, de =LM; une axiomatisation de =L sur MA SYNIF ; la construction de formules caractériques pour =L pour les processus de MAIF ; la décidabilitéde =L sur MAIF et sur MAI SYNF, et la non-décidabilité de cette relation sur A