Relaxation dynamics near the sol–gel transition: From cluster approach to mode-coupling theory

A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol–gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.     

Modal Extensions of Sub-classical Logics for Recovering Classical Logic

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 ⁰ extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems.     

Recovering a Logic from Its Fragments by Meta-Fibring

In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multiple-conclusion consequence relations and sequent calculi, respectively, are introduced. The main feature of these categories is the preservation, by morphisms, of meta-properties of the consequence relations, which allows, in several cases, to recover a logic by fibring of its fragments. The fibring in this categories is called meta−fibring. Several examples of well-known logics which can be recovered by meta-fibring its fragments (in opposition to fibring in the usual categories) are given. Finally, a general semantics for objects in Seq (and, in particular, for objects in Mcon) is proposed, obtaining a category of logic systems called Log. A general theorem of preservation of completeness by fibring in Log is also obtained.     

Frustrated percolation,spin glasses and glasses

Summary The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT _p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT _g in the same universality class of the Ising spin glass model. AboveT _p the time-dependent autocorrelation function is characterized by a single exponential, while forT _p>T>T _g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT _g the system is in glassy state with an infinitely long relaxation time. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

The NMR reciprocity theorem for arbitrary probe geometry

It is shown that the NMR reciprocity theorem is a variant of a problem considered by Lorentz in 1895. This formulation is quite general and applies to electric-dipole-based as well as coil-based or resonator-based magnetic resonance probes. The reasoning is related to, but different from, the proof of the reciprocity theorem for radiofrequency networks and for transmit/receive antenna systems in telecommunications. The signal-to-noise ratio of the NMR experiment is also discussed in very general terms.     

Dynamically induced effective interaction in periodically driven granular mixtures

We show that a granular mixture subject to horizontal oscillations can be reduced to a monodisperse system of particles interacting via an effective interaction. This interaction is attractive at short distances and strongly anisotropic, and its features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, which takes into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.     

Interplay between the glass and the gel transition

By changing the control parameters, many physical systems reach a slow dynamics regime followed by an arrested or a quasiarrested state. Examples, among others, are gels and glasses. In this paper, we discuss some experimental and theoretical results in polymer and colloidal systems, where gel and glass transitions interfere, and use models from Mode Coupling Theory(MCT)to illustrate the rich phenomenology observed. The continuous and the discontinuous transition lines, found in the MCT models,are considered suitable to describe respectively the gel and the glass transitions, so we suggest that the interplay between gel and glass may be interpreted in terms of the F_(13) MCT model, clarifying also the origin of logarithmic decays often observed in such systems. In particular, the theoretical predictions of the MCT in the F_(13) model are compared with Molecular Dynamics simulations in model systems for chemical gels and charged colloids.