Benedetto Scoppola

The westward drift of the lithosphere: A rotational drag?

Net westward rotation of the lithosphere relative to the underlying mantle is a controversial phenomenon fi rst attributed to tidal effects, and later to the dynamics of mantle convection. In spite of a number of independent geological and geophysical arguments for westward tectonic drift, this phenomenon has received little recent attention. We suggest that this differential rotation is a combined effect of three processes: (1) tidal torques act on the lithosphere generating a westerly directed torque decelerating Earth’s spin; (2) the downwelling of the denser material toward the bottom of the mantle and in the core slightly decreases the moment of inertia and speeds up Earth’s rotation, only partly counterbalancing the tidal drag; (3) thin (3– 30 km) layers of very low viscosity hydrate channels occur in the asthenosphere. It is suggested that shear heating and the mechanical fatigue self-perpetuate one or more channels of this kind, which provide the necessary decoupling zone of the lithosphere.

Beta function and Schwinger functions for a many fermions system in one dimension. Anomaly of the Fermi surface

We present a rigorous discussion of the analyticity properties of the beta function and of the effective potential for the theory of the ground state of a one dimensional system of many spinless fermions. We show that their analyticity domain as a function of the running couplings is a polydisk with positive radius bounded below, uniformly in, all the cut offs (infrared and ultraviolet) necessary to give a meaning to the formal Schwinger functions. We also prove the vanishing of the scale independent part of the beta function showing that this implies the analyticity of the effective potential and of the Schwinger functions in terms of the bare coupling. Finally we show that the pair Schwinger function has an anomalous long distance behaviour.

An improvement of the lovász local lemma via cluster expansion

An old result by Shearer relates the Lovasz local lemma with the independent set polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition function of the hard-core lattice gas on graphs. We use this connection and a recent result on the analyticity of the logarithm of the partition function of the abstract polymer gas to get an improved version of the Lovasz local lemma. As an application we obtain tighter bounds on conditions for the existence of Latin transversal matrices.

Discrete time GI/Geom/1 queueing system with priority

We study a discrete time single server system with generic distribution of the number of arrivals in a time slot, geometric distribution of the service time and two classes of customers. The customers can be served only when each time slot begins. The customers of the second class can be served only if the customers of the first class are absent. The model is motivated by the description of the congestion in the information networks. We give a complete description of this systems: we are able to compute the expected waiting time of the customers of the two classes, and solving a boundary value problem we are able to write the probability distribution of the length of the queue. To obtain these results, we use judiciously the standard technique of the generating function of the probability distribution. Although the boundary value problem is relatively easy, it is has to be pointed out that the generating function is not simply the product of two independent generating functions for the two classes.

The Analyticity Region of the Hard Sphere Gas. Improved Bounds

Abstract We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in d dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For d=2, for instance, our estimate is about 40% larger than the classical one.

On Decay of Correlations for Unbounded Spin Systems with Arbitrary Boundary Conditions

We propose a method based on cluster expansion to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external field. By this method we study the spin–spin truncated correlations of various systems, including the case of infinite range simply integrable interactions, and we show how suitable boundary conditions and/or external fields may improve the decay of the correlations.

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

Abstract: Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site Wr(𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe3/q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for Wr(𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice.

POLYMER GAS APPROACH TO N-BODY LATTICE SYSTEMS

We give a simple proof, based only on combinatorial arguments, of the Kotecký–Preiss condition for the convergence of the cluster expansion. Then we consider spin systems with long-range N-body interactions. We prove directly, using the polymer gas representation, that the pressure may be written in terms of an absolutely convergent series uniformly in the volume when the interaction is summable in a suitable sense. We also give an estimate of this radius of convergence. In order to get the proof we use a method introduced by Cassandro and Olivieri in the early 1980s. We apply this method to various concrete examples.

CRITICAL (Phi^{4}_{3,\epsilon})

The Euclidean

Some spin glass ideas applied to the clique problem

(\phi^{4})_{3,\epsilon