Graded Cluster Expansion for Lattice Systems

In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of disordered lattice systems in the Griffiths’ phase. We suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely, large regions are widely separated. We then show how it is possible to construct a convergent multi-scale cluster expansion.The authors acknowledge the support of Cofinanziamento MIUR.     

Space-time decay of Navier–Stokes flows invariant under rotations

We show that the solutions to the non-stationary Navier–Stokes equations in (d=2,3) which are left invariant under the action of discrete subgroups of the orthogonal group O(d) decay much faster as than in generic case and we compute, for each subgroup, the precise decay rates in space-time of the velocity field.     

Sliding-induced decoupling and charge transfer between the coexisting Q1 and Q2 charge density waves in NbSe3

Using high-resolution x-ray scattering in the presence of an applied current, we report evidence for a dynamical decoupling between the two NbSe3 charge-density waves (CDWs), Q1 (T(C1)=145 K) and Q2 (T(C2)=59 K), coexisting below T(C2). Simultaneous and oppositely directed shifts of the relevant CDW superlattice spots develop above a threshold current which we identify as the depinning threshold I(C1) for the more strongly pinned upper CDW Q1 (I(C1) approximately 10I(C2)). In contrast with shifts induced by current conversion processes, the present effect is not current polarized and is not limited to the current-contact regions. We propose a model which explains this instability through a sliding-induced charge transfer between the two electronic reservoirs corresponding to the Q1 and Q2 CDWs.     

Physical limits to communication

The limits posed by physics to the quantity of information that can be transmitted with a certain amount of power are investigated. The same ultimate limits are found for transmission of information encoded using matter and massless fields.     

Nonlinear Liouville theorems for Grushin and Tricomi operators

The aim of this paper is to study necessary conditions for existence of weak solutions of the inequality

     

Parallel connections over symmetric spaces

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.     

Integrable model for interacting electrons in metallic grains.

We find an integrable generalization of the BCS model with nonuniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe ansatz. Uniform pairing and Coulomb interaction are obtained as the "isotropic limit" of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.     

Influence of low intensity noise on assemblies of diffusively coupled chaotic cells

The effect of time-correlated and white Gaussian noises of low intensity on one-dimensional arrays consisting of diffusively coupled chaotic cells is analyzed. An improvement or worsening of the synchronization between cells of the array driven by low-intensity colored noise is observed for a resonant interval of time correlation values. A comparison between colored and white noise and additive and multiplicative contribution has been carried out investigating the nonlinear cooperative effects of noise strength, correlation time, and coupling strength to control spatiotemporal chaos in coupled arrays of chaotic cells. The possibility to distinguish highly correlated areas of a diffusively coupled network of cells by using low-intensity time correlated noise is discussed. (c) 2001 American Institute of Physics.     

Effect of preparation and metal content on the introduction of Fe in BEA zeolite, studied by DR UV-vis, EPR and Mössbauer spectroscopy

Fe-containing SiBEA zeolites were prepared by a two-step postsynthesis method: creation of vacant T-sites by dealumination of tetraethylammonium BEA zeolite with nitric acid and then impregnation of the resulting SiBEA zeolite with an aqueous solution of Fe(NO₃)₃. X-ray diffraction shows that iron is incorporated in SiBEA at lattice sites. The presence of Fe in its oxidation state +3 and at isolated tetrahedral sites for low metal content, was demonstrated by diffuse reflectance UV-vis, EPR and Mössbauer spectroscopy. For high iron content, diffuse reflectance UV-vis and Mössbauer spectra revealed the additional presence of extra-lattice FeO_x oligomers and superparamagnetic Fe-oxyhydroxide. Mössbauer spectroscopy identified superparamagnetic Fe-oxyhydroxide as the main phase when basic conditions are used for the preparation.     

Simple high-performance liquid chromatography method for alpha-tocopherol measurement in Rosmarinus officinalis leaves. New data on alpha-tocopherol content.

A simple HPLC method for vitamin E (alpha-tocopherol) measurement in the leaves of Rosmarinus officinalis has been developed and validated. It has enabled new data for alpha-tocopherol content to be established. The leaves, recently harvested, were dried in a microwave oven and crushed; then, alpha-tocopherol was directly extracted from portions of ground material with acetone, by probe sonication. After centrifugation the acetonic extract was analysed by HPLC with ergocalciferol (vitamin D2) added as internal standard and a gradient elution with a Nucleosil C18 column at 35 degrees C. Validation parameters of the method can be considered adequate. For standards: linearity is r=0.999, recovery is 100+/-2%, intra-assay precision has RSD=+/-3% and inter-assay precision has RSD=+/-6%. For samples: linearity is r=0.99, recovery: 93+/-7%, intra-assay precision has RSD=+/-4% and inter-assay precision has RSD=+/-7%.