Classification of Phase Transitions and Ensemble Inequivalence, in Systems with Long Range Interactions

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific heats and other non-common behaviors. We propose a classification of microcanonical phase transitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence. We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensional fluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet been observed in such systems.     

Out-of-equilibrium states as statistical equilibria of an effective dynamics in a system with long-range interactions

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Nonequilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, such as two-dimensional incompressible fluids and wave-particle interaction in a plasma.     

Strangeness enhancement in Cu-Cu and Au-Au collisions at √S(NN)=200 GeV

We report new STAR measurements of midrapidity yields for the Λ, Λ[over ˉ], K(S)(0), Ξ(-), Ξ[over ˉ](+), Ω(-), Ω[over ˉ](+) particles in Cu+Cu collisions at √S(NN)==200 GeV, and midrapidity yields for the Λ, Λ[over ˉ], K(S)(0) particles in Au+Au at √S(NN)==200 GeV. We show that, at a given number of participating nucleons, the production of strange hadrons is higher in Cu+Cu collisions than in Au+Au collisions at the same center-of-mass energy. We find that aspects of the enhancement factors for all particles can be described by a parametrization based on the fraction of participants that undergo multiple collisions.     

Photochimie d'heterocycles azotes—V : Reactions de photosubstitution en serie heterocyclique: cas des p-nitrophenyl-1 pyrazoles et imidazoles

The photosubstitution reactions of eight 1-p-nitrophenylpyrazoles and two 1-p-nitrophenylimidazoles bearing different substituents in the heterocyclic ring have been studied. In the case of pyrazole derivatives, among the different nucleophiles utilized, only the acetate, cyanate and cyanide ions gave identifiable products. The two first ones lead to the 4-formyl derivative of the starting material. With the cyanide ion the reaction is more complicated, not only the 4-cyano derivative is formed but also the 4-carboxamido and several reduced products: p-amino, p-formamido, p-acetamido, p-carbamate and p-azoxypheny 1-1 pyrazoles. In the case of 1-p-nitrophenylimidazoles, the only interesting results have been obtained with the cyanide ion: formation of cyano- and hydroxymethylene-imidazoles.     

Photochimie d'hétérocycles azotés. IV. Transposition de type photo-fries des N-acétyl benzimidazolones

The photolysis of benzene or alcoholic solutions of N-acetyl-and N,N-diacetylbenzimidazolones gave mixtures of ortho- and para-rearrangements products accompanied to some extent with de-N-acylation. The different products have been identified by means of nmr, mass spectrometry and unambiguous synthesis.     

Strain gradient elastic homogenization of bidimensional cellular media

The present paper aims at introducing an homogenization scheme for the determination of strain gradient elastic coefficients. This scheme is based on a quadratic extension of homogeneous boundary condition (HBC). It allows computing strain elastic effective tensors. This easy-to-handle computational procedure will then be used to construct overall behaviors and to verify some theoretical predictions on strain gradient elasticity.     

Recognition and assignment of meso and dl diastereomers: Dimethyl α,α′-Dibromopimelate and N-benzyl-2,6-dicarbomethoxypiperidine

The assignment of meso and dl diastereomers is carried out by NMR analysis of the signals due to the methylene protons in two simple cases, namely, dimethyl α,α′-dibromopimelate (as an acyclic compound) and N-benzyl-2,6-dicarbomethoxypiperidine (as a cyclic compound). In the case of the heterocyclic compound, an nσσ* hyperconjugative interaction between the CH bond α to the heteroatom and the lone pair of the heteroatom can be used, and leads to the same assignment.     

Theory and experiments on elastic band gaps

We study elastic band gaps in nonhomogeneous periodic finite media. The finite-difference time-domain method is used for the first time in the field of elastic band-gap materials. It is used to interpret experimental data for two-dimensional systems consisting of cylinders of fluids (Hg, air, and oil) inserted periodically in a finite slab of aluminum host. The method provides good convergence, can be applied to realistic finite composite slabs, even to composites with a huge contrast in the elastic parameters of their components, and describes well the experiments.     

On the Sperner lemma and some colorings of graphs

In this journal, Daniel I. A. Cohen [2] gave a proof of the strong Sperner lemma based on “search” techniques of paths. Klaus Wagner [5] associates a particular tree to a labeled subdivision of a geometric simplex and proves that lemma by counting the number of vertices with an odd degree of that tree. In this paper we prove a general theorem about colorings of simplicial complexes by using a method similar to Wagner's. This theorem implies the strong Sperner lemma and can be used to study some colorings of graphs.