Coulomb interaction symmetries and the Mayer series in the two-dimensional dipole gas

We study the Mayer series of the two-dimensional dipole gas in the high-temperature, low-density regime. Without performing any multiscale analysis, we obtain bounds showing that the Mayer coefficients are finite in the thermodynamic limit. These bounds are obtained by exploiting a particular partial symmetry of the interaction (which we nameO-symmetry), already used in some problems related to the two-dimensional Coulomb gas. By direct bounds on some Mayer graphs we also conjecture that any technique based uniquely on theO-symmetry will not be sufficient to prove analyticity of the series.     

A note on ω-permutable semigroups

Communicated by Dominique Perrin     

Numerical analysis of a shock-wave solution of the Enskog equation obtained via a Monte Carlo method

In this paper a planar stationary shock-wave-like solution of the Enskog equation obtained via a Monte Carlo technique is studied; both the algorithm used to obtain the solution and the qualitative behavior of the macroscopic quantities are discussed in comparison with the corresponding solution of the Boltzmann equation.     

A mixed algorithm for the calculation of rapidly varying fluid flows: The impulsively started circular cylinder

A mixed discrete Fourier transform-Finite difference algorithm is developed and used for the calculation of rapidly changing viscous fluid flows past a circular cylinder. The numerical approach has been designed to overcome certain difficulties arising for high Reynolds number simulations. The foremost advantage of the technique lies in its fast calculations of the convolution sums portraying the convective terms of the governing equations. Third-order spatial discretizations and fourth-order time marching are implemented. New schemes are proposed for the boundary conditions at the solid wall and at large distances. The techniques are tested on a case study with other schemes (summarized by Roache¹) in order to obtain an optimal choice. Definite indications on the stability and accuracy of boundary condition schemes are achieved. Support for the statement of dominant importance of boundary conditions is also given. A comparison of computational results with experimental data is presented for the case study of the flow past an impulsively started cylinder at Reynolds number 20. The time development of the symmetrical zone of recirculation, which is formed at an early stage of the flow, has been studied for 300 ≤ Re ≤ 9500 by means of the proposed algorithm. Computational results, comparisons with experimental data² and discussion of upper limits of validity of the procedure will be presented in a companion paper.     

Ab initio calculations including solvent effects of the structure of pyrazine, 4-nitropyridine and dicyanobenzenes ion pairs

The potential surfaces of pyrazine, 4-nitropyridine, 1,2-, 1,3-, 1,4- dicyanobenzene radical anions have been calculated within theab initio and electrostatic molecular potential formalism, including the effect of the solvent. These potential surfaces suggest models of ion pairs with alkali cations, which are in agreement with those deduced from related ESR spectra.     

Two-group kinetic theory of vehicular traffic

Summary We study a two-group model of vebicular traffic oli a highway which generalizes the Prigogine-Herman model. According to the two-group theory, drivers are divided into “slow” and “fast”. Correspondingly, we introduce a slow and a fast desired distribution representing the program that drivers of each of the two groups wish to follow. We first prove the existence and the uniqueness of a solution belonging to a suitable Banach space by using the theory of semigroups. Then, we indicate some sufficient conditions for the stability of an x and t independent solution.

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Sommario Si generalizza il modello di Prigogine-Herman del traffico automobilistico su un'autostrada, introducendo due gruppi di guidatori: i “lenti” ed i “veloci”. Ognuno dei due gruppi riene caratterizzato da un'opportuna funzione “desiderio”, che traduce i programmi che i guidatori intendono seguire nel corso del loro viaggio. Facendo poi uso della teoria dei semigruppi, si prova l'esistenza e l'unicità di una soluzione appartenente ad un opportuno spazio di Banach e si danno condizioni sufficienti per la stabilità.

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Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica).As the choice of the appropriate model for these problems is still a controversial matter, the Editorial Board welcomes any comment or discussion from the readers.