A general method for the calculation of the mean residence time of water in monomictic lakes of simple morphometry is worked out on the same physical assumptions as those made by Piontelli and Tonolli (1964). After a short outline of the mathematical foundation of the method, the numerical procedure is presented, on which the computer code for the determination of the mean residence time is based. Finally some examples of the application of the method to Lake Maggiore and to a lake of complex morphometry (Lake of Lugano) are presented and discussed.Sur le calcul du temps moyen de résidence dans les lacs monomictiques Résumé.Nous avons développé une méthode générale de calcul du temps moyen de résidence de l'eau dans un lac monomictique de simple moirphométrie sur la base des mêmes hypothèses physiques que celles de Piontelli et Tonolli(1964), Après un bref exposé du fondement mathématique de la méthode, nous présentons le schéma de calcul sur lequel se base le code pour l'évaluation du temps moyen de résidence. Enfin nous présentons et discutons quelques exemples d'application de la méthode au lac Majeur et à un lac de morphométrie complexe (lac de Lugano).
A hindered-translator model including damping is constructed with the aim of accounting for the oneparticle motions in a liquid, in connection with slow-neutron scattering. Liquids which exhibit the Arrhenius law for self-diffusion are considered and the activation energy [7 0 is assumed to represent the energy barrier against translations for a single particle. In the absence of dissipation and for energies below the barrier, the hindered translator is allowed to carry out harmonic oscillations with frequency coo given by the mean field of force experienced by the particle in the liquid. Dissipation is taken into account using methods of nonequilibrium statistical mechanics. Dissipation is considered, first, on the weak-collision hypothesis, and it is assumed that no transitions between vibrational and translational states occur during the time the dynamic correlation persists. By looking into the phase space of the hindered translator at thermal equilibrium, its velocity autocorrelation function is shown to be a weighted superposition of the autocorrelation functions for vibrations and translations, respectively. Explicit expressions are found for their correlation times T 1 and r n , in terms of the interatomic potential
In the framework of the interaction of a neutron with molecular nuclei and with a special view to organic molecules (polyphenyls), a preliminary analysis is made in this paper on the scattering by bound protons in the benzene molecule (this molecule is assumed to be a fundamental dynamic unit). In evaluating the effect of the molecular dynamics on the scattering of thermal neutrons, several physical hypotheses have been tried. The main purpose of these assumptions is to enable us, when considering explicitly the dynamics of the proton, to investigate both the influence of the different individual features of the molecular dynamics and the effect of different mathematical approximations on the explicit consideration of such dynamical features. This has been performed with reference to experimental results both on integral quantities (e. g. the total scattering cross-section) and on differential ones. In the framework of the gas model we have first investigated the effect of a single " structure " parameter, namely the effective mass Mo. We have then considered a " molecular gas " by introducing two parameters (Krieger-Nelkin) : one, of the effective mass Mo type, accounting for rotations and translations and a second one formally taking into account the elastic vibrational transitions from the ground state. The possibility is here discussed of calculating the best fitted value of the parameter Mo from experimental data, the value of the vibrational parameter being determined once the frequency distribution of the proton in the molecule is known. The particular structure of this vibrational spectrum induced us to discuss a " two-vibrational model " in analogy to the Nelkin model for the H2O molecule, where, in the explicit consideration of the various degrees of freedom, the complicated vibrational spectrum has been replaced by an isotropic, very simplified one. Finally we have treated as predominant the purely vibrational features (still in the frame of the harmonic approximation), considering explicitly the anisotropy of the vibrational spectrum and evaluating in a more correct way the relation of the molecular orientations. In view of this, we started by neglecting (as a first approximation) the rotational and translational degrees of freedom; these will be appropriately introduced later by means of a correction in the vibrational spectrum in the low energy region. We also made a comparison between this analysis, which—in the frame work of an analogy with a polycrystalline assembly of graphite microcrystals — adopts the formalism of Schofield and Hassitt and the set of more refined and mathematically more correct assumptions contained in the Summit code which translates the Parks' viewpoint
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