Asymptotic behaviour in some eikonal models for production

The high energy behaviour of the total cross section is investigated in the frame of eikonal models for high-energy production processes. The dynamics is introduced by means of phenimenological Hamiltonians; the results are compared with the results of other kinds of dynamics, particularly with some procedure of unitarization of the multiperipheral model.     

Pre-resonant enhancement of the Raman scattering from KI:Tl+

E_g and T_2g spectra at room and nitrogen temperature at several laser wavelengths are reported for KI:Tl⁺. As resonance with Tl⁺ -absorption bands is approached the optic phonon parts of the spectra are enhanced relative to the acoustic phonon parts, and distortions occur within the acoustic and optic parts of the spectra. A model for the scattering is employed which involves electron-phonon coupling to nearest and nn neighbors. Exchange and crystal field contributions to the electron-phonon coupling are distinguished.     

The liquid-phase oxidation of 2,4-dimethylpentane

The initiated oxidation of 2, 4-dimethylpentane in the neat liquid phase at 100°C with 760 torr O₂ gives more than 90% of a mixture of 2,4-dihydroperoxy-2,4-dimethylpentane and 2-hydroperoxy-2, 4-dimethylpentane in a ratio of 7:1. The rate of oxidation depends closely on the [initiator]^1/2, consistent with a mechanism in which chain termination occurs mostly by interactions of two 2-hydroperoxy-2, 4-dimethyl-4-pentylperoxy radicals. 2, 4-Dimethylpentane oxidizes only one sixth as fast as isobutane at the same rate of initiation at 100°C. In cooxidations of the same hydrocarbons, it is 0.71 as reactive as isobutane toward any of the peroxy radicals involved. 2, 4-Dimethylpentane oxidizes 7.5 times as fast at 1.25°C as at 50°C for the same rate of initiation, but the ratio of dihydroperoxide to monohydroperoxide increases only from 5 to 7, corresponding to a difference in activation energy between intramolecular and intermolecular abstraction of 1 kcal/mole. The overall activation energy (E_p – E_t/2) is 10.7 kcal/mole, close to the value of 12 kcal/mole found for isobutane. Absolute values for E_p, E_t, k_p, k_r, and k_t were derived. Ring closure of 2-hydroperoxy-2, 4-methyl-4-pentyl radicals to oxetane, not detected during oxidation, was observed when this radical was generated at 100°C in the near-absence of oxygen. The ratio of rate constants for oxetane formation and addition of oxygen to the 2, 4dimethyl-2-hydroperoxy-4-pentyl radical is about 5.4 × 10^?5 M at 100°C. Thus, ring closure to oxetane is too slow to compete with addition of oxygen above ?200 torr. At 100°C, 2, 3-dimethylbutane gave no evidence of any intramolecular abstraction. However, 2, 3-dimethylpentane did give at least 12% 2, 4-glycol or hydroxyketone.     

Chiral recognition ability of alpha-cyclodextrin with regard to some monoterpenoids under gas-liquid chromatographic conditions

Gas-liquid chromatography was applied to investigate the mechanism of alpha-cyclodextrin (alpha-CD) complexation processes with some chiral monoterpenoids differing from each other in chemical properties and structure. They were chosen from hydrocarbons, alcohols, aldehydes and ketones of acyclic, monocyclic and bicyclic structure. The relationships between the retention factor, k, of a guest solute (G) and alpha-CD concentration were studied. The obtained data enabled the stoichiometry, the stability of individual complexes and the separation factor of enantiomers to be determined. It was found that almost all the investigated monoterpenoids, apart from the acyclic ones, form inclusion complexes with alpha-CD. Straight-line relations (r vs. [alpha-CD]) were observed for monocyclic alcohols and pulegone, without any trace of enantioselectivity. This behaviour indicates that the 1:1 stoichiometry of the G-CD complexes does not lead to chiral recognition. Parabolic relations arising from 1:2 stoichiometry were found for limonene, alpha-phellandrene, some monocycylic ketones and all the investigated bicyclic terpenoids. It appeared that only the second step of complexation displayed marked enantioselectivity. However, a loss of efficiency resulting from slower equilibration is then noticeable. Attempts are made to rationalize the chromatographic results with respect to the structure of the investigated compounds.     

Block triangular preconditioners for linearization schemes of the Rayleigh–Bénard convection problem

In this paper, we compare two block triangular preconditioners for different linearizations of the Rayleigh–Bénard convection problem discretized with finite element methods. The two preconditioners differ in the nested or nonnested use of a certain approximation of the Schur complement associated to the Navier–Stokes block. First, bounds on the generalized eigenvalues are obtained for the preconditioned systems linearized with both Picard and Newton methods. Then, the performance of the proposed preconditioners is studied in terms of computational time. This investigation reveals some inconsistencies in the literature that are hereby discussed. We observe that the nonnested preconditioner works best both for the Picard and for the Newton cases. Therefore, we further investigate its performance by extending its application to a mixed Picard–Newton scheme. Numerical results of two‐ and three‐dimensional cases show that the convergence is robust with respect to the mesh size. We also give a characterization of the performance of the various preconditioned linearization schemes in terms of the Rayleigh number.     

Energy and radiation transfer in a finite convex body with general boundary conditions

Summary We consider a nonlinear system of equations describing the interaction of radiation with matter through a balance of the specific intensity of radiation and the specific internal energy in a convex bounded body.The boundary conditions are not homogeneous. However, suitable additive decompositions of the unknown functions lead to systems with homogeneous boundary conditions and known source terms. We give two such decompositions: one of these, suggested by physical considerations, arises from the study of a nonhomogeneous linear integral equation in a convenient Banach space. The system is studied by using the theory of semigroups of linear operators and nonlinear perturbations in an L ₁ setting. We prove the existence and uniqueness of a positive differentiable solution, which is global in time.

---

Sommario Si considera un sistema non lineare di equazioni che descrivono l'interazione della radiazione con la materia e rappresentano il bilancio dell'intensità specifica di radiazione e dell'energia specifica internu in un mezzo finito convesso. Le condizioni al contorno sono di tipo generale e non omogenee; l'introduzione di opportune scomposizioni della funzione incognita permette di ricondurci a sistemi con condizioni al contorno omogenee; ciò comporta l'introduzione di termini di sorgente noti. Si presentano due esempi di scomposizione, uno dei quali, suggerito da considerazioni fisiche, scaturisce dallo studio di un'equazione integrale lineare non omogenea in un opportuno spazio di Banach. Si riduce quindi il problema ad un'equazione di evoluzione non lineare in uno spazio di Banach di norma L ₁.Si prova l'esistenza di un'unica soluzione forte non negativa, utilizzando la teoria dei semigruppi e delle perturbazioni non lineari; tale soluzione risulta inoltre globale nel tempo.

---

---

Work performed under the auspices of C.N.R. (Gruppo Nazionale per la Fisica Matematica) and partially supported by M.P.I.