Conformation of bicyclo[n.1.0] derivatives: Part 2. Norcarane and cyclohexene epoxide

The conformation al geometries and the possible interconversion paths for bicyclo[4.1.0] heptane (norcarane) and cyclohexene epoxide have been studied by both quantum mechanical and molecular mechanics calculations. The half-chair conformation is the most stable in the two compounds even if conformational equilibria with other forms cannot be excluded. Theoretical results are compared with the experimental data of molecular geometry, heat of formation, rotational constants, dipole moment, molar Kerr constant and proton coupling constants. The results obtained by the force-field method are satisfactory and consequently the extension of the method to derivatives of this kind seems possible.     

A modified Eguchi-Kawai model

A modified version of the Eguchi-Kawai model is proposed. We show that this modified model is equivalent to U(N) gauge theory in the infinite volume when N → ∞. The argument is based on investigations both in the continuum and on a lattice. We show that our modified model does not suffer from the notorious spontaneous symmetry breaking.     

Controlling polariton coupling in intersubband microcavities

We report the external control of the intersubband polariton coupling by manipulating the carrier density in quantum wells resonantly coupled to a GaAs/AlGaAs microcavity. The electrons in the wells were tuned by means of a depletion gate bias or by utilizing charge transfer between the energetically aligned ground subbands of asymmetric tunnel-coupled quantum wells. We propose the use of tunnel-assisted control of the polariton ground state in an asymmetrically coupled quantum well for implementing ultrafast modulation of intersubband polaritons.     

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.     

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.     

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.

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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.

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