Diffusion approximation for billiards with totally accommodating scatterers

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.     

Pressure dependence of elastic behaviour and force constants of GaP

The six third order elastic constants of GaP have been obtained from measurements of the effect of hydrostatic and uniaxial pressures on ultrasonic wave velocities. The valence force field model has been used to obtain the bond-bending and stretching force constants. Confirmatory evidence is added to the hypotheses that zinc blende structure crystals undergo the densification transition under pressure when (1) a modified Born stability criterion that $\text{1}\text{2}\text{(C}{}_{11}\text{? C}{}_{12}\text{)}\text{B}$ equals about 0.2 is reached at the phase transition pressure P_t, and (2) the ratio $\text{β}{}_{\mathrm{t}}\text{α}{}_{\mathrm{t}}$ of the second order bond-bending β_t to bond-stretching α_t, force constants is about 0.1. These findings suggest that a macroscopic shear takes place at the transition     

Nouvelles applications du bis (bromomethyl)-2,3 butadiene-1,3: acces a des bis (methylene)-1,2 cyclopentanes,a des 2H-isoindoles et a des dithia-2,3 naphtalenes

2,3-Bis (bromomethyl)-1,3 butadiene 1 was found to be a good reagent for C-dialkylation by phase transfer reaction. Adducts of 1 with propiolic acid are versatile precursors of 2H-isoindoles and of 2,3-dithianaphtelenes.     

Reduction—complexation des thiophosphinates par le nickelocene

2-Phenyl-1,3,2-dioxaphosphorinane rearranges at 250°C to afford 2-phenyl-2-oxo-l,2-oxaphospholane which is, in turn, converted into the 2-thio derivative by P₄S₁₀. This cyclic thiophosphinate reacts with nickelocene and allyl iodide to yield

(L = 2-phenyl-1,2-oxaphospholane) by reduction—complexation. The same scheme is successfully applied to the 1-oxa-2-phosphacyclohepta-4,6-diene nucleus. Thus, the P^IV=S reduction—complexation process works with POC compounds. This is not the case with PSC compounds (for example, with dithiophosphinates). Some chemistry of 2-phenyl-l,3,2-dithiaphosphorinane is also described: Arbuzov reaction with PhCH₂Br, thermal rearrangement and complexation with nickelocene and allyl iodide.     

The vacuum uv emission spectrum of the 15N22+ molecular ion

The vacuum uv emission of the ¹⁵N₂²⁺ ion has been recorded for the first time. Rotational analysis of two bands, analogous to those already observed in the case of the natural isotope, confirm their assignment to the D¹Σ_u⁺-X¹Σ_g⁺ (0, 0) and (1, 1) bands. More precise data are also obtained for the ³Σ_g^? state which perturbs ground state vibrational levels.     

Théorèmes de Perron-Frobenius et Stein-Rosenberg booléens

The eigenelements of a Boolean matrix are defined. A “normal form” is given, which allows one to characterize those Boolean matrices the (Boolean) spectral radius of which is 0 or 1. Then the following results are proved: a Boolean Perron-Frobenius theorem, a “Truncated” Boolean Stein-Rosenberg theorem, and a Boolean Stein-Rosenberg theorem, which are the exact Boolean analoques of the usual corresponding theorems concerning real nonnegative matrices. Applications of these results are given elsewhere.     

Frustration and stability in random boolean networks

Discrete iterations of boolean mappings are known to yield to limit cycles [3, 8]. These limit cycles share a common stable part: the stable core which never oscillate along the different limit cycles.We show that non-frustrated circuits (defined as an extension of [7, 10]) are part of this core. We then characterize non-frustration — thus stability — in terms of the discrete derivative as introduced in [6, 11, 12].     

Microphysical nonseparability and relativistic signals

Bell's proof and recent experiments sugested by it raised questions concerning the existence of supraluminal influences and the status of these with respect to Einstein's theory of relativity. These questions are briefly examined via an approach which is independent of any model. This approach generates a clear distinction between information perceivable by an observer, which is found to be transmited with infraluminal speed and influences acting inside the microphenomena. An informational treatment gives a quantitative indication concerning acting information.