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We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation formula with particular attention to the boundary terms, and then study the sign of the principal eigenvalue of the Jacobi operator. We thus derive certain stability criteria, and in particular we recapture the Sternberg-Zumbrun result on the instability of the disconnected phases in the more general setting of several phases.

Mixtures of novolac resin and olive stone biomass in proportions 20 : 80 (w : w) are cured, pyrolyzed up to 1000°C (material C20), and activated with steam (material C20a). The adsorption properties of these materials and a commercial activated carbon (CC) are investigated based on the adsorption of nitrogen and pentane. The adsorption capacity, the surface area determined by the BET and DRK equation, and the pore volume determined as micropore volume by the DR equation, and as cumulative pore volume related to the Kelvin equation, for the materials follow the order C20a > CC > C20. The DR equation can be applied for the adsorption of nitrogen on the materials examined in the region of P/P, = 0.005 up to 0.3 that exceeds in both sides the common range for the applicability of the DR equation. The activated materials C20a and CC are mainly microporous and reveal the type I isotherms of the Brunauer classification for nitrogen adsorption. The only pyrolyzed material, C20, contains both micropores and mesopores and reveals characteristics of both types I and 11. The number of layers for C20a and CC is lower than 2 and for C20 is more than 2 . 0 1995 John Wiley & Sons, Inc.

A new, nonequilibrium stochastic theory of polymerization processes is developed. For complex polymerization reactions as those involving cyclization, size dependent reactivity, or diffusion effects, existing statistical and kinetic theories do not predict equivalent results. In the present work a unified and internally consistent procedure is developed for the analysis of size distributions resulting from such complex polymerization reactions. Our starting point is the Kolmogorov stochastic differential equations with the generator depending explicitly on the transition matrix for multifunctional systems. The functional form of the generator is derived for systems with equal reactivity and then extended to systems with unequal reactivity. The solution to the equations yields the Flory-Stockmayer distributions when the assumption of equal reactivity is valid. Statistical and kinetic theories are re-covered as special cases of the present theory.

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