Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Ge

On physical nanoscale aspects of compatibility of steels with hydrogen and natural gas

The possibilities of effective solutions of relevant technological problems are considered based on the analysis of fundamental physical aspects, elucidation of the nano-structural mechanisms and interrelations of aging and hydrogen embrittlement of materials (steels) in the hydrogen industry and gas-main industries. The adverse effects which these mechanisms and processes have on the service properties and technological lifetime of materials are analyzed. The concomitant fundamental process of formation of carbohydride-like and other segregation nanostructures at dislocations (with the segregation capacity 1 to 1.5 orders of magnitude greater than in the widely used Cottrell 'atmosphere' model) and grain boundaries is discussed in the context of how these nanostructures affect technological processes (aging, hydrogen embrittlement, stress corrosion damage, and failure) and the physicomechanical properties of the metallic materials (including the technological lifetimes of pipeline steels)