in Titre de série : | Journal of physics A : mathematical and general, Vol.28 | Titre : | A stochastic theory of grinding | Type de document : | articles et extraits | Auteurs : | M. M. R. Williams, Auteur | Année de publication : | 1995 | Importance : | p.1219-1233 | ISBN/ISSN/EAN : | 0305-4470 | Langues : | Français (fre) | Résumé : | A statistical formulation is developed for the number of particles in a given size range following a grinding action carried out over a period of time. The regeneration point method first used by Janossy in the study of cosmic rays is employed. Essentially, the method is based on the backward form of the Chapman-Kolmogoroff equation and is closely related to the theory of fluctuations in nuclear reactors. A probability balance equation is derived and converted to a more convenient form using a generating function. Some new multi-particle breakup functions are introduced and their properties discussed. It is shown that the mean value equation is identical to that conventionally used for grinding but the equations for the variance and higher moments are new. In a special case, we are able to solve the nonlinear, partial integro-differential equation for the generating function and construct the complete probability distribution of the particle number in a given size range. The method can also be employed to study fibre breakup, of interest in the paper industry, and polymer degradation; it therefore has a wide range of application.
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in Journal of physics A : mathematical and general, Vol.28. A stochastic theory of grinding [articles et extraits] / M. M. R. Williams, Auteur . - 1995 . - p.1219-1233. ISSN : 0305-4470 Langues : Français ( fre) Résumé : | A statistical formulation is developed for the number of particles in a given size range following a grinding action carried out over a period of time. The regeneration point method first used by Janossy in the study of cosmic rays is employed. Essentially, the method is based on the backward form of the Chapman-Kolmogoroff equation and is closely related to the theory of fluctuations in nuclear reactors. A probability balance equation is derived and converted to a more convenient form using a generating function. Some new multi-particle breakup functions are introduced and their properties discussed. It is shown that the mean value equation is identical to that conventionally used for grinding but the equations for the variance and higher moments are new. In a special case, we are able to solve the nonlinear, partial integro-differential equation for the generating function and construct the complete probability distribution of the particle number in a given size range. The method can also be employed to study fibre breakup, of interest in the paper industry, and polymer degradation; it therefore has a wide range of application.
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