Vovk O. Mathematical modelling and numerical analysis of formation processes of multicomponent mixes

Research object - formation process of a multicomponent powder mix. A research objective - construction of mathematical model of formation process of the multicomponent mix which components are exposed to the strong perturbations having big enough instant potency which allows to trace a modification of distributions functions of investigated mix components in time and to define stabilization time of formed mix. Research methods - methods of mathematical statistics, probability theory and theory of casual processes, theories of optimization, mathematical modelling, casual analysis, analytical modelling with use of differential equations in partial derivatives. Equipment for researches - the personal computer. Theoretical and practical outcomes - are developed mathematical models and the methods describing formation process of multicomponent mixes, intended for modelling of investigated processes on manufacture; stabilization conditions of formation process of the multicomponent mixes are formulated, the developed formation methods allow to define an instant in which the mix with guaranteed distributions of its components both in all considered area, and in its separate parts has been received. Scientific novelty - the further development was received by definition method of powder mix components distribution on a velocity of their subsidence in case of action on process of subsidence of exterior force which arises for the account of mechanical, electromagnetic or acoustic oscillations. Average magnitude of this force is defined. The deduced formulas allow to improve outcomes of definition process of particles distributions on a velocity of their subsidence in a case when on process, except gravity, additional forces operate; for the first time it is developed mathematical model of stabilization of formation processes of multicomponent mixes under the influence of the perturbations having effective enough instant potency. Theorems of focusing and stabilization of Markov process have been for this purpose used at local perturbations of its fragments. Sufficient conditions at which performance it is possible to generate a multicomponent mix with guaranteed distribution of its components are formulated. It allows to define time for which the mixture with the set distribution of its components will be generated; the mathematical model of formation process of multicomponent mixes under the influence of the strong electrohydraulic, mechanical, acoustic perturbations fast varying in time is improved. It is system of linear differential equations in partial derivatives of 1st order which solutions are metric performances of particles of investigated mixture on each small volume. Use of the received mathematical model allows to trace a modification of a cumulative distribution function of diameters of particles of mix in time. Outcomes of dissertational work are introduced at modelling of formation process of multicomponent mixtures and the analysis of the received outcomes on Open Company "the Drugstore 36" and in educational process on department of applied mathematics of the Kharkiv National University of Radio Electronics that is confirmed by introduction acts. Scientific and practical outcomes of dissertational work can be used in the pharmacological industry, instrument making and the chemical industry for improving of final distributions of the generated mixes; in educational process by preparation of experts in the field of an applied mathematics.