Work number - M 6 FILED
Authors: Bilushchak Y.I., Brukhal M.B.,Davydok A.Y.
Presented by Centre of Mathematical Modelling of Ya.S.Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of NAS of Ukraine
Аseries of the work consists of 1 chapter of monograph and 22 scientific papers published during 7 years.
A new approach to description of diffusion processes in two-phase randomly nonhomogeneous bodies is proposed. It is based on use of the generalized functions, integral equations, probability theory and the method of Green functions. The mature approach empowers to determine averaged over ensemble of phase configurations fields of concentration and flows of migrating substance taking into account essentially different diffusive properties of the phases, arbitrary sizes of inclusions and arbitrary probabilistic distribution of layers. A new equation of mass transfer is obtained for a two-phase body that takes explicitly into account jump discontinuity of the sought function and equality of the flows on the phase contact boundaries. The methodology is proposed and justified for mathematical description of field dispersion and correlation function of the field of concentration of substance diffusing in two-phase randomly nonhomogeneous stratified bodies, which uses representation of the concentration field in terms of convergent integral Neumann series and considers averaging over ensemble of phase configurations. On the basis of the relationship of mass balance a new differential equation is obtained for the function of diffusion flux of admixture particles, where nonhomogeneity of material structure is considered into the equation coefficients, initial and boundary conditions for the flow are justified. It is constructed the integro-differential equation for the function of mass flow, which is equivalent the original initial-boundary value problem. Its solution is obtained in terms of integral Neumann series. It is proposed the mathematical model describing thermostressed state of thermosensitive bodies of different transparency with account heat interchange by irradiation on the basis of the phenomenological theory of irradiation, theory of quasi-static thermoelasticity and results of kept theoretic-experimental research of scope of the heat transfer model satisfiability. The methodology is developed for solving the formulated new non-linear initial-boundary value problems of nonstationary heat interchange as well as stressed state in the bodies under consideration that is based on the finite element method.
The results of a series of the work contributes into solving the problem of mathematical modeling non-equilibrium processes in media of complex inner structure. They can be applied into geophysics, ecology, building branch, microelectronics, mechanical engineering, space and aircraft industry, nuclear and chemical energetics, ets.
The results of research are stated in 1 chapter of monograph, 22 papers (in particular, 3 in foreignjournals), 3 materials of reports, 1 certificate of authorship and 1 patent. The works of authors are cited in more then 32 scientific journals, total index of citation is 2 (as per data base SCOPUS), h-index=2.