Biomedical subjects

P S Grinchuk

Publications and source records attributed to P S Grinchuk.

3 recordsLinked to original sources

PubMed2005

Effect of random internal structure on combustion of binary powder mixtures.

Combustion of a mixture of two solid reactants is considered. A combined geometrical and physicochemical model of mixing of these reactants is proposed. The model takes into account random distribution of reactants and voids over the system. This allows description of incomplete burning of reactants. The model is used for studying the combustion wave propagation in a binary heterogeneous mixture. The obtained results are compared with those calculated from the perfect-mixing model, which implies that the deficient (with respect to the stoichiometry) component burns completely. It is shown that micrononuniformity of mixing not only reduces the combustion wave temperature and velocity but also can lead to a shift of the maximal wave velocity away from the stoichiometric composition of the mixture. The results of this study allow us to suggest that one of the main reasons for such a shift, which was observed in a number of experimental works, is structural disorder of binary mixtures.

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PubMed2003

Surfaces of percolation systems in lattice problems.

The internal and external surface area of a percolation cluster along with a full surface area of whole percolation system are investigated both analytically and numerically. Numerical simulation is performed by a Monte Carlo method for site and bond problems on square and simple cubic lattices. It is shown that both the external and full surface areas of a percolation cluster as well as the full surface area of the whole percolation system have maxima for a certain share of occupied sites (for the site problem) or permeable bonds (for a bond problem). On the basis of a probabilistic approach, analytical expressions are obtained which relate the surface area of percolation cluster to its density. The last value has been studied in more details at present that allows to analyze the behavior of the above-mentioned surface for various lattices. Two particular technological processes are discussed where the surface area of a percolation cluster plays an important part: generation of electric current in a fuel cell and self-propagating high-temperature synthesis in heterogeneous condensed systems.

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PubMed2002

Large clusters in supercritical percolation.

The statistical behavior of the size of large finite clusters in supercritical percolation on a finite lattice is investigated (below the critical dimension of the space d(c)=6). For this purpose, an approximate system of ordinary differential equations for a number of finite clusters is obtained. The correlation between the critical exponents zeta that determine the cluster decay law (ln n(s) approximately -s(zeta)) and the surface of clusters is shown. It is found that for clusters without self-intersections having a maximal surface zeta=1. For clusters with a small number of self-intersections zeta=1-eta. Here eta is a function depending on the ratio of the surface area of a cluster to its size, which tends to zero, when the surface tends to a maximum. For compact clusters with a minimum or near-minimum surface area, the first correction to the cluster decay law above percolation threshold (ln n(s) approximately -s((d-1)/d)) has been found on the basis of the drop model and the derived system of equations. The predictions are tested numerically on two- and three-dimensional lattices by Monte Carlo simulations. The results of the work allow one to conclude that above the percolation threshold majority of large clusters are compact and that the cluster surface is the main factor affecting its behavior in supercritical percolation.

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