Математическое моделирование кариозных процессов, протекающих в зубной эмали и процесса лечения начального кариеса по технологии ICON
Mechanical forces and interactions participate in ontogenesis at all scale levels: intracellular, cellular, and supra-cellular, the latter including tissue level. This concept, now almost trivial, was finding its way with difficulties, and the works of L.V. Beloussov have played a decisive role in its establishment. The continuum approach presented in this study makes it possible to take at the tissue level into account both relative motion of cells and forces that control this motion. The characteristics which allow us to take into account general active properties of the cell medium are described, possible mechanisms represented by these characteristics are discussed, and a concise review of our results obtained to date is presented. In the strain rate tensor, two separate components are distinguished, one of them being related to deformation of individual cells and the other to cell rearrangement. A separate phase (submedium) that corresponds to active subcellular elements associated with rearrangement-controlling active stresses is also introduced. Within this general approach two specific models are considered. The first made it possible to establish general mechanisms whose account enabled us to satisfactorily describe the experimental results of L.V. Beloussov and collaborators, concerning mechano-dependent reactions of embryonic epithelium explants. On the assumptions that the active stress responds to cell shape deviations and the rearrangement strain rate component depends on the active stresses developed by pseudopodia, the cell shape and tissue stress evolution observed experimentally in stretched explants, as well as their post-release deformation, are reproduced. The second particular model considers self-organization in a conglomerate of loosely connected cells in the presence of a fluid phase. In this case, the active stress was assumed to nonlocally depend on the density of cells and the rearrangement strain rate on the active and passive stresses. Due to loss of stability of the spatially homogeneous state, various structures similar to those observed in embryogenesis develop. In particular, within the conglomerate, a cavity can be formed, a certain level of the fluid pressure being necessary for this
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
We apply first principles calculations to compare the carbon and boron nitride nanotube unzipping under atomic oxygen impact. We show that the attack of several oxygen atoms can cause bond breaking in nanotubes, but the structure of boron nitride nanotubes is less damaged than the structure of carbon ones. With increasing diameter, the structural damage of nanotubes reduces
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.