Влияние проницаемости поясков Каспари для воды и растворенных веществ на величину корневого давления: математическое моделирование
The mathematical modelling is performed to study the effect of the permeability of the Casparian bands to water and solutes on the formation of the root pressure. It is shown that the pressure in the xylem vessels which stops the flow across a root cut (root pressure) decreases with increase in the permeability of the Casparian bands to solutes at a fixed hydraulic conductivity. However, if the Casparian bands are permeable to water alone and impermeable to solutes, then changes in the root pressure changes are not observed.
Basing on the information about the structure of the solution and asymptotic estimates in the problem of steady flow across the root, a system of algebraic relations similar to the commonly used compartment models is obtained. As compared with these, the method proposed has an important advantage making it possible to take into account the characteristic features of the anatomical structure of the root and the non-uniformity of the parameter distribution over its cross-section. This enables us to formulate simple finite relationships fitting with sufficient accuracy with the numerical solution obtained within the framework of the continuum model. The application of the approach proposed to solving specific problems is simpler than both the numerical solution based on the continuum model and the solution obtained by asymptotic methods.
Plasma–liquid interactions represent a growing interdisciplinary area of research involving plasma science, uid dynamics, heat and mass transfer, photolysis, multiphase chemistry and aerosol science. This review provides an assessment of the state-of-the-art of this multidisciplinary area and identi es the key research challenges. The developments in diagnostics, modeling and further extensions of cross section and reaction rate databases that are necessary to address these challenges are discussed. The review focusses on non- equilibrium plasmas.
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.
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.