Факультет математики і інформатики
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Документ Optimal long-distance transport systems in nature: control and applications(2007) Kizilova, N.Long-distance conducting systems in high plants and animals are presented by networks of rigid tubes with porous walls (in plants) or distensible tubes with impermeable walls (in animals). Geometrical relationships between the diameters, lengths and branching angles of separate conducting vessels have been studied and the results of the comparative analysis are presented. It was shown that the principles of construction of the transport systems are similar in animals and plants and correspond to the optimal pipelines with impermeable and permeable walls accordingly. The optimization criterion is the total energy expenses W for the fluid delivery and construction of the system. Global optimality at the systemic level is provided by local optimality conditions in each conducting element. It is shown that complexity of the branching system of the optimal tubes leads to certain regularities in the hydraulic and wave properties of the systems. The obtained regularities and the principles of design of the long-distance transportation networks in Nature can be used in biomedical applications and technique.Документ Novel methods of pulse wave diagnostics based on compression of a superficial artery(2007) Kizilova, N.Pulse wave propagation and reflection in the branching systems of viscoelastic tubes and complex resistances as a model of arterial vasculature is considered. Axisymmetric wave motion of a viscous incompressible liquid in the system is investigated in application to the pressure and flow wave propagation in the system. Expression for the input admittance of the system taking into account wave reflection at the end of the tube is obtained. The dependence of the input admittance on the geometrical and mechanical parameters of the system is investigated. It is shown that the parameters of the pressure wave (the modules and phases of different harmonics) at the inlet of the system give information on the state (normal or pathological) of the inner organs. It is shown that after a proper compression (slight or deep) some harmonics can be amplified while the others are attenuated. Based on the theory of resonant harmonics of different inner organs the novel method of pulse wave palpation is proposed. The results are compared to some other methods as separation of the pressure wave into the forward and backward components, estimation of the parameters of the reflected wave and wave-intensity analysis.Документ Stability of erythrocyte sedimentation in a constant magnetic field(1989) Kizilova, N.The stability of erythrocyte sedimentation in the presence of a transverse component of the ponderomotive force is investigated. The processes of erythrocyte aggregation lead to the sedimentation being unstable with respect to small variations of the uniform horizontal cell distribution in the sedimentation tube. If an axisymmetric cell distribution is assumed, the system of equations describing erythrocyte sedimentation in blood plasma can be reduced to two-dimensional form and the investigation of this system, both with and without allowance for the viscous components and inertial terms, has shown that it is unstable with respect to small perturbations. The instability may sometimes result in the widely employed ESR test not being exclusively determined by the theological characteristics of the blood modified, for example, by disease. Accidental shaking of the capillary containing the blood or some other mechanical influence may lead to aggregation of the erythrocytes at the top of the tube and a sharp acceleration of the, entire sedimentation process.Документ Flow distribution and wave propagation in arterial systems with anastomoses(2005) Kizilova, N.; Sechin, R.P.Blood flow and wave propagation in the systems of compliant tubes filled with a fluid have been examined as a model of the systemic circulation and the intraorgan arterial networks have been modeled as Windkessel elements or regular treelike branching structures. Real intraorgan vasculatures possess some geometrical regularity and can be modeled as fractal-like trees. Nevertheless blood flow in the real beds and their self-similar models have some differences. Moreover real vasculatures often have anastomoses which provide additional pathways for blood flow and wave propagation and reflection. Arterial beds in the small and large intestine, in stomach and limbs have arterial anastomoses that influence input admittance spectra of the beds in comparison with the tree-like systems.Документ Long-distance liquid transport in plants(2008) Kizilova, N.A brief review of the thermodynamic and fluid dynamic problems related to long-distance liquid flow and signalling in plants is presented. Geometrical parameters of the plant leaf venation are measured and the general relationships between the diameters and lengths of the veins, branching angles at the vein bifurcations, and the corresponding drainage areas are obtained. The same relationships had been obtained before for the bifurcations of the pathways in the arterial and bronchial systems of mammals and humans; tree trunks, branches and roots; and river basins. The identity of the principle of design of the transportation systems in the nature can be understood on the concept of optimal networks that provide liquid delivery at total minimal energy costs. The corresponding models of the optimal vessels and branching systems of vessels with impermeable and permeable walls are presented and discussed.Документ Load transfer from the growing fibre into the growing medium: application to plant leaf growth(2007) Kizilova, N.Biological materials change their mass, shape, and porosity during the growth and possess high strength and durability at general lightweight design. Biological tissues are considered to be inhomogeneous anisotropic multiphase composites reinforced by fibres. A 2D problem of the load transfer from the growing fibre into the growing plate with different own growth rates and viscosity is considered in this paper. Rheology of the growing biological tissue is described by a modified Maxwell model of viscoelastic media. Numerical calculations of the growth velocity and stress fields are carried out. The influence of rheological parameters of two media on the stress–strain state is investigated. It is shown that the stress field may provide local coordinated growth of the fibres and the plate when the rheological parameters of two materials are different and anisotropic growth is observed.Документ Pressure Wave Propagation in Liquid-Filled Tubes of Viscoelastic Material(2006) Kizilova, N.The propagation of small-amplitude waves in a thick-walled long viscoelastic tube of variable cross-section, filled with a viscous incompressible fluid, is considered with account for wave reflection at the tube end in application to arterial pulse wave propagation. A solution is obtained in the form of expansions in a small parameter. The effect of the coefficient of wave reflection at the tube end and the wall material parameters on the fluid volume flow-rate and the tube wall displacement is investigated. It is shown that the volume flow-rate phase spectrum characteristics depend only slightly on the wall properties and can be used in clinical diagnostics for finding the reflection coefficient from pressure and flow-rate records.Документ Biophysical mechanisms of long-distance transport of liquids and signaling in high plants(2004) Kizilova, N.; Posdniak, L.O.Wave phenomena have been observed in numerous experiments with whole plants. One of possible mechanisms of the long-distance high-speed signaling in high plants is connected with concentration waves that can propagate through the conducting systems of plants. One-dimensional axisymmetrical stationary flow of a viscous liquid with osmotically active dissolved component through a long thin rigid cylindrical tube is considered as a model of the conducting vessel of the plant. Constant concentrations of the component at the inlet and outlet of the vessel are maintained by the live cells of the vegetative organs of the plant. Nonlinear concentration distribution along the tube and the parabolic velocity profiles are obtained. Propagation of small excitations of concentrations and velocities along the tube is considered. Expression for the wave velocity U is presented. The range U=20-60 m/s is obtained by numerical estimations at wide variations of the parameters within the physiological limits. The time delay in signal transmission in the system root-leaves corresponds to the experimental data. In that way the concentration waves can mediate high-speed transferring of information between the organs of plants.Документ Construction principles and control over transport systems organization in biological tissues(2003) Kizilova, N.The main common principles of the long-range transport systems construction in animal and plant tissues are summarized. The results of measurement of conducting system geometry in Cotinus obovatus leaf are analyzed. It is shown that the principles of design of the conducting systems in animals and higher plants are the same and correspond to the model of optimal pipeline. The mathematical model of fluid motion in the conducting system of the leaf as a mo tion in a branching pipeline with permeable walls is investigated. The cost of a bifurcation of the vessels is analyzed. The hypothesis of the control principle of optimal transport system formation in the growing leaf is discussed. As an example the self-similar conducting system with loops is investigated and compared with some venation systems in plant leaves.Документ Common principles in construction of biological networks(2004) Kizilova, N.In the present paper the statistical data on network geometry of the venation system of Morus alba leaf are presented. The mathematical model of the sap motion in the conducting system of a leaf is proposed. On the base of the solution of an optimization problem the principle of optimal construction of a bifurcation in plant leaf venation that correspond to Murray’s law is obtained.
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