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Introduction
current research interests - numerical methods in mathematical modelling in life scienses, theory of numerical methods for hyperbolic PDE systems solving.
Current institution
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July 1984 - present
Education
September 1978 - June 1984
Publications
Publications (82)
The new method of the difference schemes for solving the Burgers equation constructing is discovered. The method is based on the two different divergent forms for the Hopf equation. To search for the optimal difference schemes in this family, an analysis in the space of insufficient coefficients was applied using the technique of self-dual problems...
Modern power transportation systems are the complex engineering systems. Such systems include both point facilities (power producers, consumers, transformer substations, etc.) and the distributed elements (f.e. power lines). Such structures are presented in the form of the graphs with different types of nodes under creating the mathematical models....
Рассматривается семейство разностных схем на явном пятиточечном шаблоне для численного решения линейного уравнения переноса. Для построения и исследования свойств разностных схем использовано обобщенное условие аппроксимации. Проводится анализ разностных схем в пространстве неопределенных коэффициентов. Задача построения оптимальной разностной схем...
Discovery and selection of the potential targets is an important issue in pharmacology. Even when all the reactions and the proteins in a biological network are known, how does one choose the optimal target? Here we review and discuss the application of the computational methods to address this problem using the blood coagulation cascade as an exam...
The mechanistic modelling of blood clotting and fibrin-polymer mesh formation is of significant value for medical and biophysics applications. This paper presents a combination of two pointwise kinetic models represented by system of ODEs. One of them represents the reaction dynamics of clotting factors including the role of the platelet membranes....
Construction of difference schemes of high approximation orders for hyperbolic problems is still an important problem. For the construction of grid-characteristic methods, difference schemes were earlier analyzed in the space of undetermined coefficients, where the coefficients of high order derivatives in the first differential approximation of th...
Mass transfer in drying drops and films is interesting with practical point
of view, since it is used in problems of evaporative lithography. Compensatory
flows arise when conditions of nonuniform evaporation from the surface
of the liquid layer are created. Its move colloidal particles in the region of
fast evaporation. This makes it possible to o...
Mass transfer in drying drops and films is interesting with practical point of view, since it is used in problems of evaporative lithography. Compensatory flows arise when conditions of nonuniform evaporation from the surface of the liquid layer are created and move colloidal particles in the region of fast evaporation. This makes it possible to ob...
Using properties of the difference schemes approximating a one-dimensional transport equation as an example, it is shown that optimization of the properties of difference schemes based on the analysis in the space of undetermined coefficients and optimization of these properties based on the method of parametric correction are dual problems. Hybrid...
A set of implicit difference schemes on the five-pointwise stensil is under construction. The analysis of properties of difference schemes is carried out in a space of undetermined coefficients. The spaces were introduced for the first time by A. S. Kholodov. Usually for properties of difference schemes investigation the problem of the linear progr...
The article investigates one-dimensional mathematical model of tumor growth represented by a system of quasi-linear parabolic equations. We assume certain restrictions on the full flow of the motile tumor cells, leading to the possible degeneration of the system into a hyperbolic type and emergence of discontinuous (weak) solution. To find weak sol...
Functional modeling of blood clotting and fibrin-polymer mesh formation is of a significant value for medical and biophysics applications. Despite the fact of some discrepancies present in simplified functional models their results are of the great interest for the experimental science as a handy tool of the analysis for research planning, data pro...
A mathematical model of fibrin polymerization is described. The problem of the propagation of phase transition wave is reduced to a nonlinear Stefan problem. A one-dimensional discontinuity fitting difference scheme is described, and the results of one-dimensional computations are presented.
A numerical method for solving equations of a model for platelet transport in blood plasma flow and platelet clot formation is modified. The full matrix for shear-induced diffusion of the platelets is used. A comparison of a blood clot’s shapes corresponding to various lengths of vessel-wall damage is given.
A mathematical model of fibrin polymerization is described. The problem of the propagation
of phase transition wave is reduced to a nonlinear Stefan problem. A one-dimensional discontinuity
fitting difference scheme is described, and the results of one-dimensional computations are presented.
The paper considers models of platelet thrombus formation in blood plasma flow in a cylindrical vessel, based on the "advection-diffusion" equation and the Fokker-Planck equation. The comparison of the results of calculations based on these models is given. Considered models show qualitatively similar behavior at the initial stage of thrombus forma...
A model of blood coagulation has been investigated. The model includes 25 “reaction-diffusion” equations describing the space-time dynamics of distribution of blood coagulation factor concentrations. The one-dimensional statement of the problem is considered. The autowave velocity has been estimated based on the spatial distribution of blood coagul...
An one-dimensional mathematical model described evolution of drop shape and viscous
fluid dynamics (vertically averaged radial flow of the liquid) as the result of evaporation from
impermeable horizontal surface is presented in this work. The model considers the influence
of volume and capillary forces. Non-steady-state approach has been used to de...
Methods for modeling blood flow and its rheological properties are reviewed. Blood is considered as a particle suspencion. The methods are boundary integral equation method (BIEM), lattice Boltzmann (LBM), finite elements on dynamic mesh, dissipative particle dynamics (DPD) and agent based modeling. The analysis of these methods applications on hig...
The work aims to study the admissibility of the quasi-steady approach application in fluid flow modeling inside of evaporating drops placed on a solid horizontal substrate. Non-steady model has been developed to compare results with a quasi-steady model. For the first time one-dimensional motion equation of fluid in a drop is proposed from a moment...
Выведены основные уравнения нестационарной математической модели одномерных (осредненных по высоте капли) течений в высыхающей капле, покоящейся на твердом основании. В результате численных расчетов показано, что процессы в капле определяются законом испарения и значением капиллярного числа. При малых значениях капиллярного числа результаты, получе...
Приведен обзор методов моделирования движения и реологических свойств крови как суспензии взвешенных частиц. Рассмотрены методы граничных интегральных уравнений, решеточных уравнений Больцмана, конечных элементов на подвижных сетках, диссипативной динамики частиц, а также агентные модели. Приведен анализ применения этих методов при расчетах на высо...
The paper reports the calculations of the dynamics of fast copper liners. The implosion time is of the order of 80 ns. The problem is considered in a two-dimensional (axisymmetrical) statement. For simulation, a system of equations of electron magnetic hydrodynamics (EMH) is solved, using splitting into physical processes. At the first stage, the i...
Biological membranes are complex environments whose physico-chemical properties are of utmost importance for the understanding of many crucial biological processes. Much attention has been given in the literature to the description of membranes along the z-axis perpendicular to the membrane. Here, we instead consider the lateral dynamics of lipids...
This article proposes a numeric method of solution of quasilinear parabolic equations, based on the flux approximation, describes the implementation of the method on a rectangular grid and presents numerical results. Unlike methods used in common practice, this method uses an approximation of flows in non-dilated template. For each iteration of the...
The problem of plasma motion in Plasma Opening Switch with the stabilized magnetic field has been investigated. The main features of the difference scheme for solving magnetic field evolu-tion equations taking into account the thermal forces was described. The effectiveness of calcula-tion on the small cluster in MIPT and “personal cluster” based o...
Blood clotting system (BCS) modelling is an important issue with a plenty of applica-tions in medicine and biophysics. The BCS main function is to form a localized clot at the site of injury preventing blood loss. Mutual influence of fibrin clot consisting mainly of fibrin polymer gel and blood flow is an important factor for BCS to function proper...
An introduction to the models of cellular automata is given. The three automata described on the plane are: Viner-Rosenbluth cellular automata, the game of Life and Kohomoto-Oono automata for modelling «reaction-diffusion» systems. There is built the generalization of cellular automata of the game of Life to arbitrary dimension of space and the gen...
A mathematical model of platelet thrombus formation has been considered. A model of platelet transfer in the shear liquid
flow has been plotted. A numerical method for the solution of the system’s equations has been described. The mathematical
model for the formation of platelet thrombus in nephritis has been considered in the appendices.
The stability of some types of solution for a set of equations representing a blood clotting model is examined using numerical
methods of solving perturbation problems and the apparatus of adjoint equations. It is concluded that spiral waves are stable
in this system, whereas traveling pulses are unstable at parameters corresponding to a chaotic re...
The mathematical model of the platelet thrombus formation has been investigated. The model of platelet transport on the shear flow is shortly described. The model can be applied for studying of inflammatory diseases of kidneys.
In certain experimental conditions, bacteria form complex spatial-temporal patterns. A striking example of such kind was reported by Budrene and Berg (1991), who observed a wide variety of different colony structures ranging from arrays of spots to radially oriented stripes or arrangements of more complex elongated spots, formed by Escherichia coli...
We proposed a mathematical model and estimated the parameters of adsorption of albumin-bilirubin complex to the surface of carbon pyropolymer. Design data corresponded to the results of experimental studies. Our findings indicate that modeling of this process should take into account fractal properties of the surface of carbon pyropolymer.
Two mathematical models of clot growth in the fluid flows have been considered. The first one is the model of embolus growth in a wall-adjacent flow. The effect of hydrodynamic flows on proceeding chemical reactions and the backward effect of the growing clot on the flow are taken into account. The growing thrombus is assumed to be porous and havin...
Results are presented from experimental studies of promising output units for high-current pulsed generators within the framework
of the program on inertial confinement fusion research with the use of fast Z-pinches. The experiments were carried out on
the S-300 facility (4 MA, 70 ns, 0.15 Ω). Specifically, sharpening systems similar to plasma flow...
Fast implosion of Z-pinches is considered as possible way to the generation of X-ray pulse on the level of some dozens MJ aimed at IFE. In this talk, experiments on the S-300 pulsed power machine are presented on the current-driven implosion of wire arrays composed of different fractions of Al and W. In the case of nested arrays, the effect of "pas...
The mathematical model of magnetic field penetration in POS plasma is studied. A numerical method
for EMHD magnetic field diffusion calculation using regular curvilinear grid is suggested. The imple
mented method allows to reproduce a number of micro-scale phenomena attributed to electron effects.
Effects of various boundary conditions for magne...
On the S-300 pulsed power generator (4.5 MA, 70 ns, 0.15 Ohm), within the frames of ICF program based on fast high-current Z-pinches, experiments are being carried out studying promising schemes of output units. In particular, a device similar to the plasma flow switch is being investigated aimed at sharpening the pulse. In the experiments with suc...
On the S‐300 pulsed power generator (4.5 MA, 70 ns, 0.15 Ohm), within the frames of ICF program based on fast high‐current Z‐pinches, experiments are being carried out studying promising schemes of output units. In particular, a nanosecond‐range plasma flow switch is being investigated aimed at sharpening the pulse. As a result, the switching rate...
We constructed a mathematical model of clotting, which is based on a current view of the molecular pathways of blood coagulation. Several hypothetical reactions are introduced to allow accurate description of the spatio-temporal dynamics of blood clotting. The resulting model describes well all spatio-temporal aspects of clotting, as well as data o...
A study is made of the method for numerical modeling of pulsed plasma systems by simultaneously solving two-temperature MHD
equations and the equations of ionization kinetics. As an example, the method is applied to simulate a relatively slow moderate-density
Z-pinch, whose dynamics is well studied experimentally. A specially devised two-dimensiona...
The properties of a system reaction-electrodiffusion were studied using two-component model of interaction and diffusion of charged particles near membrane in solutions of low ionic strength to which traditional assumptions about local electroneutrality of medium are not applicable. It is shown that the effect of self-consistent electric field lead...
A modification of the Lotka-Volterra model was proposed. The modification takes into account the factor of seasonal fluctuations in a "predator-prey" model. In this modification, interactions between species in summer are described by the Lotka-Volterra equations; in winter, individuals of both species extinct. This generalization makes the classic...
The properties of a system reaction-electrodiffusion were studied using two-component model of interaction and diffusion of charged particles near membrane in solutions of low ionic strength to which traditional assumptions about local electroneutrality of medium are not applicable. It is shown that the effect of self-consistent electric field lead...
Abstract-A modernized PC-20 facility with a plasma opening switch (POS) is described. It contains a four-module voltage pulse (Marx) generator (MXG) connected via a high-voltage feedthrough to a POS. The energy stored in the MXG is increased by a factor of 12.5 and amounts to 240 kJ at a maximum voltage of 1 MV. At such a voltage, the POS current a...
The computation of the electric field in the RS-20 POS device was performed. We solved Laplace equation in the region with many non-connected boundaries. For the acceleration of the calculation we used the personal computer cluster based on the ordinary computer laboratory in MIPT.
Based on the experimental results, mathematical model of spatial patterns formation by chem-otactic bacteria E. coli is proposed. Experimental structures and dynamic of its formation were investigated numerically.
We propose a reaction-diffusion model that describes in detail the cascade of molecular events during blood coagulation. In a reduced form, this model contains three equations in three variables, two of which are self-accelerated. One of these variables, an activator, behaves in a threshold manner. An inhibitor is also produced autocatalytically, b...
A new mechanism of pattern formation different from the Turing and oscillatory instabilities in the reaction-diffusion systems was found. It is closely connected with the resonance phenomenon that appears in the models when Jacobi's matrix of the kinetic part is equivalent to Jordan cell and diffusion coefficients are cited. Some results of numeric...
A mathematical model for the formation of dissipative structures (DSs) in electrolyte solutions under the action of an external periodic electric field was considered. Based on an analysis of a linear system of equations, the conditions of parametric resonance resulting in DSs were determined. The effect was illustrated by numerical calculations fo...
A model of electrodiffusion processes in the vicinity of cell membrane was developed. The model takes into account chemical reactions, Coulomb interactions between charged particles and the effect of external electric field. It was concluded that the applied electric field can change the characteristics of space-time patterns in the system. Dissipa...
A model is proposed that describes electrodiffusion in the layer adjacent to the cell membrane. The model takes into account chemical reactions at the membrane, Coulomb interactions between particles, their random motion (diffusion), and the effect of an external electric field. Linear analysis of the model shows a possibility of spatiotemporal pat...
Mathematical model of the intravascular thrombus formation under blood flow conditions is formulated.
Analysis revealed that under certain critical conditions blood is converted from liquid to polymerized state in a threshold manner. Critical conditions of the blood coagulation activation were numerically determined. Localized and disseminated clo...
A model of electrodiffusion processes in the vicinity of cell membrane was developed. The model takes into account chemical reactions, Coulomb interactions between charged particles and the effect of external electric field. It was concluded that the applied electric field can change the characteristics of space-time patterns in the system. Dissipa...
Mathematical models that describe processes occuring in the growth zone of plants have been developed. Based on the fact that auxin plays a key role in the division and differentiation of cells belonging to the growth zone, changes in its concentration were modelled using the following assumptions: (1) auxin transport is a vectorial process; (2) in...
The mechanism of pattern formation in excitable systems with active recovery is analyzed. The conditions for critical nucleation of macroscopic structures with axial symmetry that have a finite number of rings were found. The number of the rings was shown to be determined by initial perturbation properties and by the parameters of the system. A pos...
The report presented is a part of the program aimed to creation the powerful X-ray pulse source with the quanta energy in the range of a dozen keV, using the “liner-convertor” scheme
The first results on the 2.5-dimensional numerical simulation of the implosion dynamics of a last liner filled by a plasma are presented. The calculations correspond to the "liner-pellet" scheme, in which the pulse is sharpened due to the nonlinear heat removal onto the end face converter, for typical values of a current up to 10 MA and an implosio...
Behavior dependence of the activator growth at the begining upon initial conditions is qualitatievely investigated in the model of reaction-diffusion type/ There is shown that due to saturation term presence bifurcation is possible. Computer simulation confirmed our presumption were carried out.
On the S-300 pulsed power generator, within the frames of ICF program based on fast high-current Z-pinches, promising schemes of output units are studied. In particular, a device similar to the plasma flow switch is being investigated aimed at sharpening the pulse. The switching rate as high as 2.5 MA / 2.5 ns has been achieved. Numerical simulatio...
On the S-300 pulsed power generator (4.5 MA, 70 ns, 0.15 Ohm), within the frames of ICF program based on fast high-current Z-pinches, experiments are being carried out studying promising schemes of output units. In par-ticular, a device similar to the plasma flow switch is being investigated aimed at sharpening the pulse. In the ex-periments with s...
