Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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The role of surface conductivity in electromechanics and electrohydrodynamics of a dielectric drop
Get PDFA new technology of the electric-field manipulation by dielectric particles in dielectric liquids and drops has been developed in the last decades. To simulate electromechanics of microparticles in a weaklyconducting dielectric drop the Taylor\u27s leaky-dielectric model is extended. To achieve this electric-potential distribution inside and outside a weakly-conducting dielectric sphere embedded in a weakly-conducting dielectric in an electric field is determined taking into account the interfacial current. The conventional definition of the total, bulk plus surface, conductance of the sphere is detailed allowing for its dependence on the angular distribution of the external electric field. Technology of microparticles moving over the interface of the drop is based on the application of electrohydrodynamic (EHD) drag and dielectrophoretic (DEP) forces. The surface conductivities of the drop and individual microparticles can have a significant influence on the surface charge and thereby on the DEP and EHD drag forces. Thus, we show that recent explanation of manipulation by microparticles trapped at the interface of a silicone-oil drop immersed in castor oil is misleading. Taking into account the surface conductivity of the microparticles, we find that EHD drag and DEP forces are of the same direction but not opposite at zero or low frequencies as stated previously. Due to the reversal of the DEP force with the field frequency the motion of microparticles turns back. Surface conductivity of the drop can also explain experiments in which the prolate deformation persists after liquids of the drop and ambient medium are interchanged.Key words: dielectrophoresis, electrohydrodynamics, surface conductivity.Pages of the article in the issue: 110-117Language of the article: UkrainianA new technology of the electric-field manipulation by dielectric particles in dielectric liquids and drops has been developed in the last decades. To simulate electromechanics of microparticles in a weaklyconducting dielectric drop the Taylor\u27s leaky-dielectric model is extended. To achieve this electric-potential distribution inside and outside a weakly-conducting dielectric sphere embedded in a weakly-conducting dielectric in an electric field is determined taking into account the interfacial current. The conventional definition of the total, bulk plus surface, conductance of the sphere is detailed allowing for its dependence on the angular distribution of the external electric field. Technology of microparticles moving over the interface of the drop is based on the application of electrohydrodynamic (EHD) drag and dielectrophoretic (DEP) forces. The surface conductivities of the drop and individual microparticles can have a significant influence on the surface charge and thereby on the DEP and EHD drag forces. Thus, we show that recent explanation of manipulation by microparticles trapped at the interface of a silicone-oil drop immersed in castor oil is misleading. Taking into account the surface conductivity of the microparticles, we find that EHD drag and DEP forces are of the same direction but not opposite at zero or low frequencies as stated previously. Due to the reversal of the DEP force with the field frequency the motion of microparticles turns back. Surface conductivity of the drop can also explain experiments in which the prolate deformation persists after liquids of the drop and ambient medium are interchanged.Key words: dielectrophoresis, electrohydrodynamics, surface conductivity.Pages of the article in the issue: 110 - 117Language of the article: Ukrainia
Strengthening of a theorem on Coxeter–Euclidean type of principal partyally ordered sets.
Get PDFAmong the quadratic forms, playing an important role in modern mathematics, the Tits quadratic forms should be distinguished. Such quadratic forms were first introduced by P. Gabriel for any quiver in connection with the study of representations of quivers (also introduced by him). P. Gabriel proved that the connected quivers with positive Tits form coincide with the Dynkin quivers. This quadratic form is naturally generalized to a poset. The posets with positive quadratic Tits form (analogs of the Dynkin diagrams) were classified by the authors together with the P-critical posets (the smallest posets with non-positive quadratic Tits form). The quadratic Tits form of a P-critical poset is non-negative and corank of its symmetric matrix is 1. In this paper we study all posets with such two properties, which are called principal, related to equivalence of their quadratic Tits forms and those of Euclidean diagrams. In particular, one problem posted in 2014 is solved.Key words: positive and non-negative quadratic form, quadratic Tits form, P-critical poset, principal poset, Dynkin diagram, Euclidean diagram. Pages of the article in the issue: 8-15Language of the article: EnglishAmong the quadratic forms, playing an important role in modern mathematics, the Tits quadratic forms should be distinguished. Such quadratic forms were first introduced by P. Gabriel for any quiver in connection with the study of representations of quivers (also introduced by him). P. Gabriel proved that the connected quivers with positive Tits form coincide with the Dynkin quivers. This quadratic form is naturally generalized to a poset. The posets with positive quadratic Tits form (analogs of the Dynkin diagrams) were classified by the authors together with the P-critical posets (the smallest posets with non-positive quadratic Tits form). The quadratic Tits form of a P-critical poset is non-negative and corank of its symmetric matrix is 1. In this paper we study all posets with such two properties, which are called principal, related to equivalence of their quadratic Tits forms and those of Euclidean diagrams. In particular, one problem posted in 2014 is solved.Key words: positive and non-negative quadratic form, quadratic Tits form, P-critical poset, principal poset, Dynkin diagram, Euclidean diagram.Pages of the article in the issue: 8 - 15Language of the article: Englis
Determination of the frequencies and forms of free vibrations of pentagonal plates by the finite-element method
Get PDFFrequencies and modes of free vibrations of an isotropic thin pentagonal plate of regular shape with various configurations of rigid attachment at the edges are determined using the finite element method (FEM). The results obtained for some pentagonal plates are compared with the results obtained for square plates of an equivalent mass with corresponding boundary conditions. We present the vibration modes of the studied plates and the topology of the vibration modes for some of the considered plates corresponding to the square plates with free edges and rigidly fixed edges. The reliability of the obtained results is ensured by the use of a substantiated mathematical model, the correct formulation of the problem and the practical convergence of the calculated frequencies when using the FEM.Key words: finite element method, pentagonal plate, frequency and shape of free vibrations.Pages of the article in the issue: 61 - 66Language of the article: Ukrainia
Family memories of Yuriy Vasylyovych Kozachenko
Get PDFThe article is dedicated to the memoirs of the sister of the outstanding scientist, Doctor of Sciences in Physics and Mathematics, Professor Yuriy Kozachenko. It tells about the friendly and creative family of Kozachenkos, in which the future mathematician grew up. Some stories from the childhood of Yuriy Kozachenko are described with great warmth.Pages of the article in the issue: 30 - 32Language of the article: Ukrainia
Meetings with Kozachenko Yu.V.
Get PDFYuriy Kozachenko is an outstanding Ukrainian mathematician, my teacher. We have known each other and worked fruitfully for more than 40 years. Professor Kozachenko Yu.V. was one of the leaders of the Ukrainian school of probability theory and mathematical statistics, a world-renowned expert in the theory of modelling random processes in functional spaces, one of the creators of the theory of sub-Gaussian random processes and processes from Orlich spaces. He created a new scientific direction - simulation of random processes in different functional spaces with a given accuracy and reliability. Kozachenko Yu.V. received significant scientific results in the study of analytical properties of random processes, equations of mathematical physics with random initial conditions, statistics of random processes, wavelet analysis.This publication is about the brightest pages of our cooperation.Key words: subgaussian random processes, statistical modeling, Orlich spaces.Pages of the article in the issue: 33 - 36Language of the article: Ukrainia
The properties of the queuing model with the parallel structure
Get PDFThe present article is devoted to research the multi-channelk model with the parallel structure. It means that we consider the model which consists of two infinite-server queues.The service time in the each system has general function of distribution. In this case the stochastic dynamic of our model cannot be defined by Markov chain. As a result, analysis of such models is much more difficult than that of the corresponding Markovian queueing models. Besides we assume that customers arrive to our model according a bivariate Poisson input flow. This input process is characterized by the fact that customers arrive according to a bivariate Poisson flow simultaneously. We consider the number of customers in the systems at time t. This stochastic process describes the state of our model. In present paper we find the limit joint distribution of the number of customers in the systems. In a general way (by differentiating the corresponding generating function.) we obtain the main characteristics of this distribution, such as the expected number of customers in the nodes, its variance and correlation. In the case when parameters of our model dependent on the parameter n (number of series) the limit normal distribution was obtained for the service process in the stationary regime.Key words: network model, bivariate input flow, stationary distribution.Pages of the article in the issue: 79 - 82Language of the article: Ukrainia
Polarimetry of anisotropic surface layer on glass
Get PDFInvestigating the Stokes vector of light reflected from the surface of the optical glass, the presence of an anisotropic surface layer was established. The phase difference between radiation p- and s-components is revealed, which varies depending on the angle of incidence. This shows a weak anisotropy. Assuming that the anisotropic layer has an increased refractive index due to its chemical-mechanical treatment, it can be considered as some near-surface weakly guiding gradient burried waveguide. The possibility of coming radiation into such a planar waveguide using a coupling total reflection prism was investigated. The inspection showed a violation of the total internal reflection, unequal for p- and s-polarizations, which confirms the presence of the subsurface layer and its anisotropy. The absorption of radiation, which could be compared with the excitation of modes, is small. This is due to the properties of the prism material. Also, higher order modes are absorbed better. There is no significant angular dependence of the polarization degree of the output beam; however, it is higher in the case of s-polarization.Key words: polarimetry, inhomogeneity, surface layer, glass.Pages of the article in the issue: 95 - 98Language of the article: Ukrainia
Mathematical modelling of particle aggregation and sedimentation in the inclined tubes
Get PDFSedimentation of the aggregating particles in the gravity field is widely used as an easy and cheap test of the suspension stability of different technical suspensions, blood and nanofluids. It was established the tube inclination makes the test much faster that is known as the Boycott effect. The dependence of the sedimentation rate on the angle of inclination is complex and poorly understood yet. In this paper the two phase model of the aggregating particles is generalized to the inclined tubes. The problem is formulated in the two-dimensional case that corresponds to the narrow rectangle vessels or gaps of the viscosimeters of the cone-cone type. In the suggestion of small angles of inclination the equations are averaged over the transverse coordinate and the obtained hyperbolic system of equations is solved by the method of characteristics. Numerical computations revealed the increase in the initial concentration of the particles, their aggregation rate, external uniform force and inclination angle accelerate the sedimentation while any increase in the fluid viscosity decelerates it that is physically relevant. Anyway, the behaviors of the acceleration are different. Based on the results, a novel method of estimation of the suspension stability is proposed.Key words: Boycott effect, suspension, aggregation, sedimentation, medical diagnostics. Pages of the article in the issue: 52-57Language of the article: EnglishSedimentation of the aggregating particles in the gravity field is widely used as an easy and cheap test of the suspension stability of different technical suspensions, blood and nanofluids. It was established the tube inclination makes the test much faster that is known as the Boycott effect. The dependence of the sedimentation rate on the angle of inclination is complex and poorly understood yet. In this paper the two phase model of the aggregating particles is generalized to the inclined tubes. The problem is formulated in the two-dimensional case that corresponds to the narrow rectangle vessels or gaps of the viscosimeters of the cone-cone type. In the suggestion of small angles of inclination the equations are averaged over the transverse coordinate and the obtained hyperbolic system of equations is solved by the method of characteristics. Numerical computations revealed the increase in the initial concentration of the particles, their aggregation rate, external uniform force and inclination angle accelerate the sedimentation while any increase in the fluid viscosity decelerates it that is physically relevant. Anyway, the behaviors of the acceleration are different. Based on the results, a novel method of estimation of the suspension stability is proposed.Key words: Boycott effect, suspension, aggregation, sedimentation, medical diagnostics.Pages of the article in the issue: 52 - 57Language of the article: Englis
Machine learning for epilepsy detection and forecast review: new challenges and perspectives
Get PDFThe comparative analysis of machine learning methods has performed to solve the problem of early detection and prediction of epileptic seizures using electroencephalographic signals. Recent studies has shown that it is possible to predict seizures in prior of its physical appearance. Our goal is to present and analyse different approaches of seizure prediction techniques, particulary in machine learning and deep learning. Seizure prediction has made important advances over the last decade, nevertheless it is still a problem to provide steady algorithm of seizure early detection. Also, within individual patients exhibit distinctive dynamics, is it cruicial to find algorithms providing greater clinical utility. This article focuses of the problem of features development from electroencephalography signals in order to provide the accurate pattern recognition techniques for detection and classification of epilepsy seizures in advance. The mathematical model of the algorithms is constructed and quantitative data presented for estimating the methods efficiency.Key words: machine learning, epilepsy, electroencephalogram, preictal seizures.Pages of the article in the issue: 98-101Language of the article: UkrainianThe comparative analysis of machine learning methods has performed to solve the problem of early detection and prediction of epileptic seizures using electroencephalographic signals. Recent studies has shown that it is possible to predict seizures in prior of its physical appearance. Our goal is to present and analyse different approaches of seizure prediction techniques, particulary in machine learning and deep learning. Seizure prediction has made important advances over the last decade, nevertheless it is still a problem to provide steady algorithm of seizure early detection. Also, within individual patients exhibit distinctive dynamics, is it cruicial to find algorithms providing greater clinical utility. This article focuses of the problem of features development from electroencephalography signals in order to provide the accurate pattern recognition techniques for detection and classification of epilepsy seizures in advance. The mathematical model of the algorithms is constructed and quantitative data presented for estimating the methods efficiency.Key words: machine learning, epilepsy, electroencephalogram, preictal seizures.Pages of the article in the issue: 98 - 101Language of the article: Ukrainia
Berry-Esseen bound for nearly critical branching processes with immigration
Get PDFIn this paper, we consider a nearly critical branching process with immigration. We obtain the rate of convergence in central limit theorem for nearly critical branching processes with immigration.Key words: Branching process, immigration, Esseen inequality.Pages of the article in the issue: 42 - 49Language of the article: EnglishIn this paper, we consider a nearly critical branching process with immigration. We obtain the rate of convergence in central limit theorem for nearly critical branching processes with immigration.Key words: Branching process, immigration, Esseen inequality.Pages of the article in the issue: 42 - 49Language of the article: Englis