M Sushko - Academia.edu (original) (raw)

Papers by M Sushko

We generalize the compact group approach to conducting systems to give a self-consistent analytic... more We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core–penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially-symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents’ conductivities and volume concentrations; the latter account for the statistical microstructure of the system. The theory effectively incorporates many-particle effects and is expected to be rigorous in the static limit. Using the well-tested statistical physics results for the shell volume concentration, this conclusion is backed up by mapping the theory on available 3D random resistor network...

Technical Physics, 2009

The static permittivity of macroscopically homogeneous and isotropic heterogeneous systems is ana... more The static permittivity of macroscopically homogeneous and isotropic heterogeneous systems is analyzed using the concepts of compact groups of inhomogeneities. The method makes it possible to avoid excessive specification of mutual polarization processes in the system, which ensures effective application of this method for concentrated systems with arbitrary relations between the permittivities of system components. By way of example, the Maxwell-Garnett and Bruggeman formulas for the effective permittivity of heterogeneous matrix systems are reconstructed and their interrelation is analyzed. It is shown that the Bruggeman formula is more limited in the sense that it is based on additional model assumptions concerning the properties of the system and the type of averaging of fields over the volume of the system. Generalizations of these formulas are obtained for multicomponent heterogeneous systems consisting of inhomogeneous nonspherical particles or parts.

Optics and Spectroscopy - OPT SPECTROSC, 1987

ABSTRACT To describe the dynamics of critical fluctuations the idea of classical theory of moment... more ABSTRACT To describe the dynamics of critical fluctuations the idea of classical theory of moments is adopted. The efficiency of the method is illustrated by an analysis of the spectrum of molecular light scattering in liquid crystals near the isotropic liquid – nematic transition point. The spatial dispersion of the width function on both sides of the transition point is determined and also its dependence on the magnetic field intensity in the nematic.

arXiv: Soft Condensed Matter, 2018

A many-particle theory is presented for the effective quasistatic permittivity of macroscopically... more A many-particle theory is presented for the effective quasistatic permittivity of macroscopically homogeneous and isotropic systems of inhomogeneous dielectric particles with different degrees of penetrability. The theory is based upon our original compact-group approach, complemented by the Hashin-Shtrikman variational principle. The governing equation is obtained by summing up the statistical moments for the deviations of the local permittivity in the system from the desired effective permittivity. The latter is, in principle, recoverable from the governing equation as a functional of the constituents' volume concentrations (expressed through statistical averages of certain products of the particles' characteristic functions) and permittivity profiles. Under the suggestion that the local permittivity is determined by the shortest distance from the point of interest to the nearest sphere, a complete analysis is carried out for hard and fully penetrable spheres with piecewis...

Condensed Matter Physics, 2013

A model for the study of the effective quasistatic conductivity and permittivity of dispersed sys... more A model for the study of the effective quasistatic conductivity and permittivity of dispersed systems with particlehost interphase, within which many-particle polarization and correlation contributions are effectively incorporated, is presented. The structure of the system's components, including the interphase, is taken into account through modelling their low-frequency complex permittivity profiles. The model describes, among other things, a percolation-type behavior of the effective conductivity, accompanied by a considerable increase in the real part of the effective complex permittivity. The percolation threshold location is determined mainly by the thickness of the interphase. The "double" percolation effect is predicted. The results are contrasted with experiment.

Physical Review E, 2019

We generalize the compact group approach to conducting systems to give a self-consistent analytic... more We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core-penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially-symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents' conductivities and volume concentrations; the latter account for the statistical microstructure of the system. The theory effectively incorporates many-particle effects and is expected to be rigorous in the static limit. Using the well-tested statistical physics results for the shell volume concentration, this conclusion is backed up by mapping the theory on available 3D random resistor network simulations for hard spheres coated with fully penetrable concentric shells. Finally, the theory is shown to fit experimental data for real composite solid electrolytes. The fitting results indicate that the effect of enhanced electrical conduction is generally contributed to by several mechanisms. These are effectively taken into account through the shell conductivity profile. I.

Journal of Physical Studies, 2009

We present the compact group approach to analysis of the long-wavelength dielectric and optical c... more We present the compact group approach to analysis of the long-wavelength dielectric and optical characteristics of substances which can be modeled as macroscopically homogeneous and isotropic systems of hard dielectric particles embedded into a dielectric matrix. After the basics of the method are outlined, we discuss the results obtained with it for the effective permittivity of such systems and the single-scattering intensity of light scattered by them.

Journal of Molecular Liquids, 2016

Based on the method of compact groups of inhomogeneities, we formulate new mixing rules for suspe... more Based on the method of compact groups of inhomogeneities, we formulate new mixing rules for suspensions of charged insulating particles. They express the quasistatic conductivity and permittivity of a suspension in terms of the effective geometric and dielectric parameters of the particles, electric double layers (EDLs), and suspending liquid. Also, we present our low-frequency impedance measurements of the conductivity and permittivity of Al 2 O 3isopropyl alcohol nanofluids as functions of Al 2 O 3-particle volume concentration. Our rules give good fits for most of these data and allow us to estimate, among other things, the effective thickness, conductivity, and permittivity of the EDLs. The experimentally-recovered values agree well with elementary theoretical estimates suggesting the charging of the particles through preferential adsorption of contaminant ions. The possible effects of other mechanisms on the effective conductivity and permittivity of suspensions are also discussed.

ÁÁÊ 22.311ÿ73 À28 Ó ïîñ³áíèêó ðîçãëÿäàþòüñÿ ïîñòàíîâêà é ìåòîäè ðîçâ'ÿçóâàííÿ ïðîñòèõ ë³í³éíèõ çà... more ÁÁÊ 22.311ÿ73 À28 Ó ïîñ³áíèêó ðîçãëÿäàþòüñÿ ïîñòàíîâêà é ìåòîäè ðîçâ'ÿçóâàííÿ ïðîñòèõ ë³í³éíèõ çàäà÷ êëàñè÷íî¿ ìàòåìàòè÷íî¿ ô³çèêè. Êîëî ðîçãëÿíóòèõ ïèòàíü îõîïëþº ïðèíöèïè âàð³àö³éíîãî ÷èñëåííÿ, îäíîâèì³ðí³ êðàéîâ³ çàäà÷³ òåî𳿠êîëèâàíü ³ òåïëîïðîâ³äíîñò³ ç äîêëàäíèì àíàë³çîì êðàéîâî¿ çàäà÷³ Øòóðìà-˳óâ³ëëÿ òà îá´ðóíòóâàííÿì ìåòîäó Ôóð'º, ïðèêëàäè ðîçâ'ÿçóâàííÿ â³äïîâ³äíèõ çàäà÷ ó äâîõ ³ òðüîõ âèì³ðàõ ³ç íå-îáõ³äíèìè åëåìåíòàìè òåî𳿠ñïåö³àëüíèõ ôóíêö³é. Äëÿ ñòóäåíò³â ô³çè÷íèõ, ³íaeåíåðíî-ô³çè÷íèõ òà ìàòåìàòè÷íèõ ñïå-ö³àëüíîñòåé óí³âåðñèòåò³â. Ðåöåíçåíòè: ³ëü÷èíñüêèé Ñ. É., ä-ð ô³ç.-ìàò. íàóê, ïðîôåñîð, çàâ. êàôåäðè êâàí-òîâî¿ òåî𳿠ïîëÿ Êè¿âñüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ Òàðàñà Øåâ÷åíêà; Êðàñíèé Þ. Ï., ä-ð ô³ç.-ìàò. íàóê, ïðîôåñîð, çàâ. êàôåäðè ìàòåìàòèêè òà ìàòåìàòè÷íîãî ìîäåëþâàííÿ ̳aeíàðîäíîãî ãóìàí³òàðíîãî óí³âåðñèòåòó; Ïèâîâàð÷èê Â. Ì., ä-ð ô³ç.-ìàò. íàóê, ïðîôåñîð, çàâ. êàôåäðè ïðèêëàä-íî¿ ìàòåìàòèêè òà ³íôîðìàòèêè ϳâäåííîóêðà¿íñüêîãî íàö³îíàëüíîãî ïåäàãîã³÷íîãî óí³âåðñèòåòó ³ìåí³ Ê. Ä. Óøèíñüêîãî Ðåêîìåíäîâàíî äî äðóêó â÷åíîþ ðàäîþ Îäåñüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ ². ². Ìå÷íèêîâà. (Ïðîòîêîë ¹ 8 â³ä 26 êâ³òíÿ 2013 ð.) Ïóáë³êàö³þ êíèãè ÷àñòêîâî ï³äòðèìàíî ãðàíòîì IZ73Z0-128135 Øâåéöàðñüêîãî íàö³îíàëüíîãî ôîíäó íàóêè Ðåêîìåíäîâàíî ̳í³ñòåðñòâî îñâ³òè ³ íàóêè Óêðà¿íè ÿê íàâ÷àëüíèé ïîñ³áíèê äëÿ ñòóäåíò³â ô³çè÷íèõ òà ³íaeåíåðíî-ô³çè÷íèõ ñïåö³àëüíîñòåé âèùèõ íàâ÷àëüíèõ çàêëàä³â. (Ëèñò ¹ 1/11-4606 â³ä 31 áåðåçíÿ 2014 ð.

Low Temperature Physics, 2007

The effect of the 1.5-scattering mechanism on the time and temperature behavior of the electric f... more The effect of the 1.5-scattering mechanism on the time and temperature behavior of the electric field autocorrelation function for the light wave scattered from fluids has been studied for the case where the order-parameter fluctuations obey the diffusion-like kinetics with spatially-dependent kinetic coefficient. The leading contributions to the relevant static correlation functions of the order-parameter fluctuations were obtained by using the Ginzburg-Landau model with a cubic term, and then evaluated with the use of the Gaussian uncoupling for many-point correlation functions and the Ornstein-Zernicke form for the pair correlation function. It is shown that the presence of the 1.5-scattering effects in the overall scattering pattern may be detected in the form of a small but noticeable deviation from exponential decay of the total electric field autocorrelation function registered experimentally near the critical point. Obtained with the standard methods of analysis, the effective halfwidth of the corresponding spectrum can reveal a stronger temperature dependence and a multiplicative renormalization as compared to the halfwidth of the spectrum of the pair correlator.

Journal of Physics D: Applied Physics, 2009

We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotr... more We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotropic multicomponent mixtures of anisotropic inhomogeneous dielectric particles. Two factors of anisotropy are taken into account, the shape of the particles and anisotropy of the dielectric parameters of the particles' substances. Our approach is based upon the notion of macroscopic compact groups of particles and the procedure of averaging of the fields over volumes much greater than the typical scales of these groups. It enables us to effectively sum up the contributions from multiple interparticle reemission and short-range correlation effects, represented by all terms in the infinite iterative series for the electric field strength and induction. The expression for the effective permittivity can be given the form of the Lorentz-Lorenz type, which allows us to determine the effective polarizabilities of the particles in the mixture. These polarizabilities are found as integrals over the regions occupied by the particles and taken of explicit functions of the principal components of the permittivity tensors of the particles' substances and the permittivity of the host medium. The case of a mixture of particles of the ellipsoidal shape is considered in detail to exemplify the use of general formulas. As another example, Bruggeman-type formulas are derived under pertinent model assumptions. The ranges of validity of the results obtained are discussed as well.

Journal of Molecular Liquids, 2011

We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent te... more We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent term in the 'diameter' of the coexistence curve asymptotically close to the vapor-liquid critical point. For this purpose, we use a simple non-parametric equation of state which we develop by meeting several general requirements. Namely, we require that the desired equation (1) lead to correct asymptotic behavior for a limited number of the fluid's parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop below the critical point, and (3) be consistent with a rigorous definition of the isothermal compressibility in the critical region. For the temperature interval in question, the proposed equation approximates experimental data with an accuracy comparable to those given by Schofield's parametric equation and by other authors' equations. The desired term is obtained by applying the Maxwell rule to the equation and can be represented as D 2β |τ | 2β , where |τ | = |T − Tc|/Tc and β is the critical exponent for the order parameter. The amplitude D 2β is determined explicitly for the volume-temperature and entropy-temperature planes.

Journal of Molecular Liquids, 2011

We adduce new arguments for the significance of so-called 1.5-(or sesquialteral) molecular light ... more We adduce new arguments for the significance of so-called 1.5-(or sesquialteral) molecular light scattering in one-component fluids. For this purpose, we analyze its effect on the Landau-Placzek ratio for the critical opalescence spectrum. The results obtained are used to reveal experimental data which can be interpreted as evidence for its existence and to evaluate both the relative magnitude and the sign of the 1.5-scattering contribution.

Journal of Experimental and Theoretical Physics, 2007

ABSTRACT A strict macroscopic analysis of the limiting long-wavelength permittivity of a model su... more ABSTRACT A strict macroscopic analysis of the limiting long-wavelength permittivity of a model suspension is presented in which the suspension is considered as a finely dispersed system consisting of isotropic dielectric balls with piecewise-continuous radial permittivity profile. The analysis is performed within the framework of the notion of compact groups of inhomogeneities and the procedure of field averaging over volumes significantly exceeding the scale of these groups. The indicated value is described by the Lorentz-Lorenz formula. The effective polarizability of balls in the suspension is reconstructed from their parameters and the parameters of the medium by means of integration. The result is valid for any concentration of the balls at which the suspension remains macroscopically homogeneous and isotropic with respect to the field and for an arbitrary difference between the ball and medium permittivities.

Journal of Experimental and Theoretical Physics, 2004

ABSTRACT The “interference” contributions from compact groups of scattering centers to the total ... more ABSTRACT The “interference” contributions from compact groups of scattering centers to the total intensity of molecular scattering in a liquid are analyzed. The result of the algebra of fluctuating quantities has been restored for the case of long-range correlations between the groups. The role of short-range correlations is most significant for moderate deviations (10−3−10−2) of the dimensionless temperature from its critical value. Estimates of the relative value and temperature peculiarities of the contributions of multiplicity 1.5 proportional to the third-order moment of the density fluctuations and an analysis of experimental data indicate that they can be partially observed under conditions deviating from the critical isochore.

We generalize the compact group approach to conducting systems to give a self-consistent analytic... more We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core–penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially-symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents’ conductivities and volume concentrations; the latter account for the statistical microstructure of the system. The theory effectively incorporates many-particle effects and is expected to be rigorous in the static limit. Using the well-tested statistical physics results for the shell volume concentration, this conclusion is backed up by mapping the theory on available 3D random resistor network...

Technical Physics, 2009

The static permittivity of macroscopically homogeneous and isotropic heterogeneous systems is ana... more The static permittivity of macroscopically homogeneous and isotropic heterogeneous systems is analyzed using the concepts of compact groups of inhomogeneities. The method makes it possible to avoid excessive specification of mutual polarization processes in the system, which ensures effective application of this method for concentrated systems with arbitrary relations between the permittivities of system components. By way of example, the Maxwell-Garnett and Bruggeman formulas for the effective permittivity of heterogeneous matrix systems are reconstructed and their interrelation is analyzed. It is shown that the Bruggeman formula is more limited in the sense that it is based on additional model assumptions concerning the properties of the system and the type of averaging of fields over the volume of the system. Generalizations of these formulas are obtained for multicomponent heterogeneous systems consisting of inhomogeneous nonspherical particles or parts.

Optics and Spectroscopy - OPT SPECTROSC, 1987

ABSTRACT To describe the dynamics of critical fluctuations the idea of classical theory of moment... more ABSTRACT To describe the dynamics of critical fluctuations the idea of classical theory of moments is adopted. The efficiency of the method is illustrated by an analysis of the spectrum of molecular light scattering in liquid crystals near the isotropic liquid – nematic transition point. The spatial dispersion of the width function on both sides of the transition point is determined and also its dependence on the magnetic field intensity in the nematic.

arXiv: Soft Condensed Matter, 2018

A many-particle theory is presented for the effective quasistatic permittivity of macroscopically... more A many-particle theory is presented for the effective quasistatic permittivity of macroscopically homogeneous and isotropic systems of inhomogeneous dielectric particles with different degrees of penetrability. The theory is based upon our original compact-group approach, complemented by the Hashin-Shtrikman variational principle. The governing equation is obtained by summing up the statistical moments for the deviations of the local permittivity in the system from the desired effective permittivity. The latter is, in principle, recoverable from the governing equation as a functional of the constituents' volume concentrations (expressed through statistical averages of certain products of the particles' characteristic functions) and permittivity profiles. Under the suggestion that the local permittivity is determined by the shortest distance from the point of interest to the nearest sphere, a complete analysis is carried out for hard and fully penetrable spheres with piecewis...

Condensed Matter Physics, 2013

A model for the study of the effective quasistatic conductivity and permittivity of dispersed sys... more A model for the study of the effective quasistatic conductivity and permittivity of dispersed systems with particlehost interphase, within which many-particle polarization and correlation contributions are effectively incorporated, is presented. The structure of the system's components, including the interphase, is taken into account through modelling their low-frequency complex permittivity profiles. The model describes, among other things, a percolation-type behavior of the effective conductivity, accompanied by a considerable increase in the real part of the effective complex permittivity. The percolation threshold location is determined mainly by the thickness of the interphase. The "double" percolation effect is predicted. The results are contrasted with experiment.

Physical Review E, 2019

We generalize the compact group approach to conducting systems to give a self-consistent analytic... more We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core-penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially-symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents' conductivities and volume concentrations; the latter account for the statistical microstructure of the system. The theory effectively incorporates many-particle effects and is expected to be rigorous in the static limit. Using the well-tested statistical physics results for the shell volume concentration, this conclusion is backed up by mapping the theory on available 3D random resistor network simulations for hard spheres coated with fully penetrable concentric shells. Finally, the theory is shown to fit experimental data for real composite solid electrolytes. The fitting results indicate that the effect of enhanced electrical conduction is generally contributed to by several mechanisms. These are effectively taken into account through the shell conductivity profile. I.

Journal of Physical Studies, 2009

We present the compact group approach to analysis of the long-wavelength dielectric and optical c... more We present the compact group approach to analysis of the long-wavelength dielectric and optical characteristics of substances which can be modeled as macroscopically homogeneous and isotropic systems of hard dielectric particles embedded into a dielectric matrix. After the basics of the method are outlined, we discuss the results obtained with it for the effective permittivity of such systems and the single-scattering intensity of light scattered by them.

Journal of Molecular Liquids, 2016

Based on the method of compact groups of inhomogeneities, we formulate new mixing rules for suspe... more Based on the method of compact groups of inhomogeneities, we formulate new mixing rules for suspensions of charged insulating particles. They express the quasistatic conductivity and permittivity of a suspension in terms of the effective geometric and dielectric parameters of the particles, electric double layers (EDLs), and suspending liquid. Also, we present our low-frequency impedance measurements of the conductivity and permittivity of Al 2 O 3isopropyl alcohol nanofluids as functions of Al 2 O 3-particle volume concentration. Our rules give good fits for most of these data and allow us to estimate, among other things, the effective thickness, conductivity, and permittivity of the EDLs. The experimentally-recovered values agree well with elementary theoretical estimates suggesting the charging of the particles through preferential adsorption of contaminant ions. The possible effects of other mechanisms on the effective conductivity and permittivity of suspensions are also discussed.

ÁÁÊ 22.311ÿ73 À28 Ó ïîñ³áíèêó ðîçãëÿäàþòüñÿ ïîñòàíîâêà é ìåòîäè ðîçâ'ÿçóâàííÿ ïðîñòèõ ë³í³éíèõ çà... more ÁÁÊ 22.311ÿ73 À28 Ó ïîñ³áíèêó ðîçãëÿäàþòüñÿ ïîñòàíîâêà é ìåòîäè ðîçâ'ÿçóâàííÿ ïðîñòèõ ë³í³éíèõ çàäà÷ êëàñè÷íî¿ ìàòåìàòè÷íî¿ ô³çèêè. Êîëî ðîçãëÿíóòèõ ïèòàíü îõîïëþº ïðèíöèïè âàð³àö³éíîãî ÷èñëåííÿ, îäíîâèì³ðí³ êðàéîâ³ çàäà÷³ òåî𳿠êîëèâàíü ³ òåïëîïðîâ³äíîñò³ ç äîêëàäíèì àíàë³çîì êðàéîâî¿ çàäà÷³ Øòóðìà-˳óâ³ëëÿ òà îá´ðóíòóâàííÿì ìåòîäó Ôóð'º, ïðèêëàäè ðîçâ'ÿçóâàííÿ â³äïîâ³äíèõ çàäà÷ ó äâîõ ³ òðüîõ âèì³ðàõ ³ç íå-îáõ³äíèìè åëåìåíòàìè òåî𳿠ñïåö³àëüíèõ ôóíêö³é. Äëÿ ñòóäåíò³â ô³çè÷íèõ, ³íaeåíåðíî-ô³çè÷íèõ òà ìàòåìàòè÷íèõ ñïå-ö³àëüíîñòåé óí³âåðñèòåò³â. Ðåöåíçåíòè: ³ëü÷èíñüêèé Ñ. É., ä-ð ô³ç.-ìàò. íàóê, ïðîôåñîð, çàâ. êàôåäðè êâàí-òîâî¿ òåî𳿠ïîëÿ Êè¿âñüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ Òàðàñà Øåâ÷åíêà; Êðàñíèé Þ. Ï., ä-ð ô³ç.-ìàò. íàóê, ïðîôåñîð, çàâ. êàôåäðè ìàòåìàòèêè òà ìàòåìàòè÷íîãî ìîäåëþâàííÿ ̳aeíàðîäíîãî ãóìàí³òàðíîãî óí³âåðñèòåòó; Ïèâîâàð÷èê Â. Ì., ä-ð ô³ç.-ìàò. íàóê, ïðîôåñîð, çàâ. êàôåäðè ïðèêëàä-íî¿ ìàòåìàòèêè òà ³íôîðìàòèêè ϳâäåííîóêðà¿íñüêîãî íàö³îíàëüíîãî ïåäàãîã³÷íîãî óí³âåðñèòåòó ³ìåí³ Ê. Ä. Óøèíñüêîãî Ðåêîìåíäîâàíî äî äðóêó â÷åíîþ ðàäîþ Îäåñüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ ². ². Ìå÷íèêîâà. (Ïðîòîêîë ¹ 8 â³ä 26 êâ³òíÿ 2013 ð.) Ïóáë³êàö³þ êíèãè ÷àñòêîâî ï³äòðèìàíî ãðàíòîì IZ73Z0-128135 Øâåéöàðñüêîãî íàö³îíàëüíîãî ôîíäó íàóêè Ðåêîìåíäîâàíî ̳í³ñòåðñòâî îñâ³òè ³ íàóêè Óêðà¿íè ÿê íàâ÷àëüíèé ïîñ³áíèê äëÿ ñòóäåíò³â ô³çè÷íèõ òà ³íaeåíåðíî-ô³çè÷íèõ ñïåö³àëüíîñòåé âèùèõ íàâ÷àëüíèõ çàêëàä³â. (Ëèñò ¹ 1/11-4606 â³ä 31 áåðåçíÿ 2014 ð.

Low Temperature Physics, 2007

The effect of the 1.5-scattering mechanism on the time and temperature behavior of the electric f... more The effect of the 1.5-scattering mechanism on the time and temperature behavior of the electric field autocorrelation function for the light wave scattered from fluids has been studied for the case where the order-parameter fluctuations obey the diffusion-like kinetics with spatially-dependent kinetic coefficient. The leading contributions to the relevant static correlation functions of the order-parameter fluctuations were obtained by using the Ginzburg-Landau model with a cubic term, and then evaluated with the use of the Gaussian uncoupling for many-point correlation functions and the Ornstein-Zernicke form for the pair correlation function. It is shown that the presence of the 1.5-scattering effects in the overall scattering pattern may be detected in the form of a small but noticeable deviation from exponential decay of the total electric field autocorrelation function registered experimentally near the critical point. Obtained with the standard methods of analysis, the effective halfwidth of the corresponding spectrum can reveal a stronger temperature dependence and a multiplicative renormalization as compared to the halfwidth of the spectrum of the pair correlator.

Journal of Physics D: Applied Physics, 2009

We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotr... more We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotropic multicomponent mixtures of anisotropic inhomogeneous dielectric particles. Two factors of anisotropy are taken into account, the shape of the particles and anisotropy of the dielectric parameters of the particles' substances. Our approach is based upon the notion of macroscopic compact groups of particles and the procedure of averaging of the fields over volumes much greater than the typical scales of these groups. It enables us to effectively sum up the contributions from multiple interparticle reemission and short-range correlation effects, represented by all terms in the infinite iterative series for the electric field strength and induction. The expression for the effective permittivity can be given the form of the Lorentz-Lorenz type, which allows us to determine the effective polarizabilities of the particles in the mixture. These polarizabilities are found as integrals over the regions occupied by the particles and taken of explicit functions of the principal components of the permittivity tensors of the particles' substances and the permittivity of the host medium. The case of a mixture of particles of the ellipsoidal shape is considered in detail to exemplify the use of general formulas. As another example, Bruggeman-type formulas are derived under pertinent model assumptions. The ranges of validity of the results obtained are discussed as well.

Journal of Molecular Liquids, 2011

We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent te... more We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent term in the 'diameter' of the coexistence curve asymptotically close to the vapor-liquid critical point. For this purpose, we use a simple non-parametric equation of state which we develop by meeting several general requirements. Namely, we require that the desired equation (1) lead to correct asymptotic behavior for a limited number of the fluid's parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop below the critical point, and (3) be consistent with a rigorous definition of the isothermal compressibility in the critical region. For the temperature interval in question, the proposed equation approximates experimental data with an accuracy comparable to those given by Schofield's parametric equation and by other authors' equations. The desired term is obtained by applying the Maxwell rule to the equation and can be represented as D 2β |τ | 2β , where |τ | = |T − Tc|/Tc and β is the critical exponent for the order parameter. The amplitude D 2β is determined explicitly for the volume-temperature and entropy-temperature planes.

Journal of Molecular Liquids, 2011

We adduce new arguments for the significance of so-called 1.5-(or sesquialteral) molecular light ... more We adduce new arguments for the significance of so-called 1.5-(or sesquialteral) molecular light scattering in one-component fluids. For this purpose, we analyze its effect on the Landau-Placzek ratio for the critical opalescence spectrum. The results obtained are used to reveal experimental data which can be interpreted as evidence for its existence and to evaluate both the relative magnitude and the sign of the 1.5-scattering contribution.

Journal of Experimental and Theoretical Physics, 2007

ABSTRACT A strict macroscopic analysis of the limiting long-wavelength permittivity of a model su... more ABSTRACT A strict macroscopic analysis of the limiting long-wavelength permittivity of a model suspension is presented in which the suspension is considered as a finely dispersed system consisting of isotropic dielectric balls with piecewise-continuous radial permittivity profile. The analysis is performed within the framework of the notion of compact groups of inhomogeneities and the procedure of field averaging over volumes significantly exceeding the scale of these groups. The indicated value is described by the Lorentz-Lorenz formula. The effective polarizability of balls in the suspension is reconstructed from their parameters and the parameters of the medium by means of integration. The result is valid for any concentration of the balls at which the suspension remains macroscopically homogeneous and isotropic with respect to the field and for an arbitrary difference between the ball and medium permittivities.

Journal of Experimental and Theoretical Physics, 2004

ABSTRACT The “interference” contributions from compact groups of scattering centers to the total ... more ABSTRACT The “interference” contributions from compact groups of scattering centers to the total intensity of molecular scattering in a liquid are analyzed. The result of the algebra of fluctuating quantities has been restored for the case of long-range correlations between the groups. The role of short-range correlations is most significant for moderate deviations (10−3−10−2) of the dimensionless temperature from its critical value. Estimates of the relative value and temperature peculiarities of the contributions of multiplicity 1.5 proportional to the third-order moment of the density fluctuations and an analysis of experimental data indicate that they can be partially observed under conditions deviating from the critical isochore.