Publications by authors named "GA Martynov"

Statistical theory of critical phenomena in fluids.

Phys Rev E Stat Nonlin Soft Matter Phys

March 2009

We show that there are two classes of the closure equations for the Ornstein-Zernike equation: The analytical equations for the bridge functional B=B;{(an)} like hypernetted-chain approximation, Percus-Yevick approximation, etc., and nonanalytic equation B=B;{(nan)} , where B;{(nan)}=B;{(rg)}+B;{(cr)} and B;{(rg)} is the regular (analytical) component of the bridge functional, and B;{(cr)} is the critical (nonanalytical) component of B;{(nan)} . The closure equation B;{(an)} defines coordinates of the critical point and other individual features of critical phenomena, and B;{(nan)} defines all the known relations between critical exponents.

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It is shown that there are two classes of closure equations for the Ornstein-Zernike (OZ) equation: the analytical equations B=B((an)) type of hyper-netted-chain approximation, Percus-Yevick approximation etc., and the nonanalytical equation B=B((non)), where B((nan))=B((RG))+B((cr)); B((RG)) is the regular (analytical) component of the bridge functional, and B((cr)) is the critical (nonanalytical) component of B((nan)). The closure equation B((an)) defines coordinates of a critical point and other individual features of critical phenomena, and B((nan)) defines known relations between critical exponents.

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The line of thermodynamic states with a unit value of the compressibility factor was calculated for a Lennard-Jones system using four different approaches. We show that all four approaches give rise to a straight line on the density-temperature plane. Thus, we theoretically confirm that the Lennard-Jones system satisfies Zeno line regularity.

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Summary. The paper provides comparative characteristics of water quality in the assessment of a risk for intestinal infections in drinking water use. It has shown that of the greatest predictive value is direct detection of potentially pathogenic microorganisms, as well as the integral indicator determined by glucose fermentation, such as glucose-positive coliform bacteria.

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We calculate the convergence curve of the virial expansion for a Lennard-Jones system in the density-temperature plane using the approximate method based on the density expansion of the Ornstein-Zernike equation and the condition of thermodynamic consistency [J. Chem. Phys.

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We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions.

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We demonstrate for the first time that (a) the straight line of the unit compressibility factor (Zeno line) tends asymptotically to the liquid branch of binodal at low temperatures, (b) the straight line with a half density has to be close to the average of vapor-liquid densities along the binodal curve (rectilinear diameter), and (c) the phase coexistence curves are inscribed into the right triangle in the density-temperature plane, which is formed by the Zeno line and by the segments which this line cuts off on the axes. These statements are confirmed for model systems and for a wide group of real substances (for the first time including metals: Hg, Cs, and Cu). Critical parameters of all substances under study are located in the vicinity of the triangle median, drawn to the density axis, with a dispersion on the order of 2 in reduced units.

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Data on the relationship between the incidence of intestinal infections, including hepatitis A, and communal conditions of settlements and quality of drinking water are presented.

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