The calculation of singular points in the supercritical region for a system with a Lennard—Jones interaction potential

In this work the positions of the critical point, the supercritical point, and the maximum fluctuation point in a supercritical isotherm were found for a system with the Lennard—Jones interaction potential. Virial coefficients and methods based on accelerated convergence of the perturbation-theory series, which are well known for such systems, were used. The results were compared with computer-simulation data. As has been established, if one uses the positively defined Weeks—Chandler—Andersen potential as a reference system, the calculated parameters tend monotonically to exact values as a function of the number of virial coefficients. This decomposition is favorably different from the virial one, where the aspiration is not monotonic. These results indicate that this method makes it possible to determine the positions of the three vertices of the supercritical triangle with an accuracy that is comparable to that of a simulated experiment.     

The kinetics of liquid-gas phase transitions of a Van der Waals substance with fluctuations taken into account

The isotherm of a Van der Waals substance, containing only stable points, is obtained on the basis of using the thermodynamic potential for nonequilibrium states and taking fluctuations into account. It is shown that in the vicinity of two-phase states this isotherm is close to the horizontal phase equilibrium line, defined by Maxwell's rule. The lifetimes of the metastable states of the Van der Waals substance, which depend on the intensity of the external fluctuations and the number of particles in the system, are estimated. (c) 1994 American Institute of Physics.     

Distinctive features of random local motions in critical and supercritical fluids

Equations for large-scale local fluctuations in fluids, from an ideal gas to an incompressible fluid, including the critical and supercritical state are derived for the first time based on the first principles. The modern phenomenological representation of the critical state of fluids is confirmed and essentially refined; in particular, it is demonstrated that that local density fluctuations in a compressible fluid are accompanied by nonthermodynamic fluctuations in the collective velocity and temperature of the fluid. Distinctive features of the development of these fluctuations near the critical point determine the specific behavior of fluids in the critical and supercritical states.     

Non-stationary measurements of Chiral Magnetic Effect

We discuss the Chiral Magnetic Effect from the quantum theory of measurements point of view for non-stationary measurements. The effect of anisotropy for fluctuations of electric currents in a magnetic field is addressed. It is shown that anisotropy caused by nonzero axial chemical potential is indistinguishable in this framework from anisotropy caused by finite measurement time or finite lifetime of the magnetic field, and in all cases it is related to abelian triangle anomaly. Possible P-odd effects in central heavy-ion collisions (where the Chiral Magnetic Effect is absent) are discussed in this context. This paper is dedicated to the memory of Professor Mikhail Polikarpov (1952–2013).     

Solutions of the Yvon-Born-Green equation for a system of square-well molecules at a temperature below the triple point

The Yvon-Born-Green equation (with superposition approximation) is solved numerically for the pair correlation function for a system of molecules interacting via the square-well potential (with σ₂/σ₁ = 1·85), for an isotherm below the triple point, and over a broad range of densities. The correlation function data and attendant thermodynamics generated for this isotherm are compared with results reported previously by the authors for several supercritical and subcritical isotherms of the square-well fluid. To facilitate the interpretation of these results, particularly in those regions of (T, ρ) space where phase transitions may occur, a geometrical representation of the data is presented (motivated, in part, by recent work by René Thom), and the location of the triple point is discussed in terms of this construction. The differences anticipated between results reported here and those that would be obtained in an exact statistical mechanical analysis, are identified.     

Foundations of the fluctuation theory of adsorption on microcrystalline particles

Fundamentals of the equilibrium fluctuation theory of adsorption of molecules on microcrystalline particles taking into account the atomic structure of nonuniform surfaces were developed. The importance of taking into account the discrete character of adsorption centers in constructing adsorption isotherm equations was demonstrated. This changes the type of the mathematical apparatus in the search for a maximum distribution function term in a grand canonical ensemble: instead of differential derivatives, symmetrized difference derivatives should be used. The fluctuation theory of adsorption was generalized to ideal multicomponent mixtures of molecules. Adsorption isotherm equations for multicomponent mixtures on uniform and nonuniform surfaces taking into account limited sizes of the surface of various microcrystal faces and fluctuation contributions were obtained. The equations describe the influence of equilibrium fluctuations on adsorption isotherms for adsorbent particles of all sizes, from nanometric to macroscopic. An analysis of the equations showed that the influence of fluctuations was strongest at low coverages for each microcrystal face. The simplest case of taking fluctuations into account in the presence of contributions of lateral interactions in the mean field approximation was discussed.     

Parastatistics and phase transition from a cluster as a fluctuation to a cluster as a distinguishable object

A phase transition of the first kind is a jump of a function, a phase transition of the second kind is a jump of its first derivative, a phase transition of the third kind, a jump of the second derivative. A phase transition from one statistic to another is very gradual, but finally it is as considerable as the phase transition of the first kind. However, we cannot introduce a clearly defined parameter to which this transition corresponds. This is due to the fact that the fluctuations near the critical point are huge, and this violates, in the vicinity of that point, the main law of equilibrium thermodynamics, which asserts that fluctuations are relatively small. The paper describes the transition in the supercritical fluid region of equilibrium thermodynamics from parastatistics to mixed statistics, in which the Boltzmann statistics is realized for long-living clusters. In economics this corresponds to a negative nominal credit rate. Examples of this non-standard situation are presented.     

Phase Transition and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility ehows a clear size-dependent behaviorin low temperature region. This means that it should be divergent in this region.     

Free energies of supercritical solvation from molecular dynamics simulation and integral equation studies

We present here molecular dynamics (MD) simulation and integral equation (IE) studies on free energies of solvation of a non-polar solute in a dilute supercritical solvent to estimate the contribution of inhomogeneities in solvent density to the free energy of solvation. The solvation of a Xe-like solute in an Ne-like solvent as well as that of naphthalene in CO₂ have been investigated. At state points in the compressible region in the neighborhood of the solvent critical point, we have utilized the IE estimates of free energies to model the ideal situation where local density inhomogeneities would be absent. The difference between the free energies in the presence (as derived from MD simulation) and in the absence (from IE) of local density inhomogeneities was studied as a function of density along an isotherm close to the critical point. Although for low density supercritical solvents, a marked difference is observed, a study of the density dependence of this difference across the critical density does not directly reveal any signature of local density enhancement on the thermodynamics of solvation.     

Three-dimensional phase diagram of a ferroelectric

On the basis of the molecular-dynamic theory, by phenomenologically generalizing the expression for the energy of a ferroelectric, an equation of state is derived here for a ferroelectric in electric field intensity as well as temperature and mechanical stress. The σ(mechanical stress) — T(temperature) phase diagram is analyzed, whereupon ths spinodal, the critical point, and the supercritical line extending into the low-temperature range are plotted. A superposition of this diagram with the E (electric field intensity) — T(temperature) diagram yields a three-dimensional phase diagram in all three state variables. Its elements are the spinodal surface, the critical line, and the supercritical surface bordering on the critical line.     

The concentration fluctuations and the mutual diffusion coefficient in the supercritical solution

Molecular dynamics simulations on Lennard-Jones mixture in the supercritical region are performed. The number of the molecules in the unit cell is 23328 and the mole fraction is 0.5. The concentration fluctuations near the critical point are large compared to the ideal mixing. The mutual diffusion coefficient normalized by the self-diffusion coefficient has a small value near the critical density because of the large concentration fluctuation. The heat capacity, partial molar volume and correlation lengths of density and concentration in the supercritical region are compared with those at the normal density.     

Hydrothermal Synthesis of Metal Oxide Nanoparticles at Supercritical Conditions

Hydrothermal synthesis of CeO₂ and AlO(OH) were conducted using a flow type apparatus over the range of temperature from 523 to 673 K at 30 MPa. Nanosize crystals were formed at supercritical conditions. The mechanism of nanoparticle formation at supercritical conditions was discussed based on the metal oxide solubility and kinetics of the hydrothermal synthesis reaction. The reaction rate of Ce(NO₃)₃ and Al(NO₃)₃ was evaluated using a flow type reactor. The Arrhenius plot of the first order rate constant fell on a straight line in the subcritical region, while it deviated from the straight line to the higher values above the critical point. The solubility of Ce(OH)₃ and AlO(OH) was estimated by using a modified HKF model in a wide range of pH and temperature. In acidic conditions, where hydrothermal synthesis reaction is concerned, solubility gradually decreased with increasing temperature and then drastically dropped above the critical point. The trend of the solubility and the kinetics around the critical point could be explained by taking account of the dielectric constant effect on the reactions. There are two reasons why nanoparticle are formed at supercritical conditions. Larger particles are produced at subcritical conditions due to Ostwald ripening; that could not be observed in supercritical water because of the extremely low solubility. Second reason is the faster nucleation rate in supercritical water because of the lower solubility and the extremely fast reaction rate.     

Quantum critical end point for the Kondo volume collapse model

The Kondo volume collapse describes valence transitions in f-electron metals and is characterized by a line of first order transitions in the pressure-temperature phase plane terminated at critical end points. We analyze the quantum critical end point, when the lower end point is tuned to T=0, and determine the specific heat, thermal expansion, and compressibility. We find that the inclusion of quantum critical fluctuations leads to a novel bifurcation of the first order phase line. Finally, we show that critical strain fluctuations can cause both, superconductivity and non-Fermi liquid behavior near the critical point.     

Optical properties of the locally anisotropic liquid L-phase in a chiral anticlinic liquid crystal series

Optical Rotatory Power (ORP) measurements and Raman scattering experiments have been performed in various compounds of the nCTBB9 chiral series, which displays a locally anisotropic liquid phase referred to as “L-phase”. The ORP results are very reminiscent of the behaviour theoretically predicted for the Blue Phase III-to-Isotropic transition, close to and above the critical point in the temperature-chirality phase diagram. It is suggested however, considering both the Raman scattering results and the high stability of smectic phases in this series, that the supercritical state should be characterized by both chiral and smectic order with short correlation lengths. Received 20 December 1999 and Received in final form 6 March 2000     

Noise spectrum of a multicircuit oscillator

We study the inherent power fluctuations in multicircuit self-oscillating systems, which can be represented by an oscillating circuit with a nonlinear element connected in series, and by a multiresonance linear system. We obtain in a general form the expressions for the spectral density of power fluctuations. We show that the shape of the spectral line of a multicircuit self-oscillator is, in general, asymmetric, and the pedestal has a number of maxima. The structure of the pedestal is determined by the roots of the characteristic stability equation. An estimate of the width of the spectral line is given. As examples, we consider the line shape of two- and three-circuit frequency stabilization systems. We take into account the noise contributions of separate circuits at various temperatures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 71–78, January, 1984.In conclusion, the authors express their gratitude to I. I. Minakova for the useful discussions of the results of the paper.     

Interaction of a Hopf bifurcation and a symmetry-breaking bifurcation: Stochastic potential and spatial correlations

The multivariate master equation for a general reaction-diffusion system is solved perturbatively in the stationary state, in a range of parameters in which a symmetry-breaking bifurcation and a Hopf bifurcation occur simultaneously. Thestochastic potential U is, in general, not analytic. However, in the vicinity of the bifurcation point and under precise conditions on the kinetic constants, it is possible to define a fourth-order expansion ofU around the bifurcating fixed point. Under these conditions, the domains of existence of different attractors, including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors, are determined analytically. The role of fluctuations in the existence and stability of the various patterns is pointed out.     

Wavelet profiling of wind velocity using intensity fluctuations of laser beam propagating in the atmosphere

A method for the remote determination of the crosswind velocity profile using a wavelet analysis of fluctuations in the intensity of transmitted laser radiation is proposed. Results of an experimental investigation are presented that show how turbulent flow inhomogeneities (intensity fluctuations) localized in separate parts of the path contribute to the total distortions of the intensity distribution in a beam propagating along the path. It is demonstrated that, by separating fluctuations on various scales in the beam intensity distribution and following the evolution of these fluctuations, it is possible to determine the arrangement of turbulent zones along the path of propagation of the laser beam and to evaluate the velocity of motion of the medium in these zones. Wavelet estimates of the wind velocity from fluctuations of the transmitted radiation intensity for a given point of the atmospheric path agree with the results of direct velocity measurements at this point.     

Singular point of a system of Lennard-Jones particles at negative pressures

The method of molecular dynamics is used in a system of 2048 Lennard-Jones particles to determine the spinodal of a stretched liquid and crystal and the lines of their phase equilibrium at negative pressures. It is shown that a metastable extension of the melting line does not reach the zero isotherm, and ends on the spinodal of a stretched liquid. The point of termination of metastable liquid-crystal phase equilibrium is the singular point at a thermodynamic surface of states.     

Theory of the vortex matter transformations in high-Tc superconductor YBCO

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transition line. The line, however, makes a wiggle near the experimentally claimed critical point at 12 T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy, and the specific heat discontinuities at melting compare well with experiments.