176 research outputs found
Gibbs free energy and Helmholtz free energy for a three-dimensional Ising-like model
The critical behavior of a 3D Ising-like system is studied at the microscopic
level of consideration. The free energy of ordering is calculated analytically
as an explicit function of temperature, an external field and the initial
parameters of the model. Within a unified approach, both Gibbs and Helmholtz
free energies are obtained and the dependencies of them on the external field
and the order parameter, respectively, are presented graphically. The regions
of stability, metastability, and unstability are established on the order
parameter-temperature plane. The way of implementation of the well-known
Maxwell construction is proposed at microscopic level.Comment: 10 pages, 4 figure
A non-classical van der Waals loop: Collective variables method
The equation of state is investigated for an Ising-like model in the
framework of collective variables method. The peculiar feature of the theory is
that a non-classical van der Waals loop is extracted. The results are compared
with the ones of a trigonometric parametric model in terms of normalized
magnetization, \tilde{M}, and field, \tilde{H}.Comment: 9 pages, 2 figure
The equation of state of a cell fluid model in the supercritical region
The analytic method for deriving the equation of state of a cell fluid model
in the region above the critical temperature () is
elaborated using the renormalization group transformation in the collective
variables set. Mathematical description with allowance for non-Gaussian
fluctuations of the order parameter is performed in the vicinity of the
critical point on the basis of the model. The proposed method of
calculation of the grand partition function allows one to obtain the equation
for the critical temperature of the fluid model in addition to universal
quantities such as critical exponents of the correlation length. The isothermal
compressibility is plotted as a function of density. The line of extrema of the
compressibility in the supercritical region is also represented.Comment: 26 pages, 6 figures, 1 tabl
The Procedure of Termination of the Criminal Case (Criminal Prosecution) on Rehabilitation Bases in the Russian Federation and Mongolia
The article describes the features of the modern criminal procedure of Mongolia, which consist in the absence of the stage of initiation of criminal proceedings, confluence of a decision of initiation of criminal proceedings and decision about prosecution as an accused, in existence of uniform termination procedure of investigation of the criminal cases subject to termination or referral to court. Comparative legal analysis of rehabilitating grounds for termination of criminal case (criminal prosecution) is carried out. The content of criminal procedural activities at the end of the investigation is considered. The procedure for appealing against decisions on termination of the criminal case is researched. It is characterized by a lack of judicial control in pre-trial proceedings in Mongolia. The procedure and law enforcement practice of realization of the right to rehabilitation is analyzed. The conclusion that departmental regulation hinders its implementation is made. The Authors state that the procedure for termination of the criminal case provided by the Criminal procedure code of Mongolia contains fairly extended guarantees of establishing the truth. The normative regulation completely excludes multiple transfer of the criminal case from the police to prosecutor in the event of discrepancy in the assessment of the qualification of the crime and the completeness of the investigation. The absence of a procedure for the termination of criminal prosecution due to non-involvement is a serious drawback of Mongolian legislation. In general, the mechanism of termination of the criminal case in the criminal procedure legislation of Mongolia is conceptually more consistent and logical, but in terms of elaboration of procedural mechanisms is much inferior to Russian legislation
Analytical calculation of the critical temperature and estimation of the critical region size for a fluid model
An analytical procedure for calculating the critical temperature and
estimating the size of critical region for a cell fluid model is developed. Our
numerical calculations are illustrated by the case of the Morse potential
parameters characterizing the alkali metals (sodium and potassium). The
critical temperatures found for liquid sodium and potassium as solutions of the
resulting quadratic equation agree with experimental data. The expression for
the relative temperature determining the critical region size is obtained
proceeding from the condition for the critical regime existence. In the cases
of sodium and potassium, the value of this temperature is of the order of a few
hundredths.Comment: 15 pages, 2 table
Morse fluids in the immediate vicinity of the critical point: Calculation of thermodynamic coefficients
The previously proposed approach for the microscopic description of the
critical behavior of Morse liquids based on the cell fluid model is applied to
the case where the parameters of the Morse interaction potential correspond to
alkali metals (sodium and potassium). The critical temperatures, densities, and
pressures obtained for sodium and potassium agree with the experimental
results. The thermodynamic coefficients (isothermal compressibility, density
fluctuations, and thermal expansion) of sodium are investigated in the
supercritical temperature region. Numerical calculations of thermodynamic
coefficients are performed close to the critical point, where carrying out
theoretical and experimental research is challenging. The change in
compressibility with increasing density at various temperature values is
traced. The behavior of density fluctuations approaching the critical point is
shown for different temperatures. The variation in the magnitude of the thermal
expansion with increasing temperature for different pressure values is
illustrated.Comment: 14 pages, 6 figures, 1 tabl
Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture
A microscopic approach to the investigation of the behaviour of a symmetrical
binary fluid mixture in the vicinity of the vapour-liquid critical point is
proposed. It is shown that the problem can be reduced to the calculation of the
partition function of a 3D Ising model in an external field. For a square-well
symmetrical binary mixture we calculate the parameters of the critical point as
functions of the microscopic parameter r measuring the relative strength of
interactions between the particles of dissimilar and similar species. The
calculations are performed at intermediate () and moderately long
() intermolecular potential ranges. The obtained results agree
well with the ones of computer simulations.Comment: 14 pages, Latex2e, 5 eps-figures included, submitted to
J.Phys:Cond.Ma
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