Heat capacity of inhomogeneous substance in gravitational field in the vicinity of critical point

Altitude and temperature dependences of inhomogeneous substance heat capacity have been studied in the gravitational field of the Earth in the vicinity of critical point on the basis of the fluctuation theory of phase transitions and the theory of gravitational effect. The obtained data prove non-monotonous field and temperature dependences of heat capacity of spatially inhomogeneous substance that is supported by experimental research of heat capacity in macro and confined systems under terrestrial conditions and at space flight micro-gravitation.     

Extended equation for the coexistence curve of molecular liquids in the vicinity of a critical point

An extended equation of state for substances along a phase interface, based on the Van der Waals model of a gas with fluctuations of the order parameter is confirmed by experimental data along the coexistence curve of a wide class of homogeneous and inhomogeneous molecular liquids under the Earth’s field of gravity. It is shown that the parameters of the extended equation for the coexistence curve of homogeneous and spatially inhomogeneous molecular liquids are linear functions of the compressibility factor. This allows us to predict the parameters of the equations of state of molecular liquids that are difficult to investigate experimentally.     

Van der Waals model and equation of state of nitrobenzene-alkanes solutions near the critical consolute temperature

On the basis of the fluctuation theory of phase transitions a system close to the critical point is the ideal gas of order parameter fluctuations. An extended equation of state for binary solutions close to the critical consolute temperature has been proposed taking into account the properties of a real Van der Waals gas in this model. This equation has been used to analyze the temperature dependences of the concentrations of a series of nitrobenzene + alkane binary solutions in terms of different order parameters. It has been shown that the molar concentration of the solution should be used as an order parameter of the analyzed systems. It has been determined that the parameters of the extended equation of state are linear functions of (a) the number of carbon atoms in alkanes and (b) the compressibility factor of the solution components.     

Soliton and Periodic Wave Solutions of the Nonlinear Loaded (3+1)-Dimensional Version of the Benjamin-Ono Equation by Functional Variable Method

In this article, we establish new travelling wave solutions for the nonlinear loaded (3+1)-dimensional version of the Benjamin-Ono equation by the functional variable method. The performance of this method is reliable and effective and the method provides the exact solitary wave solutions and periodic wave solutions. The solution procedure is very simple and the traveling wave solutions are expressed by hyperbolic functions and trigonometric functions. After visualizing the graphs of the soliton solutions and the periodic wave solutions, the use of distinct values of random parameters is demonstrated to better understand their physical features. It has been shown that the method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.