Thermal fluctuations of pair interaction forces in liquid Yukawa systems
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Thermal Fluctuations of Pair Interaction Forces in Liquid Yukawa Systems O. S. Vaulina* Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 127412 Russia *e-mail: [email protected] Received February 3, 2016
Abstract—The dynamics of charged particles in two- and three-dimensional Yukawa systems is studied using numerical methods. Nonideal systems are simulated in a wide range of their parameters. The density of thermal fluctuations of pair interaction forces in liquid structures is obtained and compared with the internal energy density of the systems under study. DOI: 10.1134/S1063780X17010135
( m = 2, n = r p−2 ), where rp is the average interparticle distance. As the temperature decreases (T → 0 ), the internal energy density U tends to the Madelung energy U 0 (the energy density of the solid body at T = 0 ). If the potential of interaction between particles in the system is known, U0 can easily be calculated for any type of crystalline lattice, e.g., for the face centered cubic (FCC) and body centered cubic (BCC) lattices or for the two-dimensional hexagonal (i.e., primitive triangle) lattice [10]. A simple analytic approximation for the energy density in liquid systems was proposed in [8–10] on the basis of the semiempirical theory of jumps, detailed balance principle, and absorption/adsorption theory for strongly nonideal two-dimensional (m = 2 ) and three-dimensional ( m = 3 ) liquid systems with the 2 effective coupling parameter Γ * = r p2φ ( ) /(2T ) in the
1. INTRODUCTION Studies of the physical properties of systems of interacting particles is of great importance for different branches of science and technology, such as astronomy, plasma physics, polymer physics, biology, medicine, etc. [1–7]. The key problem in such studies is that an adequate theory of liquid that would allow one to derive simple parameterized relations for the equation of liquid state, thermodynamic characteristics, and kinetic coefficients is still lacking. In studying the properties of nonideal systems, various semiempirical approaches and different numerical methods (methods of molecular dynamics and the Monte Carlo method) are widely used [1–6]. In particular, the thermodynamic properties of liquids (such as the volume coefficient of thermal expansion, heat capacity, isothermal compressibility, etc.) are usually analyzed using numerical calculations and/or approximate equations of state (thermal and/or caloric) [6–12]. For nonideal systems with isotropic pair interactions, the thermodynamic functions of liquid, such as the internal energy and pressure, are determined by the temperature Т, density n, interaction energy φ(r ), and pair correlation function g(r ) (the latter can be found experimentally or by numerical simulation) [1– 3, 6–10]. The internal energy density U of the system can be written as [6–10]
range from Γ * ≈ 10 to Γ * = Γ *m , where Γ *m is the value of the parameter Г* at the melting curve of the system and φ(2) is the second derivative of the pair interaction energy at the
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