Simple dispersion relations for Coulomb and Yukawa fluids

Very simple explicit analytical expressions, which are able to describe the dispersion relations of collective modes in strongly coupled plasma fluids, are summarized. The accuracy of these expressions is demonstrated using the comparison with available results from benchmark numerical simulations.Comment: To be published in a special issue of IEEE Trans. Plasma Sci. devoted to ICPDP 2017 in Pragu

Note: Melting criterion for soft particle systems in two dimensions

A simple criterion for melting of two-dimensional crystals with soft long-ranged interactions is proposed. It states that the ratio of the transverse sound velocity of an ideal crystalline lattice to the thermal velocity is a quasi-universal number close to $4.3$ at melting. This criterion is arrived by reference to the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory of two-dimensional melting, combined with the observation that the ratio of transverse-to-longitudinal sound velocities is small in the soft interaction limit. Application of this criteria allows estimating melting lines in a simple yet relatively accurate manner. Two-dimensional weakly screened Yukawa systems represent one relevant example considered.Comment: 2 pages note in JC

Accurate transport cross sections for the Lennard-Jones potential

Physically motivated expressions for the transport cross sections describing classical scattering in the Lennard-Jones potential are proposed. These expressions, which agree with the numerical results better than to within $\pm 1$, can be easy implemented in practical situations. Some relevant examples are provided.Comment: 6 page

Practical expressions for the internal energy and pressure of Yukawa fluids

Simple practical expressions are put forward, which allow to estimate thermodynamic properties of Yukawa fluids in a wide range of coupling, up to the fluid-solid phase transition. These expressions demonstrate excellent agreement with the available results from numerical simulations. The approach provides simple and accurate tool to estimate thermodynamic properties of Yukawa fluids and related systems in a broad range of parameters.Comment: To be published in Phys. Rev.

High-frequency elastic moduli of two-dimensional Yukawa fluids and solids

An approach to calculate high-frequency bulk and shear modului of two-dimensional (2D) weakly screened Yukawa fluids and solids is presented. Elastic moduli are directly related to sound velocities and other important characteristics of the system. In this article we discuss these relations and present exemplary calculation of the longitudinal, transverse, and instantaneous sound velocities and derive a differential equation for the Einstein frequency. Simple analytical results presented demonstrate good accuracy when compared with numerical calculations. The obtained results can be particularly useful in the context of 2D colloidal and complex (dusty) plasma monolayers.Comment: To be published in Phys. Plasma

Classical scattering in strongly attractive potentials

Scattering in central attractive potentials is investigated systematically, in the limit of strong interaction, when large-angles scattering dominates. In particular, three important model interactions (Lennard-Jones, Yukawa, and exponential), which are qualitatively different from each other, are studied in detail. It is shown that for each of these interactions the dependence of the scattering angle on the properly normalized impact parameter exhibits a quasi-universal behavior. This implies simple scaling of the transport cross sections with energy in the considered limit. Accurate fits for the momentum transfer cross section are suggested. Applications of the obtained results are discussed.Comment: Phys. Rev. E (in press

Effective Coulomb Logarithm for One Component Plasma

An expression for the effective Coulomb logarithm in one-component-plasma is proposed, which allows to extend the applicability of the classical formula for the self-diffusion coefficient to the strongly coupled regime. The proposed analytical approximation demonstrates reasonable agreement with previous numerical simulation results. Relevance to weakly screened Yukawa systems (and, in particular, complex plasmas) is discussed.Comment: 4 pages, 3 figure

Accurate momentum transfer cross section for the attractive Yukawa potential

Accurate expression for the momentum transfer cross section for the attractive Yukawa potential is proposed. This simple analytic expression agrees with the numerical results better than to within $\pm 2\%$ in the regime relevant for ion-particle collisions in complex (dusty) plasmas.Comment: to be published in Physics of Plasma

Thermodynamics of two-dimensional Yukawa systems across coupling regimes

Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-H\"uckel) systems is studied systematically using molecular dynamics (MD) simulations. Simulations cover very broad parameter range spanning from weakly coupled gaseous states to strongly coupled fluid and crystalline states. Important thermodynamic quantities such as internal energy and pressure are obtained and accurate physically motivated fits are proposed. This allows us to put forward simple practical expressions to describe thermodynamic properties of two-dimensional Yukawa systems. For crystals, in addition to numerical simulations, the recently developed shortest-graph interpolation method is applied to describe pair correlations and hence thermodynamic properties. It is shown that the finite-temperature effects can be accounted for by using simple correction of peaks in the pair correlation function. The corresponding correction coefficients are evaluated using MD simulation. The relevance of the obtained results in the context of colloidal systems, complex (dusty) plasmas, ions absorbed to interfaces in electrolytes is pointed out.Comment: 11 pages, 3 figures, 5 table

Accurate freezing and melting equations for the Lennard-Jones system

Analyzing three approximate methods to locate liquid-solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the conventional Lennard-Jones system. The emerging equations can be written as $T={\mathcal A}\rho^4+{\mathcal B}\rho^2$ in normalized units. We suggest to determine the values of the coefficients ${\mathcal A}$ at freezing and melting from the high-temperature limit, governed by the inverse twelfth power repulsive potential. The coefficients ${\mathcal B}$ can be determined from the triple point parameters of the LJ fluid. This produces freezing and melting equations which are exact in the high-temperature limit and at the triple point, and show remarkably good agreement with numerical simulation data in the intermediate region.Comment: 6 pages, 1 figur