arXiv subjects

I. M. Mryglod

Publications and source records attributed to I. M. Mryglod.

14 recordsLinked to original sources

arXiv2019

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches

Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the MD data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode (GCM) theory, the mode coupling theory (MCT), and some other theoretical approaches.

cond-mat.stat-mech↗

arXiv2018

Spatiotemporal pattern formation in a three-variable CO oxidation reaction model

The spatiotemporal pattern formation is studied in the catalytic carbon monoxide oxidation reaction that takes into account the diffusion processes over the Pt(110) surface, which may contain structurally different areas. These areas are formed during CO-induced transition from a reconstructed phase with $1\times2$ geometry of the overlayer to a bulk-like ($1\times1$) phase with square atomic arrangement. Despite the CO oxidation reaction being non-autocatalytic, we have shown that the analytic conditions of the existence of the Turing and the Hopf bifurcations can be satisfied in such systems. Thus, the system may lose its stability in two ways --- either through the Hopf bifurcation leading to the formation of temporal patterns in the system or through the Turing bifurcation leading to the formation of regular spatial patterns. At a simultaneous implementation of both scenarios, spatiotemporal patterns for CO and oxygen coverages are obtained in the system.

cond-mat.stat-mech↗

arXiv2018

A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales

A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions, which have a purely kinetic origin. The VAFs obtained within our approach are compared with the results of the Markovian approximation for memory kernels. It is shown that although in the "overdamped" regime both approaches agree to a large extent at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities of spectral functions in the complex frequency plane.

cond-mat.stat-mech↗

arXiv2009

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass-asymmetry

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio $μ$, including the limiting case $μ=\infty$, for different mole fractions $x$. Within a large range of $x$ and $μ$ the product of the diffusion coefficient of the heavy species $D_{2}$ and the total shear viscosity of the mixture $η_{m}$ is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function and the van Hove correlation function.

cond-mat.soft↗

arXiv2007

Crossover behavior in fluids with Coulomb interactions

According to extensive experimental findings, the Ginzburg temperature $t_{G}$ for ionic fluids differs substantially from that of nonionic fluids [Schröer W., Weigärtner H. 2004 {\it Pure Appl. Chem.} {\bf 76} 19]. A theoretical investigation of this outcome is proposed here by a mean field analysis of the interplay of short and long range interactions on the value of $t_{G}$. We consider a quite general continuous charge-asymmetric model made of charged hard spheres with additional short-range interactions (without electrostatic interactions the model belongs to the same universality class as the 3D Ising model). The effective Landau-Ginzburg Hamiltonian of the full system near its gas-liquid critical point is derived from which the Ginzburg temperature is calculated as a function of the ionicity. The results obtained in this way for $t_{G}$ are in good qualitative and sufficient quantitative agreement with available experimental data.

cond-mat.soft↗

arXiv2004

XY Spin Fluid in an External Magnetic Field

A method of integral equations is developed to study inhomogeneous fluids with planar spins in an external field. As a result, the calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids. The approach proposed is applied to the ferromagnetic XY spin fluid in a magnetic field using a soft mean spherical closure and the Born-Green-Yvon equation. This provides an accurate reproduction of the complicated phase diagram behavior obtained by cumbersome Gibbs ensemble simulation and multiple histogram reweighting techniques.

cond-mat.stat-mech↗

arXiv2004

Ising fluids in an external magnetic field: an integral equation approach

The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field $H$ for a wide class of Ising fluid models with various ratios $R$ for the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths $z_1$ and $z_2$, corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in $R$ as well as in $z_1$ and $z_2$ can lead to different topologies of the phase diagrams. In particular, depending on the value of $R$, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing $H$. The para-ferro magnetic transition is also affected by changes in $R$ and the screening lengths. At H=0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For $H \to \infty$, it reduces to a pure nonmagnetic fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated, that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when $z_1$ and $z_2$ are large). In the Kac limit $z_1,z_2 \to +0$, both approaches tend to nearly the same results.

cond-mat.stat-mech↗

arXiv2003

Critical behavior of the restricted primitive model

We study the critical behavior of the systems dominated by Coulombic interaction. For this purpose we used the method of collective variables with a reference system. Starting from the Hamiltonian of the restricted primitive model (RPM), the simplest model of ionic fluids, we obtain the functional of the grand partition function given in terms of the two collective variables: the collective variables $ρ_{\mathbf{k}}$ and $c_{\mathbf{k}}$ describing fluctuations of the total number density and charge density, respectively. As the result of integration over the variables $c_{\mathbf{k}}$, the microscopic based effective Hamiltonian of the RPM at the vicinity of its gas-liquid critical point was constructed. The coefficients of the effective Hamiltonian, describing the density fluctuations nearby the gas-liquid critical point, are analyzed. It is shown that, in spite of the long-range character of the Coulombic potential, the effective interactions appeared at this level of the description have the short-range character. As a result, the effective Hamiltonian obtained for the RPM in the vicinity of the critical point has the form of the Ginzburg-Landau-Wilson Hamiltonian of an Ising-like model in a magnetic field. This confirms the fact that the critical behavior of the RPM nearby the gas-liquid critical point belongs to the universal class of a 3D Ising model.

cond-mat.soft↗

arXiv2003

Phase diagrams of classical spin fluids: the influence of an external magnetic field on the liquid-gas transition

The influence of an external magnetic field on the liquid-gas phase transition in Ising, XY, and Heisenberg spin fluid models is studied using a modified mean field theory and Gibbs ensemble Monte Carlo simulations. It is demonstrated that the theory is able to reproduce quantitatively all characteristic features of the field dependence of the critical temperature T_c(H) for all the three models. These features include a monotonic decrease of T_c with rising H in the case of the Ising fluid as well as a more complicated nonmonotonic behavior for the XY and Heisenberg models. The nonmonotonicity consists in a decrease of T_c with increasing H at weak external fields, an increase of T_c with rising H in the strong field regime, and the existence of a minimum in T_c(H) at intermediate values of H. Analytical expressions for T_c(H) in the large field limit are presented as well. The magnetic para-ferro phase transition is also considered in simulations and described within the mean field theory.

cond-mat.stat-mech↗

arXiv2000

Corrections to scaling in systems with thermodynamic constraints

Using thermodynamic arguments treatment it is shown that, independently on whether Fisher renormalization changes the critical exponents near a phase transition in a constrained system or not, new corrections to scaling with correction exponents proportional to the specific heat index $α$ appear. Because of the smallness $α$ for the Ising, the XY, and the Heisenberg universality classes these corrections are dominant and can cause strong crossover effects. It is proven that the appearance of Fisher corrections to scaling is a quite general feature of the systems with constraints.

cond-mat.stat-mech↗

arXiv2000

Molecular dynamics simulations of spin and pure liquids with preserving all the conservation laws

A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the time step, all the conservation laws inherent in the description without breaking the time reversibility. As a result, an implicit second-order algorithm is derived and applied to pure as well as spin liquids for which the dynamics is characterized by the conservation of total energy, linear and angular momenta as well as magnetization and individual spin lengths. It is demonstrated on the basis of Lennard-Jones and Heisenberg fluid models that when such quantities as energy and magnetization must be conserved perfectly, the new algorithm turns out to be more efficient than popular decomposition integrators and standard predictor-corrector schemes.

cond-mat.stat-mech↗

arXiv2000

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling (FSS) technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent $α$. The appearance of such new corrections to scaling is a general feature of systems with constraints.

cond-mat.stat-mech↗

arXiv2000

Conservation-laws-preserving algorithms for spin dynamics simulations

We propose new algorithms for numerical integration of the equations of motion for classical spin systems with fixed spatial site positions. The algorithms are derived on the basis of a mid-point scheme in conjunction with the multiple time staging propagation. Contrary to existing predictor-corrector and decomposition approaches, the algorithms introduced preserve all the integrals of motion inherent in the basic equations. As is demonstrated for a lattice ferromagnet model, the present approach appears to be more efficient even over the recently developed decomposition method.

cond-mat.stat-mech↗

arXiv2000

Algorithm for molecular dynamics simulations of spin liquids

A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the algorithm exactly conserves spin lengths and can be used with much larger time steps than those inherent in standard predictor-corrector schemes. The results obtained for time correlation functions demonstrate the evident dynamic interplay between the liquid and magnetic subsystems.

cond-mat.soft↗