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.Comment: 11 pages, 6 figures, 1 tabl

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.Comment: 14 pages, 2 figure

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.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

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.Comment: 13 pages, 2 figure

Academic research groups: evaluation of their quality and quality of their evaluation

In recent years, evaluation of the quality of academic research has become an increasingly important and influential business. It determines, often to a large extent, the amount of research funding flowing into universities and similar institutes from governmental agencies and it impacts upon academic careers. Policy makers are becoming increasingly reliant upon, and influenced by, the outcomes of such evaluations. In response, university managers are increasingly attracted to simple indicators as guides to the dynamics of the positions of their various institutions in league tables. However, these league tables are frequently drawn up by inexpert bodies such as newspapers and magazines, using rather arbitrary measures and criteria. Terms such as "critical mass' and "metrics" are often bandied about without proper understanding of what they actually mean. Rather than accepting the rise and fall of universities, departments and individuals on a turbulent sea of arbitrary measures, we suggest it is incumbent upon the scientific community itself to clarify their nature. Here we report on recent attempts to do that by properly defining critical mass and showing how group size influences research quality. We also examine currently predominant metrics and show that these fail as reliable indicators of group research quality.Comment: Presented at the International Conference on Computer Simulation in Physics and Beyond in Moscow, 2015. The Proceedings will appear in Journal of Physics: Conference Series (JPCS

The collective variables representation of simple fluids from the point of view of statistical field theory

The collective variable representation (CV) of classical statistical systems such as, for instance, simple liquids has been intensively developed by the Ukrainian school after seminal works by Prof. Ihor Yukhnovskii. The basis and the structure of the CV representation are reexamined here from the point of view of statistical field theory and compared with another exact statistical field representation of liquids based upon a Hubbard-Stratonovich transform. We derive a two-loop expansion for the grand potential and free energy of a simple fluid in both versions of the theory. The results obtained by the two approaches are shown to coincide at each order of the loop expansion. The one-loop results are identical to those obtained within the framework of the random phase approximation of the theory of liquids. However, at the second-loop level, new expressions for pressure and the free energy are obtained, yielding a new type of approximation.Започаткований в роботах професора Ігоря Юхновського метод колективних змінних (КЗ) був успішно розвинутий до опису класичних статистичних систем українською школою. В даній роботі основи і структура представлення КЗ для рідин вивчається з точки зору статистико-польового підходу і порівнюється з іншими точними теоріями, що використовують перетворення Габбарда-Стратоновича. Для випадку простого плину отримано вираз для вільної енергії в обох версіях теорії і показано, що отримані результати співпадають в кожному порядку петлевого розвинення. Результати, отримані в однопетлевому наближенні є ідентичними до отриманих в наближенні хаотичних фаз. Проте, двопетлеве наближення дає новий вираз для тиску і вільної енергії і є новим типом наближення

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 $\alpha$. The appearance of such new corrections to scaling is a general feature of systems with constraints.Comment: 12 pages, 2 figures; submitted to Phys. Rev. Let

Optimized Verlet-like algorithms for molecular dynamics simulations

New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the new algorithms appear to be more efficient than the original Verlet versions which correspond to a particular case when the introduced parameter is equal to zero. Like the original versions, the proposed counterparts are symplectic and time reversible, but lead to an improved accuracy in the generated solutions at the same overall computational costs. The advantages of the new algorithms are demonstrated in molecular dynamics simulations of a Lennard-Jones fluid.Comment: 5 pages, 2 figures; submitted to Phys. Rev.