Thermodynamic properties of two-dimensional Yukawa systems

The simple analytical approximation for the energy densities in two-dimensional Yukawa systems is proposed for the wide range of parameters of non-ideal fluids. The use of this approach allows determining all thermodynamic functions and characteristics on the base of general thermodynamic relationships. The comparisons of obtained results with the numerical study of thermodynamic properties are presented. Simulations were performed for parameters typical for the laboratory dusty plasma experiments.     

Thermodynamics and phase transitions in two-dimensional Yukawa systems

The results of numerical simulations of strongly-coupled two-dimensional dissipative Yukawa systems are presented. The thermodynamic characteristics of these systems were studied, namely the internal energy, the specific heat and the entropy. For the first time, it is discovered that the considered characteristics have two singular points on the melting line; one of these points corresponds to the first-order phase transition from crystal to the hexatic phase, and another point corresponds to the second-order phase transition from the hexatic phase to the isotropic liquid. The obtained results are compared to the existing numerical and analytical data.     

Orientational order and topological defects in two-dimensional Yukawa systems

New numerical results concerned with formation of orientational order and topological defects in non-ideal systems of particles, interacted via screened Coulomb potential, are presented. Calculations have been performed in a wide range of parameters, corresponding to the experimental conditions in the laboratory dusty plasmas. Relations between a number of topological defects and shape of a bond-angular correlation function are obtained for the first time.     

Heat transfer in a two-dimensional crystalline complex (dusty) plasma

Heating and heat transfer were studied in a two-dimensional crystalline complex plasma at the kinetic level. The lattice was formed of microspheres levitated in a plasma sheath. One half of the crystal was heated anisotropically to obtain higher kinetic temperatures in one direction and heat conduction was observed in real time. It was found that the longitudinal phonons conduct heat better than the transverse. The thermometric conductivity coefficient was measured to be 53 mm2/s for longitudinal heating and 30 mm2/s for transverse heating. Heat decay lengths and energy exchange times between the temperature components were determined.     

Mayer coefficients in two-dimensional coulomb systems

We show that, for neutral systems of particles of arbitrary charges in two dimensions, with hard cores, coefficients of the Mayer series for the pressure exist in the thermodynamic limit below certain thresholds in the temperature. Our methods apply also to correlation functions and yield bounds on the asymptotic behavior of their Mayer coefficients.     

Shear viscosity of two-dimensional Yukawa systems in the liquid state

The shear viscosity of a two-dimensional (2D) liquid was calculated using molecular dynamics simulations with a Yukawa potential. The viscosity has a minimum at a Coulomb coupling parameter Gamma of about 17, arising from the temperature dependence of the kinetic and potential contributions. Previous calculations of 2D viscosity were less extensive as well as for a different potential. The stress autocorrelation function was found to decay rapidly, contrary to earlier work. These results are useful for 2D condensed matter systems and are compared to a dusty plasma experiment.     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.     

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.     

Emerging trends in numerical simulations of combustion systems

Numerical simulations have played a vital role in the design of modern combustion systems. Over the last two decades, the focus of research has been on the development of the large eddy simulation (LES) approach, which leveraged the vast increase in computing power to dramatically improve predictive accuracy. Even with the anticipated increase in supercomputing capabilities, the use of LES in design is limited by its high computational cost. Moreover, to aid decision making, such LES computations have to be augmented to estimate underlying uncertainties in simulation components. At the same time, other changes are happening across industries that build or use combustion devices. While efficiency and emissions reduction are still the primary design objectives, reducing cost of operation by optimizing maintenance and repair is becoming an important segment of the enterprise. This latter quest is aided by the digitization of combustors, which allows collection and storage of operational data from a host of sensors over a fleet of devices. Moreover, several levels of computing including low-power hardware present on board the combustion systems are becoming available. Such large data sets create unique opportunities for design and maintenance if appropriate numerical tools are made available. As LES revolutionized computing-guided design by leveraging supercomputing, a new generation of numerical approaches is needed to utilize this vast amount of data and the varied nature of computing hardware. In this article, a review of emerging computational approaches for this heterogeneous data-driven environment is provided. A case is made that new but unconventional opportunities for physics-based combustion modeling exist in this realm.     

Cutoff wave number for shear waves in a two-dimensional Yukawa system (dusty plasma)

The cutoff wave number for shear waves in a liquid-state strongly coupled plasma was measured experimentally. The phonon spectra of random particle motion were measured at various temperatures in a monolayer dusty plasma, where microspheres interact with a Yukawa potential. In the liquid state of this particle suspension, shear waves were detected only for wavelengths smaller than 20 to 40 Wigner-Seitz radii, depending on the Coulomb coupling parameter. The temperature of the suspension was controlled using a laser-heating method.     

Microscopic-scale simulations of macroscopic flow patterns in non-equilibrium two-dimensional systems

Summary We have used a molecular-dynamics simulation for reproducing the behaviour of a two-dimensional fluid flow submitted to external perturbations and embedded in a non-inertial reference frame. This simple model has been used to verify current hypotheses on the causes generating a cyclonic circulation in the North Tyrrhenian basin, provided one uses suitable perturbation strenghts scaled from the real-world dynamics. Results put in evidence that the onset of a stationary cyclonic circulation which superimposes to the S-N flow requires the simultaneous presence of an orthogonal and an anti-parallel stream. This finding is in agreement with the hypotheses suggested by a preliminary analysis of experimental data. The limits of such models are discussed together with possible extensions to reproduce mesoscopic systems, in order to simulate the coexistence of large- and small-scale dynamics. The model is particularly suited to deal with boundary conditions of general analytical shapes.     

New proposal for numerical simulations of theta-vacuum-like systems

We propose a new approach to perform numerical simulations of theta-vacuum-like systems, test it in two analytically solvable models, and apply it to CP3. The main new ingredient in our approach is the method used to compute the probability distribution function of the topological charge at theta=0. We do not get unphysical phase transitions (flattening behavior of the free energy density) and reproduce the exact analytical results for the order parameter in the whole theta range within a few percent.     

Scaling law for the fluid-solid phase transition in Yukawa systems (dusty plasmas)

Yukawa systems serve as models for plasmas and colloidal suspensions of charged particles. The state of these systems is determined by two dimensionless parameters: k = a/λ _D , which is the ratio of the mean interparticle distance to the Debye length λ _D , and Γ = Z _d ² e ²/aT _d , which is the ratio of the Coulomb potential energy to the particle temperature T _d (Z _d is the charge of each particle). We propose an empirical scaling law for the critical coupling parameter Γ _c needed for crystallization in Yukawa systems. The dependence of Γ _c on k is in good agreement with recent molecular dynamics simulations.     

Shear viscosity and shear thinning in two-dimensional Yukawa liquids

A two-dimensional Yukawa liquid is studied using two different nonequilibrium molecular dynamics simulation methods. Shear viscosity values in the limit of small shear rates are reported for a wide range of Coulomb coupling parameter and screening lengths. At high shear rates it is demonstrated that this liquid exhibits shear thinning; i.e., the viscosity eta diminishes with increasing shear rate. It is expected that two-dimensional dusty plasmas will exhibit this effect.     

Strong coupling effects in binary Yukawa systems

We analyze the acoustic collective excitations in two- and three-dimensional binary Yukawa systems, consisting of two components with different masses. A theoretical analysis reveals a profound difference between the weakly and strongly correlated limits: at weak coupling the two components interact via the mean field only and the oscillation frequency is governed by the light component. In the strongly correlated limit the mode frequency is governed by the combined mass, where the heavy component dominates. Computer simulations in the full coupling range extend and confirm the theoretical results.     

Test of the Stokes-Einstein relation in a two-dimensional Yukawa liquid

The Stokes-Einstein relation, relating the diffusion and viscosity coefficients D and eta, is tested in two dimensions. An equilibrium molecular-dynamics simulation was used with a Yukawa pair potential. Regimes are identified where motion is diffusive and D is meaningful. The Stokes-Einstein relation, Deta proportional k(B)T, was found to be violated near the disordering transition; under these conditions collective particle motion exhibits dynamical heterogeneity. At slightly higher temperatures, however, the Stokes-Einstein relation is valid. These results may be testable in strongly coupled dusty plasma experiments.     

Two-stage melting in quasi-two-dimensional dissipative Yukawa systems

The results of numerical study of physical characteristics (the pair and triplet correlation functions, the isothermal compressibility, the heat capacities, and the diffusion constants) are presented for quasi-2D dissipative Yukawa systems. The specific features of these characteristics (reflecting the two-stage melting scenario) are investigated.     

二维自旋系统aging现象的数值模拟研究

应用动力学蒙特卡罗模拟方法，对二维Ising模型和二维XY模型的aging现象展开数值研究.系统在零外场条件下从高温无序相淬火到临界温度T_c时，通过测量自关联函数A(t,t′)，观察到二维Ising模型和二维XY模型的aging现象，获得更精确的动力学临界指数λ_c和z的值.特别是对二维XY模型，当初始态为完全无序态时，模拟结果证实存在关于标度行为的对数修正. 关键词： 蒙特卡罗模拟 相变和临界行为 aging现象