Power law decay of correlations in stationary nonequilibrium lattice gases with conservative dynamics

We report computer simulations and high-temperature approximations of the pair correlation in a stationary nonequilibrium system, a lattice gas subject to a strong uniform driving fieldE. The dynamics of the system is given by hoppings of particles to adjacent empty sites with rates biased for jumps in the direction ofE. We study the anisotropic short-distance behavior as well as the long-distance decay properties of the two-point correlations along the principal axes. The simulations as well as the (approximate) expansion in strongly suggest that the correlations in this system have a power law decay,r ^–D for dimensionsD=2 and 3, even at high temperatures.     

Renormalized equilibria of a Schlögl model lattice gas

A lattice gas model for Schlögl's second chemical reaction is described and analyzed. Because the lattice gas does not obey a semi-detailed-balance condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent set of equations for the exact homogeneous equilibria are described, using a generalized cluster-expansion scheme. These equations are solved in the two-particle BBGKY approximation, and the results are compared to numerical experiment. It is found that this approximation describes the equilibria far more accurately than the Boltzmann approximation. It is also found, however, that it can give rise to spurious solutions to the equilibrium equations.     

Monatomic gas as a singular limit of polyatomic gas in molecular extended thermodynamics with many moments

The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations with different hierarchy structures due to whether the internal degrees of freedom of a molecule are incorporated in their distribution functions or not. In particular, the number of balance equations in the MET theory of polyatomic gases is greater than the number in the corresponding theory of monatomic gases. The closure procedure for the system of balance equations of polyatomic gases obtained in a recent paper (Arima et al., 2014) is adopted. We prove that the solutions for polyatomic gases converge, in the limit where the degrees of freedom of a molecule D$D$ tend to 3, to the ones for monatomic gases provided that we impose appropriate initial conditions compatible with monatomic gases. Thus a MET theory of rarefied monatomic gases can be identified as a singular limit of the corresponding MET theory of rarefied polyatomic gases. As illustrative examples, the asymptotic behaviors when D→3$D\to 3$ in the dispersion relation of ultrasonic waves and in the shock wave structure are shown.     

Hydrodynamic limit of a nongradient interacting particle process

A simple example of a nongradient stochastic interacting particle system is analyzed. In this model, symmetric simple exclusion in one dimension in a periodic environment, the dynamical term in the Green-Kubo formula contributes to the bulk diffusion constant. The law of large numbers for the density field and the central limit theorem for the density fluctuation field are proven, and the Green-Kubo expression for the diffusion constant is computed exactly. The hydrodynamic equation for the model turns out to be linear.     

小体积比两相分离早期过程的三维格子气模型研究

采用Monte Carlo模拟方法研究了小体积比三维格子气模型中的相分离过程, 比较了sc, fcc, bcc 等3种晶格类型和T/T_c=0.45–0.85等 5个相对温度的系统演化行为, 计算了系统的结构因子函数, 发现结构因子在相分离早期不满足标度关系, 生长指数等于1/6, 小于经典Lifshitz-Slyozov理论的值. 关键词： 格子气模型 相分离过程 Monte Carlo模拟 生长律     

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe–ion direct correlation function and ion–ion dynamic structure factor. Although the power law decay is reminiscent of Debye–Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.     

Bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry

The influence of system parameters such as the flame location, Peclet number and Damköhler number on the bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry is presented in this paper. In the bifurcation plot with flame location as the bifurcation parameter, subcritical Hopf bifurcation is found for lower values of flame location and supercritical Hopf bifurcation for higher values of flame location, for all the Damköhler numbers used in this study. The flame shapes are captured at eight different phases of a cycle of time series data of acoustic velocity at both the fold and Hopf points for bifurcation with flame location as the parameter. We find that the range of flame height variations at the Hopf point is more than the range of flame height variations obtained at the fold point. We also find that the flame oscillates in the same phase as pressure fluctuation but in a phase different from both velocity and heat release rate fluctuations in the region of hysteresis for bifurcation with flame location. The non-dimensional hysteresis width is plotted as a function of Damköhler number for variation of flame location in the subcritical region. An inverse power law relation is found between the non-dimensional hysteresis width and the Damköhler number. The bifurcation plot with Peclet number as parameter shows a subcritical Hopf bifurcation.     

Kinetic modeling of a high power fast-axial-flow CO2 laser with computational fluid dynamics method

A new computational fluid dynamics (CFD) method for the simulation of fast-axial-flow CO2 laser is developed.The model which is solved by CFD software uses a set of dynamic differential equations to describe the dynamic process in one discharge tube.The velocity,temperature,pressure and turbulence energy distributions in discharge passage are presented.There is a good agreement between the theoretical prediction and the experimental results.This result indicates that the parameters of the laser have significant effect on the flow distribution in the discharge passage.It is helpful to optimize the output of high power CO2 laser by mastering its kinetic characteristics.