Spatial Correlation of Fluctuations and Formation of Dissipative Structures in Nonequilibrium Reaction Diffusion Systems and Hydrodynamic Systems

1.我们将熵推广到多组分流体的非平衡态热力学，使熵是重心流和扩散流的函数。这种推广使我们能够推导出存在惯性效应时扩散流松弛的本构方程。对化学反应体系的宏观描述预示，如果违反了详细的平衡条件，则反应物浓度之间可能出现非平衡空间相关性。我们在反应硬球的模型系统中对这种相关性进行了分子动力学模拟。我们确实发现了长期相关性，这是由流体力学描述所预测的。由于动力作用，在短距离内会有一些偏差。从朗之万方程出发，得到了描述湍流介质中初始接近标记粒子的均方距离的非线性演化方程。在稳定漂移的情况下，均方距离的初始-t^3和中间指数增长仍然存在。

1.We formulate nonequilibrium thermodynamics of multi-component fluids by generalizing entropy in order that entropy is a function of barycentric flow and diffusion flows. This generalization enables us to derive constitutive equation for the relaxation of diffusion flows in the presence of inertial effects.2.The macroscopic description of a system with chemical reactions predicts that if the detailed balance conditon is violated, then nonequilibrium spatial correlation between concentrations of reactants may appear. We made molecular dynamics simulations of such correlations in a model sysem of reactiing hard spheres. We indeed found the long range correlations, which was predicted by the hydrodynamic description. There is some deviation in a short distance due to kinetic effects.Starting from the Langevin equation a nonlinear evolution equation describing the mean square distance of initially close tagged particles in a turbulent medium is obtained. The initial-t^3 and intermediate exponential growth of the mean square distance subsist even under the presence of stable drift.