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arXiv 0812.1113cond-mat.softcond-mat.stat-mech
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分子和胶体流体的动力学密度泛函理论:流体力学的微观方法

Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics

A. J. Archer

摘要:

近年来,发展了一系列动力学密度泛函理论(DDFTs)来描述胶体和原子流体的单体密度动力学。在胶体的情况下,粒子被假定为具有随机运动方程和理论存在的情况下,当粒子运动是过阻尼的,也在该政权的惯性效应是相关的。在本文中,我们扩展的理论和探索微观DDFT和连续流体力学的运动方程之间的联系。特别是,从控制系统相空间概率分布函数动力学的Kramers方程开始,我们表明可以获得近似的DDFT,它是欧拉方程的推广。该DDFT能够描述流体密度分布的动态,直到单个颗粒的尺度。与先前的DDFT一样,动力学方程需要来自平衡密度泛函理论(DFT)的亥姆霍兹自由能泛函作为输入。对于一个平衡系统,该理论预测的流体单体密度分布与从DFT中获得的相同。作进一步的近似,我们表明,该理论可用于获得模式耦合理论,被广泛用于描述从液体到玻璃态的过渡。

英文摘要:

In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is over-damped and also in the regime where inertial effects are relevant. In this paper we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalisation of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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