Memory effects in fluctuating dynamic density-functional theory: theory and simulations
Memory effects in fluctuating dynamic density-functional theory: theory and simulations
复制标题
波动动态密度泛函理论中的记忆效应：理论与模拟
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
S. Kalliadasis
中科院分区：
文献类型：
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作者：
A. Russo;M. Durán;P. Yatsyshin;S. Kalliadasis
本工作介绍了一个理论框架来描述反应的多组分流体系统的动态平衡和平衡外。我们的出发点是系统的广义朗之万方程描述的组成粒子的位置和动量的演变。一个特殊的困难，这个系统的广义朗之万方程表现出的是存在一个历史依赖（即非马尔可夫）项，这反过来又使系统的动态依赖于自己的过去的历史。与当地的数密度和动量场的适当的定义，我们能够推导出一个非马尔可夫的Navier-Stokes方程组构成的推广的迪恩-川崎模型。然而，这些方程仍然依赖于粒子相空间坐标的完整集合。为了消除这种对微观水平的依赖，而不洗掉介观描述的波动效应特征，我们需要仔细地对我们的广义迪恩-川崎方程进行平均。这种处理的结果是一组非马尔可夫波动流体力学方程的时间演化的介观密度和动量场。此外，通过引入一个能量泛函，恢复了经典密度泛函理论中使用的能量泛函及其在局部平衡近似下的动态扩展（DDFT），我们得到了一个新的非马尔可夫波动DDFT（FDDFT）反应多组分流体系统。为了将波动动力学减少到密度场的单个方程，在经典DDFT的精神中，我们使用反卷积算子，这使得可以获得非马尔可夫FDDFT的过阻尼版本。一个有限体积离散推导出的非马尔可夫FDDFT，然后提出。有了这个，我们验证我们的理论框架，在和出的平衡，通过比较结果对原子模拟。最后，我们说明了非马尔可夫效应对非线性化学反应流体系统的动力学的影响，详细研究了记忆驱动的图灵模式。
This work introduces a theoretical framework to describe the dynamics of reacting multi-species fluid systems in-and-out of equilibrium. Our starting point is the system of generalised Langevin equations which describes the evolution of the positions and momenta of the constituent particles. One particular difficulty that this system of generalised Langevin equations exhibits is the presence of a history-dependent (i.e. non-Markovian) term, which in turn makes the system’s dynamics dependent on its own past history. With the appropriate definitions of the local number density and momentum fields, we are able to derive a non-Markovian Navier–Stokes-like system of equations constituting a generalisation of the Dean–Kawasaki model. These equations, however, still depend on the full set of particles phase-space coordinates. To remove this dependence on the microscopic level without washing out the fluctuation effects characteristic of a mesoscopic description, we need to carefully ensemble-average our generalised Dean–Kawasaki equations. The outcome of such a treatment is a set of non-Markovian fluctuating hydrodynamic equations governing the time evolution of the mesoscopic density and momentum fields. Moreover, with the introduction of an energy functional which recovers the one used in classical density-functional theory and its dynamic extension (DDFT) under the local-equilibrium approximation, we derive a novel non-Markovian fluctuating DDFT (FDDFT) for reacting multi-species fluid systems. With the aim of reducing the fluctuating dynamics to a single equation for the density field, in the spirit of classical DDFT, we make use of a deconvolution operator which makes it possible to obtain the overdamped version of the non-Markovian FDDFT. A finite-volume discretization of the derived non-Markovian FDDFT is then proposed. With this, we validate our theoretical framework in-and-out-of-equilibrium by comparing results against atomistic simulations. Finally, we illustrate the influence of non-Markovian effects on the dynamics of non-linear chemically reacting fluid systems with a detailed study of memory-driven Turing patterns.
影响因子：
3
作者：
Bernardi, Rafael C.;Melo, Marcelo C. R.;Schulten, Klaus
通讯作者：
Schulten, Klaus