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首页> 美国卫生研究院文献>The Journal of Chemical Physics >Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise
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Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

机译：使用有限元方法的纳米粒子的广义兰格文动力学：具有相关噪声的恒温

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A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.
机译：采用直接数值模拟（DNS）程序，通过广义Langevin方法研究了不可压缩牛顿固定流体介质中纳米粒子的热运动。我们同时考虑了马尔可夫（白噪声）和非马尔可夫（Ornstein-Uhlenbeck噪声和Mittag-Leffler噪声）过程。粒子的初始位置与边界壁之间的距离各不相同，以描绘壁效应。在热平衡下，通过将计算的颗粒平移和旋转温度与从均分定理获得的温度进行比较，可以验证数值结果。通过将速度自相关函数和均方位移与分析结果进行比较，可以验证流体动力相互作用的性质。将墙体与颗粒相互作用的均方位移的数值预测与分析结果进行了比较。在非Markovian Langevin方法中，需要适当选择有色噪声，才能长时间满足速度自相关函数中的幂律衰减。通过使用非马尔可夫Mittag-Leffler噪声获得的结果同时满足了等分定理和流体动力学相关性在一段内存相关时间范围内的长期行为。 Ornstein-Uhlenbeck过程没有提供适当的流体动力学关系。将我们的DNS结果与一维广义Langevin方程的解进行比较，可以观察到恒温器遵守均分定理时，噪声中的特征存储时间与存储内核的固有时间尺度一致。讨论了针对各种噪声方案的恒温器相对于平衡和动态特性的性能。

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