论耗散粒子动力学与伊藤-斯特拉托诺维奇难题之间的联系
On the connection between dissipative particle dynamics and the Itô-Stratonovich dilemma
摘要：
耗散粒子动力学（DPD）是研究具有不可忽略的平衡热涨落的系统的流体动力学行为的一种流行的模拟模型。DPD采用系统粒子之间的软核排斥相互作用，从而允许它们重叠。这应该允许相对较大的积分时间步长，这是大时间尺度上的模拟的重要特征。然而，在实践中，积分时间步长的增加导致采样统计中越来越大的系统误差。在这里，我们证明了这些系统误差的主要来源是朗之万方程中热噪声项的乘法性质，即，它取决于粒子的瞬时坐标。这导致了随机微分朗之万方程的解释的模糊性，被称为伊藤-斯特拉托诺维奇困境。基于以前的研究的困境的见解，我们提出了一种新的算法DPD模拟表现出几乎一个数量级的精度提高，和常用的DPD Langevin恒温器的效率的近两倍。
英文摘要：
Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system particles, thus allowing them to overlap. This supposedly permits relatively large integration time steps, which is an important feature for simulations on large temporal scales. In practice, however, an increase in the integration time step leads to increasingly larger systematic errors in the sampling statistics. Here, we demonstrate that the prime origin of these systematic errors is the multiplicative nature of the thermal noise term in Langevin's equation, i.e., the fact that it depends on the instantaneous coordinates of the particles. This lead to an ambiguity in the interpretation of the stochastic differential Langevin equation, known as the Itô-Stratonovich dilemma. Based on insights from previous studies of the dilemma, we propose a novel algorithm for DPD simulations exhibiting almost an order of magnitude improvement in accuracy, and nearly twice the efficiency of commonly used DPD Langevin thermostats.
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