Towards Fast and Stable Schemes for Brownian Dynamics with Hydrodynamic Interactions

具有流体动力相互作用的布朗动力学的快速稳定方案

• 批准号: 1212058
• 负责人: Nawaf Bou-Rabee
• 金额: $ 14.2万
• 依托单位: Rutgers University Camden
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1212058&HistoricalAwards=false
• 关键词: Towards; Fast; Stable; Schemes; Brownian

Simulation of polymers in flow is a formidable computational problem. It requires a mathematical model that accurately captures both the polymer and the effect of the surrounding solvent. The resulting dynamics involve a nontrivial interplay between hydrodynamic, molecular and thermal forces that give rise to governing stochastic differential equations (SDE). Brownian dynamics with hydrodynamic interactions refers to the time-integration of these equations. These SDEs are fraught with numerical difficulties such as high dimensionality, multiplicative noise, nonlinear drifts, multiple time-scales and complex coupling with the surrounding solvent. While some schemes have been proposed to simulate such systems, none satisfy the fundamental requirement of numerical stability, which is a main motivation for this project. This project will deliver novel techniques to solve these SDEs in a numerically stable and practical way. With fluorescence microscopy, scientists can now briefly watch individual DNA molecules move in all sorts of flow fields. However illuminating these glimpses of DNA motion might be, they are not precise enough to answer fundamental questions such as how can certain shearing flows induce DNA to fragment or concatenate? To answer such questions, numerical simulation is essential, and this example emphasizes the significant role that quantitative simulations play in the burgeoning area of DNA nanotechnology. Simulations combined with fluorescence microscopy enable scientists to comprehensively study the mechanisms behind DNA dynamics in a variety of flow fields. This project will lead to the development of powerful new numerical tools to simulate DNA in flow. It will also provide student training through two research assistantships at Rutgers-Camden.

聚合物流动模拟是一个艰巨的计算问题。它需要一个数学模型来准确捕捉聚合物和周围溶剂的影响。 由此产生的动力学涉及流体动力、分子力和热力之间的重要相互作用，从而产生控制随机微分方程（SDE）。 具有流体动力相互作用的布朗动力学是指这些方程的时间积分。 这些 SDE 充满了数值困难，例如高维、乘性噪声、非线性漂移、多时间尺度以及与周围溶剂的复杂耦合。 虽然已经提出了一些方案来模拟此类系统，但没有一个能够满足数值稳定性的基本要求，而数值稳定性是该项目的主要动机。 该项目将提供新颖的技术，以数值稳定且实用的方式解决这些 SDE。 借助荧光显微镜，科学家现在可以简单地观察单个 DNA 分子在各种流场中的移动。 无论这些 DNA 运动的一瞥如何阐明，它们都不够精确，无法回答一些基本问题，例如某些剪切流如何诱导 DNA 断裂或连接？ 为了回答这些问题，数值模拟至关重要，这个例子强调了定量模拟在 DNA 纳米技术这一新兴领域中发挥的重要作用。 模拟与荧光显微镜相结合使科学家能够全面研究各种流场中 DNA 动力学背后的机制。该项目将导致强大的新型数值工具的开发，以模拟流动中的 DNA。 它还将通过罗格斯大学卡姆登分校的两项研究助理提供学生培训。