Collaborative Research:Computational and Data-Enabled Science and Engineering: Characterizing Dynamics of Particle-based Systems

合作研究：计算和数据支持的科学与工程：表征基于粒子的系统的动力学

• 批准号: 1521717
• 负责人: Lou Kondic
• 金额: $ 12.5万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1521717&HistoricalAwards=false
• 关键词: Collaborative; Research; Computational; Data; Enabled

A significant part of the research in applied fields of science and engineering focuses on the systems built up from discrete objects. This includes the systems relevant to materials science, such as dry and wet granular systems, but also many other soft-matter systems such as foams, colloids, and liquid crystals. There is also an increasingly relevant and active field of active matter where the systems of interest are built out of particles governed by some type of internal forces, such as bacteria and the similar. Going back to the systems relevant to materials science, one could note important applications, involving trillions of dollars per year in the US alone. Despite wide-ranging appearance of systems built out of granular particles, our ability to predict their behavior lags far behind that for more conventional materials such as Newtonian fluids. Similar, even stronger, conclusions could be reached for the other particulate-based systems that are just becoming to be considered. Lack of continuum-based models for many of the listed systems requires carrying out discrete element simulations that focus on modeling particle-particle interactions. Due to increased computational power, current simulations are able to provide realistic description of the experimental systems and can often be used with predictive power. However, the separation of spatial and temporal scales describing particles and their interactions, and of those describing meso- or macro-scales that are of interest when considering properties of a system as a whole, leads to increasingly large and essentially unmanageable amount of data. This proposal focuses on development of a technique, based on computational homology, which allows us to reach deeper understanding of the dynamical properties of the considered complex systems by extracting required information from these large data sets.The proposed work is based on topological data analysis, and in particular it focuses on development of techniques based on persistent homology, algebraic topological techniques from nonlinear dynamics, and algorithms and software to compute homological invariants that are capable of identifying and characterizing the nonlinear dynamics of complex spatio-temporal systems. These techniques will be applied to the results of discrete element simulations of particulate-based systems that will be developed in parallel. These simulations will consider large number of particles interacting by both attractive and repulsive forces, both in two and three spatial dimensions. We will consider circular/spherical particles, as well as the particles of polygonal/polyhedral shapes. As an outcome of the proposed project, we expect to develop much better understanding of the dynamical properties of the considered systems, which will be then passed to scientists and engineers working on their applications. The implications of success in this project are far reaching. Developing new computationally efficient mathematical tools for understanding and predicting the dynamics of complex patterns on large scale data sets provides the foundations for the analysis of a wide range of problems involving complex nonequilibrium systems. In the context of particulate-based systems, this includes (i) dry granular matter built out of particles interacting by repulsive force, with the examples coming from nature - including avalanches, debris flows, and earthquakes, technology - processing of coal, ores, and pharmaceuticals; (ii) `wet' systems built out of particles interacting by a combination of repulsion and attraction, in particular relevant to porous media applications, and (iii) a number of multiphase systems including suspensions and active matter. In all of these systems, understanding and prediction of complex behavior of special structures is desired.

科学和工程应用领域的研究的一个重要部分集中于由离散对象构建的系统。这包括与材料科学相关的系统，例如干和湿颗粒系统，还包括许多其他软物质系统，例如泡沫、胶体和液晶。还有一个日益相关和活跃的活性物质领域，其中感兴趣的系统是由受某种类型的内力控制的粒子构建的，例如细菌等。回到与材料科学相关的系统，人们可以注意到重要的应用，仅在美国每年就涉及数万亿美元。尽管由粒状粒子构建的系统的出现范围很广，但我们预测其行为的能力远远落后于牛顿流体等更传统的材料。对于其他刚刚开始考虑的基于颗粒的系统，也可以得出类似的、甚至更强的结论。许多列出的系统缺乏基于连续体的模型，需要进行离散元模拟，重点是对粒子与粒子相互作用进行建模。由于计算能力的增强，当前的模拟能够提供实验系统的真实描述，并且通常可以与预测能力一起使用。然而，描述粒子及其相互作用的空间和时间尺度的分离，以及在考虑整个系统的属性时所感兴趣的描述中观或宏观尺度的分离，导致数据量越来越大并且基本上难以管理。该提案的重点是开发一种基于计算同源性的技术，该技术使我们能够通过从这些大数据集中提取所需的信息来更深入地了解所考虑的复杂系统的动力学特性。所提出的工作基于拓扑数据分析，特别是它侧重于开发基于持久同调性的技术、非线性动力学的代数拓扑技术以及计算同调不变量的算法和软件，这些同调不变量能够识别和表征复杂时空系统的非线性动力学。这些技术将应用于并行开发的基于颗粒的系统的离散元模拟结果。这些模拟将考虑大量粒子在二维和三维空间中通过吸引力和排斥力相互作用。我们将考虑圆形/球形颗粒，以及多边形/多面体形状的颗粒。作为拟议项目的成果，我们希望更好地了解所考虑系统的动力学特性，然后将其传递给从事其应用的科学家和工程师。该项目的成功意义深远。开发新的计算高效的数学工具来理解和预测大规模数据集上复杂模式的动态，为分析涉及复杂非平衡系统的各种问题奠定了基础。在基于颗粒的系统中，这包括（i）由通过排斥力相互作用的颗粒构成的干燥粒状物质，例子来自自然 - 包括雪崩、泥石流和地震，技术 - 煤炭、矿石的加工，和药品； (ii) 由通过排斥和吸引力的组合相互作用的颗粒构建的“湿”系统，特别是与多孔介质应用相关，以及(iii) 包括悬浮液和活性物质的许多多相系统。在所有这些系统中，需要理解和预测特殊结构的复杂行为。