MANNA 2017: Modeling, Analysis, and Numerics for Nonlocal Applications

MANNA 2017：非局部应用的建模、分析和数值

• 批准号: 1747867
• 负责人: George Karniadakis
• 金额: $ 1.5万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-12-01 至 2018-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1747867&HistoricalAwards=false
• 关键词: MANNA; 2017; Modeling; Analysis; Numerics

The workshop, "Modeling, Analysis, and Numerics for Nonlocal Applications", will take 11-15 December 2017 in Sante Fe, New Mexico; information is at the website: sites.google.com/site/manna2017abq. The focus of this workshop is on non-local mathematical models, a topic of increasing interest in several diverse scientific and engineering applications related to, as an example, material science, biology, and environmental studies. Non-local calculus and the corresponding models have emerged as a powerful tool for modeling multi-scale phenomena, including overlapping microscopic and macroscopic scales. In the computational mathematics community, two relatively separate groups of researchers (i.e., the "fractional derivatives" and the "non-local operators" communities) are concurrently working on the analysis and simulation of these relevant problems. One of the main goals of this workshop is to unite these separate communities providing significant benefit from their interaction and opportunity to exchange their recent progress and results on the topic. Central to the workshop is also the involvement of students or young researches, not necessarily already engaged in non-local research, who will have the opportunity to interact and learn from worldwide experts. The main topics that will be addressed are the analysis and improvement of such non-local models and their efficient simulation by means of cutting-edge algorithms on the newest computer architectures. Non-local operators provide a new framework to overcome limitations that are present in classical PDE-based models. This workshop is designed to facilitate the exchange of information between the (tempered) fractional calculus and non-local vector calculus and the establishment of connections between them; this will lead to the design of new improved non-local models and will facilitate their analysis and simulation. As a result, the workshop will lead to new research in applications of national interest such as subsurface flow simulations, energy storage systems, contaminant transport, polymer and complex fluid flow, material failure and damage, or any applications in complex systems and disordered media that exhibit anomalous transport and diffusion. The goals and objectives of the workshop include establishing synergies between participants working on fractional PDEs with those working on general non-local integral models; maximizing both the breadth and depth of the information imparted to and exchanged among participants; providing researchers at all career stages with the opportunity to present their state-of-the-art results or to learn from experts in the field; and identifying the most important needs and most potentially fruitful avenues for future non-local related research and related applications. This will be facilitated by the discussion session at the end of each day that will focus on a review of the recent past and near-future directions of research in each area.

研讨会，“建模，分析和数值非本地应用程序”，将于2017年12月11日至15日在圣达菲，新墨西哥州;信息在网站：sites.google.com/site/manna2017abq。本次研讨会的重点是非本地的数学模型，在几个不同的科学和工程应用相关的，例如，材料科学，生物学和环境研究越来越感兴趣的话题。非局部微积分及其相应的模型已经成为一个强大的工具，用于模拟多尺度现象，包括重叠的微观和宏观尺度。 在计算数学界，两个相对独立的研究小组（即，“分数阶导数”和“非局部算子”团体）同时致力于这些相关问题的分析和模拟。本次研讨会的主要目标之一是团结这些独立的社区，从他们的互动和交流该主题最近进展和成果的机会中获得重大利益。研讨会的核心也是学生或年轻研究人员的参与，他们不一定已经从事非本地研究，他们将有机会与世界各地的专家互动和学习。将解决的主要议题是分析和改进这种非本地模型和他们的有效模拟通过最新的计算机架构上的尖端算法。非本地运营商提供了一个新的框架，以克服传统的偏微分方程为基础的模型中存在的局限性。该研讨会旨在促进（调和）分数微积分和非局部向量微积分之间的信息交流，并建立它们之间的联系;这将导致新的改进非局部模型的设计，并将促进其分析和模拟。因此，该研讨会将导致在国家利益的应用，如地下流动模拟，能源储存系统，污染物运输，聚合物和复杂的流体流动，材料故障和损坏，或在复杂系统和无序介质中的任何应用，表现出异常的运输和扩散的新研究。讲习班的目的和目标包括：在从事分数偏微分方程工作的参与者与从事一般非局部积分模型工作的参与者之间建立协同作用;最大限度地扩大向参与者传授和在参与者之间交流的信息的广度和深度;为处于职业生涯各个阶段的研究人员提供展示其最新成果或向该领域专家学习的机会;以及为未来的非本地相关研究和相关应用，找出最重要的需要和最具成效的途径。这将通过每天结束时的讨论会来促进，讨论会将侧重于审查每个领域最近的过去和不久的将来的研究方向。