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

Brown University, Providence RI

Investigators

Abstract

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.