Applied Mathematics

MURI Fractional PDE 

The ARO MURI project on Fractional Partial Differential Equations seeks to address the common physical themes of anomalous transport, exponentially accelerated fronts, non-Markovian behavior and long-range interactions, self-similarity and scaling, singular behavior, interfaces, and finite-domain decorrelation effects.  In addition, investigators will develop rigorous mathematical theory, algorithms, and software for data-driven fractional PDEs that will provide significant breakthroughs toward modeling, analyzing, and subsequently controlling complex multiscale systems characterized by the aforementioned phenomena in a computationally scalable way.  This project will demonstrate the physical relevance and effectiveness of our framework in diverse applications of interest to the Department of Defense, characterized by the common themes of conservation, monotonicity, adaptive refinement, and high-order accuracy.

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RTG:  Integrating Dynamics And Stochastics

The goal of this Research Training Group (RTG) on "Integrating Dynamics and Stochastics (IDyaS) is to broaden and enhance the scope and quality of the educational and research training provided to graduate students and postdoctoral fellows by integrating research and education in the fields of dynamics, stochastics, and their applications and to involve more undergraduate students in courses and research experiences in applied mathematics.  This Research Training Group is funded by the National Science Foundation through grant DMS-1148284, and is part of the Lefschetz Center for Dynamical Systems.

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This IGERT award entitled, "Reverse Ecology:  Computational Integration of Genomes, Organisms, and Environments," supports a novel graduate program to train PhDs at the interface of computational biology, genomics and environmental science. It leverages new education and research collaborations between Brown University and the Marine Biological Laboratories. Reverse Ecology is the application of genomic approaches to living systems to uncover the genetic bases of functional variation in nature. The revolution in high-throughput DNA sequencing and gene expression technologies redefines the notion of a 'model' organism. The interrogation of genomes from animals, plants, microbes or communities of organisms can identify genetic markers of processes at any scale: ecological, physiological, developmental, transcriptional, etc. The full interpretation of these powerful datasets demands intellectual dialogue between ecosystems ecologists, microbial geneticists, biogeochemists, and computational biologists. We will train a cohort of PhDs who can apply these technologies creatively and convert genomic and computational power into novel insights of how organisms function in their natural environments.