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Collaboratory on mathematics for mesocopic modeling of materials (CM4)

Collaboratory on mathematics for mesocopic modeling of materials (CM4) –DOE/PNNL

Pacific Northwest National Laboratory
Modeling Mesoscale Processes of Scalable Synthesis

Center Director: Prof. George E. Karniadakis, PNNL; Phone: (401) 863-1217 

Co-PIs: Dr. M. L. Parks, SNL
Prof. M. Maxey, Brown University
Prof. P. Stinis, PNNL
Prof. E. Darve, Stanford University
Prof. W. E, Princeton University
Prof. P. Atzberger, UC Santa Barbara
Prof. J. Xu, Penn State University

Many DOE mission critical applications, such as biofuel production, carbon capture and sequestration, and energy storage, require processes to be effective at mesoscale. Underlying all these is the common grand challenge of scalable synthesis in chemistry and biology. At the fundamental level, these scientific drivers all require a deep and integrated understanding of physical and biophysical phenomena. The scientific challenge is to discover the principles that give rise to emergent macroscopic phenomena in directed- and self-assembly of materials with the desired composition and structure based on the understanding of microscopic interactions.

Currently, it is not known how to bridge these processes across regimes. Hence, mesoscale and multiscale phenomena are treated in isolation or coupled only through ad hoc scale separation and parameter passing. A major computational challenge is to formulate rigorous and efficient ways to seamlessly simulate a system from the molecular to the macroscopic scale. Our Center will focus on developing systematic mathematical foundations for the understanding and control of the fundamental mechanisms in mesoscale processes. This will enable scalable synthesis of complex materials, through the design of efficient modeling methods and corresponding scalable algorithms. In particular, we will develop particle-based, grid-based and stochastic methods as well as concurrent coupling between them. We will employ rigorous theory, e.g. working with the Mori-Zwanzig formalism to derive new governing equations for coarse graining. We will develop general algorithmic frameworks involving optimization algorithms on multi-layer overlapped domains with heterogeneous discretizations to facilitate disparate spatio-temporal scales. We will address the inherent stochasticity at mesoscale as well as the propagation of uncertainty across scales by developing stochastic modeling and uncertainty quantification techniques using both sampling- and pdf-based approaches. We will investigate the numerical stiffness induced by multiscale phenomena and explore new fast solution techniques that are effective at the exascale level. We will develop all these mathematical and computational tools not in isolation but in coordinated and integrated fashion and in the context of the aforementioned applications.

Our research team consists of two DOE Labs and six Universities with most of our academic partners holding positions in applied math departments. Of central importance is the adaptability of mathematical research to directions set by the DOE collaborators. We plan to hold weekly video-conferencing sessions in which the director and the leads of each area will report on progress and address challenges. We will make it a requirement for all postdocs and students (when possible) to share their time between the universities and the labs. An external advisory committee will be appointed to advise the director and the leads of each area. We will reach out to other DOE labs as well as international teams for collaborations.  We envision the new Center as the premier world venue for developing mathematical methods and computational tools for mesoscale and multiscale modeling of complex materials, and for training a new cadre of mesoscale and multiscale modeling scientists.