Mathematics

Rivers are a large source of dissolved organic matter (DOM) of terrestrial origin to the oceans and thus are important ecosystems that contribute to the global biogeochemical cycles. In these terrestrially influenced ecosystems, microbes depend on DOM and function as a metabolic force that decomposes and transforms DOM and are thus important contributors to the global carbon sequestration and export. Despite their importance, very little is known about the relationships between microbial metabolic capabilities and DOM composition found within and among river ecosystems.

In many applications the resolution of mesoscale heterogeneities remain a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the grain scale plays a fundamental role in material failure, capturing mechanisms at this scale is often computationally intractable due to the resolution required. Multiscale methods aim to overcome these difficulties through judicious choice of subscale problem and a robust manner of passing information between scales.