Oct

23

2018

We consider a certain two-parameter family of automorphisms of the affine plane over a complete, locally compact non-Archimedean field. Each of these automorphisms admits a chaotic attractor on which it is topologically conjugate to a full two-sided shift map, and the attractor supports a unit Borel measure which describes the distribution of the forward orbit of Haar-almost all points in the basin of attraction. We also compute the Hausdorff dimension of the attractor, which is non-integral.

Oct

24

2018

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.

Oct

24

2018

Oct

26

2018

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.

Oct

29

2018

The existence of minimal blowup-generating initial data, under the assumption that there exists an initial data leading to finite-time singularity, has been studied by Rusin and Sverak (2011), Jia and Sverak (2013), and Gallagher, Koch and Planchon (2013, 2016) in several critical spaces on the whole space. Our aim is to study the influence of the boundary on the existence of minimal blowup data. We introduce a type of weighted critical spaces for the external force that is better-suited for our analysis than the usual Lebesgue spaces.