Partial regularity for a surface growth model

We prove two partial regularity results for the scalar equation $u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the physical process of molecular epitaxy. We show that the set of space-time singularities has (upper) box-counting dimension no larger than $7/6$ and $1$-dimensional (parabolic) Hausdorff measure zero. These parallel the results available for the three-dimensional Navier--Stokes equations. In fact the mathematical theory of the surface growth model is known to share a number of striking similarities with the Navier--Stokes equations, and the partial regularity results are the next step towards understanding this remarkable similarity. As far as we know the surface growth model is the only lower-dimensional "mini-model" of the Navier--Stokes equations for which such an analogue of the partial regularity theory has been proved. In the course of our proof, which is inspired by the rescaling analysis of Lin (1998) and Ladyzhenskaya & Seregin (1999), we develop certain nonlinear parabolic Poincar\'e inequality, which is a concept of independent interest. We believe that similar inequalities could be applicable in other parabolic equations.Comment: 29 page

Vitrification and determination of the crystallization time scales of the bulk-metallic-glass-forming liquid Zr58.5Nb2.8Cu15.6Ni12.8Al10.3

The crystallization kinetics of Zr58.5Nb2.8Cu15.6Ni12.8Al10.3 were studied in an electrostatic levitation (ESL) apparatus. The measured critical cooling rate is 1.75 K/s. Zr58.5Nb2.8Cu15.6Ni12.8Al10.3 is the first bulk-metallic-glass-forming liquid that does not contain beryllium to be vitrified by purely radiative cooling in the ESL. Furthermore, the sluggish crystallization kinetics enable the determination of the time-temperature-transformation (TTT) diagram between the liquidus and the glass transition temperatures. The shortest time to reach crystallization in an isothermal experiment; i.e., the nose of the TTT diagram is 32 s. The nose of the TTT diagram is at 900 K and positioned about 200 K below the liquidus temperature

The SPAR thermal analyzer: Present and future

The SPAR thermal analyzer, a system of finite-element processors for performing steady-state and transient thermal analyses, is described. The processors communicate with each other through the SPAR random access data base. As each processor is executed, all pertinent source data is extracted from the data base and results are stored in the data base. Steady state temperature distributions are determined by a direct solution method for linear problems and a modified Newton-Raphson method for nonlinear problems. An explicit and several implicit methods are available for the solution of transient heat transfer problems. Finite element plotting capability is available for model checkout and verification

Does elevated CO2 alter silica uptake in trees?

© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Frontiers in Plant Science 5 (2015): 793, doi:10.3389/fpls.2014.00793.Human activities have greatly altered global carbon (C) and Nitrogen (N) cycling. In fact, atmospheric concentrations of carbon dioxide (CO2) have increased 40% over the last century and the amount of N cycling in the biosphere has more than doubled. In an effort to understand how plants will respond to continued global CO2 fertilization, long-term free-air CO2 enrichment experiments have been conducted at sites around the globe. Here we examine how atmospheric CO2 enrichment and N fertilization affects the uptake of silicon (Si) in the Duke Forest, North Carolina, a stand dominated by Pinus taeda (loblolly pine), and five hardwood species. Specifically, we measured foliar biogenic silica concentrations in five deciduous and one coniferous species across three treatments: CO2 enrichment, N enrichment, and N and CO2 enrichment. We found no consistent trends in foliar Si concentration under elevated CO2, N fertilization, or combined elevated CO2 and N fertilization. However, two-thirds of the tree species studied here have Si foliar concentrations greater than well-known Si accumulators, such as grasses. Based on net primary production values and aboveground Si concentrations in these trees, we calculated forest Si uptake rates under control and elevated CO2 concentrations. Due largely to increased primary production, elevated CO2 enhanced the magnitude of Si uptake between 20 and 26%, likely intensifying the terrestrial silica pump. This uptake of Si by forests has important implications for Si export from terrestrial systems, with the potential to impact C sequestration and higher trophic levels in downstream ecosystems.This research was supported in part by the Sloan Foundation in a fellowship to Robinson W. Fulweiler. The Duke Forest FACE was supported by his study was supported by the US Department of Energy (Grant No. DE-FG02-95ER62083) through the Office of Biological and Environmental Research (BER) and its National Institute for Global Environmental Change (NIGEC), Southeast Regional Center (SERC) at the University of Alabama, and by the US Forest Service through both the Southern Global Climate Change Program and the Southern Research Station. Adrien C. Finzi acknowledges ancillary support from the US NSF (DEB0236356)

Anatomy of a catchment: the relation of physical attributes of the Plynlimon catchments to variations in hydrology and water status

International audienceThe Plynlimon headwater catchments in mid-Wales have been a landmark study of water resources in the UK uplands for over 30 years. The main physical features of the catchments have been digitised as the basis for linking new model developments and process understanding. Examples are given of how the main physical attributes are related to land management, hydrology and water quality. These data are also being used to provide insights into catchment processes that may underpin the development of new research. This work is particularly relevant given the need for the assessment of water status under the Water Framework Directive. The paper presents hypothetical management scenarios for the catchments, to show how ecological status may be improved, for example, by selectively restructuring areas of commercial forest. Keywords: Plynlimon, GIS, catchment study, forestry, hydrology, WF