A New Framework for Evaluating Estimates of Symbiotic Nitrogen Fixation in Forests.

Symbiotic nitrogen fixation (SNF) makes atmospheric nitrogen biologically available and regulates carbon storage in many terrestrial ecosystems. Despite its global importance, estimates of SNF rates are highly uncertain, particularly in tropical forests where rates are assumed to be high. Here we provide a framework for evaluating the uncertainty of sample-based SNF estimates and discuss its implications for quantifying SNF and thus understanding of forest function. We apply this framework to field data sets from six lowland tropical rainforests (mature and secondary) in Brazil and Costa Rica. We use this data set to estimate parameters influencing SNF estimation error, notably the root nodule abundance and variation in SNF rates among soil cores containing root nodules. We then use simulations to gauge the relationship between sampling effort and SNF estimation accuracy for a combination of parameters. Field data illuminate a highly right-skewed lognormal distribution of SNF rates among soil cores containing root nodules that were rare and spanned five orders of magnitude. Consequently, simulations demonstrated that sample sizes of hundreds to even thousands of soil cores are needed to obtain estimates of SNF that are within, for example, a factor of 2 of the actual rate with 75% probability. This represents sample sizes that are larger than most studies to date. As a result of this previously undescribed uncertainty, we suggest that current estimates of SNF in tropical forests are not sufficiently constrained to elucidate forest stand-level controls of SNF, which hinders our understanding of the impact of SNF on tropical forest ecosystem processes.

Emergence and detailed structure of terraced surfaces produced by oblique-incidence ion sputtering.

We study the nanoscale terraced topographies that arise when a solid surface is bombarded with a broad ion beam that has a relatively high angle of incidence θ. We find that the surface is not completely flat between the regions in which the surface slope changes rapidly with position: Instead, small-amplitude ripples propagate along the surface. Our analytical work on these ripples yields their propagation velocity as well as the scaling behavior of their amplitude. Our simulations establish that the surfaces exhibit interrupted coarsening, i.e., the characteristic width and height of the surface disturbance grow for a time but ultimately asymptote to finite values as the fully terraced state develops. In addition, as θ is reduced, the surface can undergo a transition from a terraced morphology that changes little with time as it propagates over the surface to an unterraced state that appears to exhibit spatiotemporal chaos. For different ranges of the parameters, our equation of motion produces unterraced topographies that are remarkably similar to those seen in various experiments, including pyramidal structures that are elongated along the projected beam direction and isolated lenticular depressions.

Producing virtually defect-free nanoscale ripples by ion bombardment of rocked solid surfaces.

Bombardment of a solid surface with a broad, obliquely incident ion beam frequently produces nanoscale surface ripples. The primary obstacle that prevents the adoption of ion bombardment as a nanofabrication tool is the high density of defects in the patterns that are typically formed. Our simulations indicate that ion bombardment can produce nearly defect-free ripples on the surface of an elemental solid if the sample is concurrently and periodically rocked about an axis orthogonal to the surface normal and the incident beam direction. We also investigate the conditions necessary for rocking to produce highly ordered ripples and discuss how the results of our simulations can be reproduced experimentally. Finally, our simulations show that periodic temporal oscillations of coefficients in the Kuramoto-Sivashinsky equation can suppress spatiotemporal chaos and lead to patterns with a high degree of order.

Nanoscale patterns formed by ion bombardment of rotating binary materials.

We explore the effects of sample rotation during ion sputtering of binary materials, as well as its effects during surfactant sputtering. We find that the rate with which the surface roughens or smooths depends on the period of rotation t(0) in the early time regime, in contrast to the behavior of elemental materials. In addition, the characteristic length scale l of the patterns that emerge can be tuned merely by changing the value of t(0). Finally, we demonstrate that l can even exhibit a jump discontinuity as t(0) is varied.