Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

How do we estimate survival? External validation of a tool for survival estimation in patients with metastatic bone disease-decision analysis and comparison of three international patient populations.

Abstract BACKGROUND: We recently developed a clinical decision support tool, capable of estimating the likelihood of survival at 3 and 12 months following surgery for patients with operable skeletal metastases. After making it publicly available on www.PATHFx.org , we attempted to externally validate it using independent, international data. METHODS: We collected data from patients treated at 13 Italian orthopaedic oncology referral centers between 2010 and 2013, then applied to PATHFx, which generated a probability of survival at three and 12-months for each patient. We assessed accuracy using the area under the receiver-operating characteristic curve (AUC), clinical utility using Decision Curve Analysis (DCA), and compared the Italian patient data to the training set (United States) and first external validation set (Scandinavia). RESULTS: The Italian dataset contained 287 records with at least 12 months follow-up information. The AUCs for the three-month and 12-month estimates was 0.80 and 0.77, respectively. There were missing data, including the surgeon's estimate of survival that was missing in the majority of records. Physiologically, Italian patients were similar to patients in the training and first validation sets. However notable differences were observed in the proportion of those surviving three and 12-months, suggesting differences in referral patterns and perhaps indications for surgery. CONCLUSIONS: PATHFx was successfully validated in an Italian dataset containing missing data. This study demonstrates its broad applicability to European patients, even in centers with differing treatment philosophies from those previously studied

Growth and Competitive Effects of Centaurea stoebe Populations in Response to Simulated Nitrogen Deposition

Increased resource availability can promote invasion by exotic plants, raising concerns over the potential effects of global increases in the deposition of nitrogen (N). It is poorly understood why increased N favors exotics over natives. Fast growth may be a general trait of good invaders and these species may have exceptional abilities to increase growth rates in response to N deposition. Additionally, invaders commonly displace locals, and thus may have inherently greater competitive abilities. The mean growth response of Centaurea stoebe to two N levels was significantly greater than that of North American (NA) species. Growth responses to N did not vary among C. stoebe populations or NA species. Without supplemental N, NA species were better competitors than C. stoebe, and C. stoebe populations varied in competitive effects. The competitive effects of C. stoebe populations increased with N whereas the competitive effects of NA species decreased, eliminating the overall competitive advantage demonstrated by NA species in soil without N added. These results suggest that simulated N deposition may enhance C. stoebe invasion through increasing its growth and relative competitive advantage, and also indicate the possibility of local adaptation in competitive effects across the introduced range of an invader

Dynamics of soil organic carbon following land-use change: insights from stable C-isotope analysis in black soil of Northeast China

Intensive soil tillage is a significant factor in soil organic matter decline in cultivated soils. Both cultivation abandonment and foregoing tillage have been encouraged in the past 30 years to reduce greenhouse gas emissions and soil erosion. However, the dynamic processes of soil organic carbon (SOC) in areas of either continuous cultivation or abandonment remain unclear and inconsistent. Our aims were to assess and model the dynamic processes of SOC under continuous tillage and after cultivation abandonment in the black soil of Northeast China. Soil profiles were collected of cultivated or abandoned land with cultivation history of 0–100 years. An isotope mass balance equation was used to calculate the proportion of SOC derived from corn debris (C4) and from natural vegetation (C3) to deduce the dynamic process. Approximately 40% of SOC in the natural surface soil (0–10 cm) was eroded in the first 5 years of cultivation, increasing to about 75% within 40 years, before a slow recovery. C4 above 30 cm soil depth increased by 4.5%–5% or 0.11–0.12 g·kg−1 on average per year under continuous cultivation, while it decreased by approximately 0.34% annually in the surface soil after cultivation abandonment. The increase in the percentage of C4 was fitted to a linear equation with given intercepts in the upper 30 cm of soil in cultivated land. A significant relationship between the change of C4 and time was found only in the surface soil after abandonment of cultivation. These results demonstrate the loss and accumulation of corn-derived SOC in surface black soil of Northeast China under continuous tillage or cultivation abandonment

Stable Carbon and Nitrogen Isotopes in a Peat Profile Are Influenced by Early Stage Diagenesis and Changes in Atmospheric CO2 and N Deposition

In this study, we test whether the δ13C and δ15N in a peat profile are, respectively, linked to the recent dilution of atmospheric δ13CO2 caused by increased fossil fuel combustion and changes in atmospheric δ15N deposition. We analysed bulk peat and Sphagnum fuscum branch C and N concentrations and bulk peat, S. fuscum branch and Andromeda polifolia leaf δ13C and δ15N from a 30-cm hummock-like peat profile from an Aapa mire in northern Finland. Statistically significant correlations were found between the dilution of atmospheric δ13CO2 and bulk peat δ13C, as well as between historically increasing wet N deposition and bulk peat δ15N. However, these correlations may be affected by early stage kinetic fractionation during decomposition and possibly other processes. We conclude that bulk peat stable carbon and nitrogen isotope ratios may reflect the dilution of atmospheric δ13CO2 and the changes in δ15N deposition, but probably also reflect the effects of early stage kinetic fractionation during diagenesis. This needs to be taken into account when interpreting palaeodata. There is a need for further studies of δ15N profiles in sufficiently old dated cores from sites with different rates of decomposition: These would facilitate more reliable separation of depositional δ15N from patterns caused by other processes