Convergence and Instability in PCG Methods for Bordered Systems

Bordered almost block diagonal systems arise from discretizing a linearized first-order system of n ordinary differential equations in a twopoint boundary value problem with non-separated boundary conditions. The discretization may use spline collocation, finite differences, or multiple shooting. After internal condensation, if necessary, the bordered almost block diagonal system reduces to a standard finite difference structure, which can be solved using a preconditioned conjugate gradient method based on a simple matrix splitting technique. This preconditioned conjugate gradient method is "guaranteed" to converge in at most 2n + 1 iterations. We exhibit a significant collection of two-point boundary value problems for which this preconditioned conjugate gradient method is unstable and hence convergence is not achieved. Keywords: Boundary Value Problems, Ordinary Differential Equations, Preconditioned Conjugate Gradients, Bordered Almost Block Diagonal Systems author for correspond..

Clintonville Sustainability Plan : Transportation & Mobility [poster]

This is part of a project submitted to fulfill the requirements of the course "City and Regional Planning 724 : Introduction to Planning for Sustainable Development", completed Fall Quarter of 2007 at The Ohio State University in Columbus, Ohio

Rigid versus Flexible Ligands on Carbon Nanotubes for the Enhanced Sensitivity of Cobalt Ions

Carbon nanotubes have shown great promise in the fabrication of ultracompact and highly sensitive chemical and biological sensors. Additional chemical functionalization schemes can controllably improve selectivity of the carbon nanotube-based sensors; however, the exact transduction mechanism is still under debate. In this article we detail the synthesis and selective response of single-walled carbon nanotubes (SWNTs) functionalized with polyazomethine (PAM) polymer toward the application of a specific trace metal ion detector. The response of the polymer system was compared to shape persistent macrocycle (MAC) comprised of identical ion coordination ligands. While ion detection with rigid MAC/SWNT chemiresistor was comparable to bare SWNT, flexible PAM offers significant SWNT signal amplification, allowing for picomolar detection of Co²⁺ ions with both selectivity and a fast response. We hypothesized that rearrangement of the flexible PAM on the SWNT network is a sensing mechanism which allows for ultrasensitive detection of metal ions. The electron transfer and polymer rearrangement on the SWNT were studied by a combination of optical spectroscopy and electrical measurementsultimately allowing for a better understanding of fundamental mechanisms that prompt device response

Metastable Ta2N3 with highly tunable electrical conductivity via oxygen incorporation.

The binary Ta-N chemical system includes several compounds with notable prospects in microelectronics, solar energy harvesting, and catalysis. Among these, metallic TaN and semiconducting Ta3N5 have garnered significant interest, in part due to their synthetic accessibility. However, tantalum sesquinitride (Ta2N3) possesses an intermediate composition and largely unknown physical properties owing to its metastable nature. Herein, Ta2N3 is directly deposited by reactive magnetron sputtering and its optoelectronic properties are characterized. Combining these results with density functional theory provides insights into the critical role of oxygen in both synthesis and electronic structure. While the inclusion of oxygen in the process gas is critical to Ta2N3 formation, the resulting oxygen incorporation in structural vacancies drastically modifies the free electron concentration in the as-grown material, thus leading to a semiconducting character with a 1.9 eV bandgap. Reducing the oxygen impurity concentration via post-synthetic ammonia annealing increases the conductivity by seven orders of magnitude and yields the metallic characteristics of a degenerate semiconductor, consistent with theoretical predictions. Thus, this inverse oxygen doping approach - by which the carrier concentration is reduced by the oxygen impurity - offers a unique opportunity to tailor the optoelectronic properties of Ta2N3 for applications ranging from photochemical energy conversion to advanced photonics

Clintonville Sustainability Plan : Final Report

This is part of a project submitted to fulfill the requirements of the course "City and Regional Planning 724 : Introduction to Planning for Sustainable Development", completed Fall Quarter of 2007 at The Ohio State University in Columbus, Ohio

Low Serum Bicarbonate and Kidney Function Decline: The Multi-Ethnic Study of Atherosclerosis (MESA)

BACKGROUND: Among populations with established chronic kidney disease (CKD), metabolic acidosis is associated with more rapid progression of kidney disease. The association of serum bicarbonate concentrations with early declines in kidney function is less clear. STUDY DESIGN: Retrospective cohort study. SETTING & PARTICIPANTS: 6380 participants in the Multi-Ethnic Study of Atherosclerosis (MESA) with a baseline estimated glomerular filtration rate (eGFR) >60 mL/min/1.73m(2) using the CKD-EPI (CKD Epidemiology Collaboration) creatinine–cystatin C equation. PREDICTORS: Serum bicarbonate concentrations. OUTCOMES: Rapid kidney function decline (eGFR decline >5% per year) and incident reduced eGFR (eGFR<60 mL/min/1.73 m(2) with minimum rate of eGFR loss of 1 mL/min/1.73 m(2) per year). RESULTS: The average bicarbonate concentration was 23.2 ± 1.8 mEq/L. 1730 (33%) participants had rapid kidney function decline, and 487 had incident reduced eGFR during follow-up. Each 1-SD lower baseline bicarbonate concentration was associated with 12% higher adjusted odds of rapid kidney function decline (95% CI, 6%–20%) and higher risk of incident reduced eGFR (adjusted incidence rate ratio, 1.11; 95% CI, 1.03–1.20) in models adjusting for demographics, baseline eGFR, albuminuria, and CKD risk factors. The OR for the associations of bicarbonate <21mEq/L relative to 23–24 mEq/L was 1.35 (95% CI, 1.05–1.73) for rapid kidney function decline, and the incidence rate ratio was 1.16 (95% CI, 0.83–1.62) for incident reduced eGFR. LIMITATIONS: Etiology of metabolic acidosis cannot be determined in this study. CONCLUSIONS: Lower serum bicarbonate concentrations are independently associated with rapid kidney function decline independent of eGFR or albuminuria in community-living persons with a baseline eGFR >60 mL/min/1.73 m(2). If confirmed, our findings suggest that metabolic acidosis may indicate either early kidney disease that is not captured by eGFR or albuminuria, or may have a causal role in the development of an eGFR <60 mL/min/1.73 m(2)