Mappings and accuracy for Chebyshev pseudo-spectral approximations

The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed

On the coupling between a supersonic boundary layer and a flexible surface

The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. We find that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer which may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface is also studied. We find that the disturbance level is higher over the vibrating flexible surface than that obtained when the surface is rigid, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance level over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance which does not couple with the flexible surface

Coupling between plate vibration and acoustic radiation

A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far-field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far-field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance

Low Mach number modeling of Type I X-ray burst deflagrations

The Low Mach Number Approximation (LMNA) is applied to 2D hydrodynamical modeling of Type I X-ray bursts on a rectangular patch on the surface of a non-rotating neutron star. Because such phenomena involve decidedly subsonic flows, the timestep increase offered by the LMNA makes routine simulations of these deflagrations feasible in an environment where strong gravity produces significant stratification, while allowing for potentially significant lateral differences in temperature and density. The model is employed to simulate the heating, peak, and initial cooling stages in the deep envelope layers of a burst. During the deflagration, Benard-like cells naturally fill up a vertically expanding convective layer. The Mach number is always less than 0.15 throughout the simulation, thus justifying the low Mach number approximation. While the convective layer is superadiabatic on average, significant fluctuations in adiabaticity occur within it on subconvective timescales. Due to convective layer expansion, significant compositional mixing naturally occurs, but tracer particle penetration through the convective layer boundaries on convective timescales is temporary and spatially limited. Thus, mixing occurs on the relatively slow burst timescale through thermal expansion of the convective layer rather than from mass penetration of the convective layer boundary through particle convection. At the convective layer boundaries where mixing is less efficient, the actual temperature gradient more closely follows the Ledoux criteria.Comment: 40 pages, 13 figures, accepted by ApJ, high resolution version: http://www.astro.northwestern.edu/~lin/references/Lin_LMNA_ApJ_2006.pd

Differences in 4-year health outcomes for elderly and poor, chronically ill patients treated in HMO and fee-for-service systems. Results from the Medical Outcomes Study

OBJECTIVE: To compare physical and mental health outcomes of chronically ill adults, including elderly and poor subgroups, treated in health maintenance organization (HMO) and fee-for-service (FFS) systems. STUDY DESIGN: A 4-year observational study of 2235 patients (18 to 97 years of age) with hypertension, non-insulin-dependent diabetes mellitus (NIDDM), recent acute myocardial infarction, congestive heart failure, and depressive disorder sampled from HMO and FFS systems in 1986 and followed up through 1990. Those aged 65 years and older covered under Medicare and low-income patients (200% of poverty) were analyzed separately. SETTING AND PARTICIPANTS: Offices of physicians practicing family medicine, internal medicine, endocrinology, cardiology, and psychiatry, in HMO and FFS systems of care. Types of practices included both prepaid group (72% of patients) and independent practice association (28%) types of HMOs, large multispecialty groups, and solo or small, single-specialty practices in Boston, Mass, Chicago, Ill, and Los Angeles, Calif. OUTCOME MEASURES: Differences between initial and 4-year follow-up scores of summary physical and mental health scales from the Medical Outcomes Study 36-Item Short-Form Health Survey (SF-36) for all patients and practice settings. RESULTS: On average, physical health declined and mental health remained stable during the 4-year follow-up period, with physical declines larger for the elderly than for the nonelderly (P\u3c.001). In comparisons between HMO and FFS systems, physical and mental health outcomes did not differ for the average patient; however, they did differ for subgroups of the population differing in age and poverty status. For elderly patients (those aged 65 years and older) treated under Medicare, declines in physical health were more common in HMOs than in FFS plans (54% vs 28%; P\u3c.001). In 1 site, mental health outcomes were better (P\u3c.05) for elderly patients in HMOs relative to FFS but not in 2 other sites. For patients differing in poverty status, opposite patterns of physical health (P\u3c.05) and for mental health (P\u3c.001) outcomes were observed across systems; outcomes favored FFS over HMOs for the poverty group and favored HMOs over FFS for the nonpoverty group. CONCLUSIONS: During the study period, elderly and poor chronically ill patients had worse physical health outcomes in HMOs than in FFS systems; mental health outcomes varied by study site and patient characteristics. Current health care plans should carefully monitor the health outcomes of these vulnerable subgroups