Development of an hp-version finite element method for computational optimal control

The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind

Association between socioeconomic factors and soft drink consumption among adults in Cambodia: a cross-sectional study

Background: Soft drinks are an attractive and popular drink, consumed by many people to fulfill their energy. However, soft drink consumption is an important risk factor for non-communicable diseases. This study aimed to investigate the association between socioeconomic factors and soft drink consumption among adults in Cambodia. Methods: A cross-sectional analytical study with multi-stage random sampling was used to select 749 respondents from 12 communes across 5 districts in Phnom Penh, the capital city of Cambodia. A structured questionnaire was used to assess socioeconomic factors and soft drink consumption. Data were analyzed using bivariate and multivariable logistic regression. Crude odds ratios and adjusted odds ratios (AORs) with 95% confident intervals (CI) were calculated to show the strength of associations.Results: The overall prevalence of soft drink consumption was 44.73% (95%CI: 41.16-48.30%) across the sample population. The final model of multiple logistic regression showed only four factors to be significantly associated with soft drink consumption: gender, age, family size and income. Respondents most likely to consume soft drinks were men (AOR: 1.49, 95%CI: 1.10-2.00; p=0.009), those aged 31-59 years (AOR: 1.93, 95%CI: 1.98-4.62;

Editors' introduction: the book, the conference, and fighting back

This book makes a strong case for the abiding relevance of Dewey's notion of learning through experience, with a community of others, and what this implies for democratic 21st century education

The Kinematic and Plasma Properties of X-ray Knots in Cassiopeia A from the Chandra HETGS

We present high-resolution X-ray spectra from the young supernova remnant Cas A using a 70-ks observation taken by the Chandra High Energy Transmission Grating Spectrometer (HETGS). Line emission, dominated by Si and S ions, is used for high-resolution spectral analysis of many bright, narrow regions of Cas A to examine their kinematics and plasma state. These data allow a 3D reconstruction using the unprecedented X-ray kinematic results: we derive unambiguous Doppler shifts for these selected regions, with values ranging between -2500 and +4000 km/s. Plasma diagnostics of these regions, derived from line ratios of resolved He-like triplet lines and H-like lines of Si, indicate temperatures largely around 1 keV, which we model as O-rich reverse-shocked ejecta. The ionization age also does not vary considerably over these regions of the remnant. The gratings analysis was complemented by the non-dispersed spectra from the same dataset, which provided information on emission measure and elemental abundances for the selected Cas A regions. The derived electron density of X-ray emitting ejecta varies from 20 to 200 cm^{-3}. The measured abundances of Mg, Si, S and Ca are consistent with O being the dominant element in the Cas A plasma. With a diameter of 5 arcmin, Cas A is the largest source observed with the HETGS to date. We, therefore, describe the technique we use and some of the challenges we face in the HETGS data reduction from such an extended, complex object.Comment: 26 pages, 16 figures, evised version (minor changes), accepted for publication in ApJ (Oct 20 2006

Optimal guidance law development for an advanced launch system

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems

The Formation of the Double Pulsar PSR J0737-3039A/B

Recent timing observations of the double pulsar J0737-3039A/B have shown that its transverse velocity is extremely low, only 10 km/s, and nearly in the Plane of the Galaxy. With this new information, we rigorously re-examine the history and formation of this system, determining estimates of the pre-supernova companion mass, supernova kick and misalignment angle between the pre- and post-supernova orbital planes. We find that the progenitor to the recently formed `B' pulsar was probably less than 2 MSun, lending credence to suggestions that this object may not have formed in a normal supernova involving the collapse of an iron core. At the same time, the supernova kick was likely non-zero. A comparison to the history of the double-neutron-star binary B1534+12 suggests a range of possible parameters for the progenitors of these systems, which should be taken into account in future binary population syntheses and in predictions of the rate and spatial distribution of short gamma-ray burst events.Comment: To appear in MNRAS Letters. Title typo fix only; no change to pape

Studies of the Relativistic Binary Pulsar PSR B1534+12. II. Origin and Evolution

We have recently measured the angle between the spin and orbital angular momenta of PSR B1534+12 to be either 25+/-4 deg or 155+/-4 deg. This misalignment was almost certainly caused by an asymmetry in the supernova explosion that formed its companion neutron star. Here we combine the misalignment measurement with measurements of the pulsar and companion masses, the orbital elements, proper motion, and interstellar scintillation. We show that the orbit of the binary in the Galaxy is inconsistent with a velocity kick large enough to produce a nearly antialigned spin axis, so the true misalignment must be ~25 deg. Similar arguments lead to bounds on the mass of the companion star immediately before its supernova: 3+/-1 Msun. The result is a coherent scenario for the formation of the observed binary. After the first supernova explosion, the neutron star that would eventually become the observed pulsar was in a Be/X-ray type binary system with a companion of at least 10--12 Msun. During hydrogen (or possibly helium) shell burning, mass transfer occurred in a common envelope phase, leaving the neutron star in a roughly half-day orbit with a helium star with mass above ~3.3 Msun. A second phase of mass transfer was then initiated by Roche lobe overflow during shell helium burning, further reducing both the helium star mass and orbital period before the second supernova. Scenarios that avoid Roche lobe overflow by the helium star require larger helium star masses and predict space velocities inconsistent with our measurements. The companion neutron star experienced a velocity kick of 230+/-60 km/s at birth, leading to a systemic kick to the binary of 180+/-60 km/s.Comment: 9 pages, submitted to ApJ. Abstract shortened. Version with high-resolution figures available at http://www.astro.ubc.ca/people/stairs/papers/tds04_orig.ps.g

Ionization Structure and the Reverse Shock in E0102-72

The young oxygen-rich supernova remnant E0102-72 in the Small Magellanic Cloud has been observed with the High Energy Transmission Grating Spectrometer of Chandra. The high resolution X-ray spectrum reveals images of the remnant in the light of individual emission lines of oxygen, neon, magnesium and silicon. The peak emission region for hydrogen-like ions lies at larger radial distance from the SNR center than the corresponding helium-like ions, suggesting passage of the ejecta through the "reverse shock". We examine models which test this interpretation, and we discuss the implications.Comment: 4 pages, 6 figures; To appear in "Young Supernova Remnants" (11th Annual Astrophysics Conference in Maryland), S. S. Holt & U. Hwang (eds), AIP, New York (2001

Chandra observations of SN 1987A: the soft X-ray light curve revisited

We report on the present stage of SN 1987A as observed by the Chandra X-ray Observatory. We reanalyze published Chandra observations and add three more epochs of Chandra data to get a consistent picture of the evolution of the X-ray fluxes in several energy bands. We discuss the implications of several calibration issues for Chandra data. Using the most recent Chandra calibration files, we find that the 0.5-2.0 keV band fluxes of SN 1987A have increased by ~6 x 10 ^-13 erg s^-1 cm^-2 per year since 2009. This is in contrast with our previous result that the 0.5-2.0 keV light curve showed a sudden flattening in 2009. Based on our new analysis, we conclude that the forward shock is still in full interaction with the equatorial ring.Comment: Accepted for publication by ApJ, 7 pages, 5 figure