Numerical solution of a class of random boundary value problems

AbstractThis paper deals with the nonlinear two point boundary value problem y″ = f(x, y, y′, R1,…, Rn), x0 < x < xf S1y(x0) + S2 y′(x0) = S3, S4 y(xf) + S5 y′(xf) = S6 where R1,…, Rn, S1,…, S6 are bounded continuous random variables. An approximate probability distribution function for y(x) is constructed by numerical integration of a set of related deterministic problems. Two distinct methods are described, and in each case convergence of the approximate distribution function to the actual distribution function is established. Primary attention is placed on problems with two random variables, but various generalizations are noted. As an example, a nonlinear one-dimensional heat conduction problem containing one or two random variables is studied in some detail

A Critique of the Delaware Valley Regional Planning Commission 1985 Regional Transportation Plan

The 1985 Regional Transportation Plan of the Delaware Valley Regional Planning Commission (Plan Report No. 5) is one of the most detailed and informative reports published to date by a transportation planning agency. The Report reflects several advances in urban transportation planning procedures made by DVRPC. Nevertheless, the Report does contain a number of very serious deficiencies. In an attempt to make a constructive contribution to transportation planning in the Delaware Valley Region, the authors of this Critique analyze these deficiencies and propose general and specific improvements for the Transportation Plan

A Complete Sample of Megaparsec Size Double Radio Sources from SUMSS

We present a complete sample of megaparsec-size double radio sources compiled from the Sydney University Molonglo Sky Survey (SUMSS). Almost complete redshift information has been obtained for the sample. The sample has the following defining criteria: Galactic latitude |b| > 12.5 deg, declination < -50 deg and angular size > 5 arcmin. All the sources have projected linear size larger than 0.7 Mpc (assuming H_o = 71 km/s/Mpc). The sample is chosen from a region of the sky covering 2100 square degrees. In this paper, we present 843-MHz radio images of the extended radio morphologies made using the Molonglo Observatory Synthesis Telescope (MOST), higher resolution radio observations of any compact radio structures using the Australia Telescope Compact Array (ATCA), and low resolution optical spectra of the host galaxies from the 2.3-m Australian National University (ANU) telescope at Siding Spring Observatory. The sample presented here is the first in the southern hemisphere and significantly enhances the database of known giant radio sources. The giant radio sources with linear size exceeding 0.7 Mpc have an abundance of (215 Mpc)^(-3) at the sensitivity of the survey. In the low redshift universe, the survey may be suggesting the possibility that giant radio sources with relict lobes are more numerous than giant sources in which beams from the centre currently energize the lobes.Comment: 67 pages, 29 figures, for full resolution figures see http://www.astrop.physics.usyd.edu.au/SUMSS/PAPERS/Submit-May11-ms.pd

Developing and testing intervention theory by incorporating a views synthesis into a qualitative comparative analysis of intervention effectiveness.

Qualitative comparative analysis (QCA) was originally developed as a tool for cross-national comparisons in macrosociology, but its use in evaluation and evidence synthesis of complex interventions is rapidly developing. QCA is theory-driven and relies on Boolean logic to identify pathways to an outcome (eg, is the intervention effective or not?). We use the example of two linked systematic reviews on weight management programs (WMPs) for adults-one focusing on user views (a "views synthesis") and one focusing on the effectiveness of WMPs incorporating dietary and physical activity-to demonstrate how a synthesis of user views can supply a working theory to structure a QCA. We discuss how a views synthesis is especially apt to supply this working theory because user views can (a) represent a "middle-range theory" of the intervention; (b) bring a participatory, democratic perspective; and (c) provide an idiographic understanding of how the intervention works that external taxonomies may not be able to furnish. We then discuss the practical role that the views synthesis played in our QCA examining pathways to effectiveness: (a) by suggesting specific intervention features and sharpening the focus on the most salient features to be examined, (b) by supporting interpretation of findings, and (c) by bounding data analysis to prevent data dredging

J0316+4328: a Probable "Asymmetric Double" Lens

We report a probable gravitational lens J0316+4328, one of 19 candidate asymmetric double lenses (2 images at a high flux density ratio) from CLASS. Observations with the Very Large Array (VLA), MERLIN and the Very Long Baseline Array (VLBA) imply that J0316+4328 is a lens with high confidence. It has 2 images separated by 0.40", with 6 GHz flux densities of 62 mJy and 3.2 mJy. The flux density ratio of ~19 (constant over the frequency range 6-22 GHz) is the largest for any 2 image gravitational lens. High resolution optical imaging and deeper VLBI maps should confirm the lensing interpretation and provide inputs to detailed lens models. The unique configuration will give strong constraints on the lens galaxy's mass profile.Comment: Accepted to MNRAS Letters. 5 pages, 6 figures, 3 table

The geometry of thermodynamic control

A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold, and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory

Demixing of aqueous polymer two-phase systems in low gravity

When polymers such as dextran and poly(ethylene glycol) are mixed in aqueous solution biphasic systems often form. On Earth the emulsion formed by mixing the phases rapidly demixes because of phase density differences. Biological materials can be purified by selective partitioning between the phases. In the case of cells and other particulates the efficiency of these separations appears to be somewhat compromised by the demixing process. To modify this process and to evaluate the potential of two-phase partitioning in space, experiments on the effects of gravity on phase emulsion demixing were undertaken. The behavior of phase systems with essentially identical phase densities was studied at one-g and during low-g parabolic aircraft maneuvers. The results indicate the demixing can occur rather rapidly in space, although more slowly than on Earth. The demixing process was examined from a theoretical standpoint by applying the theory of Ostwald ripening. This theory predicts demizing rates many orders of magnitude lower than observed. Other possible demixing mechanisms are considered