Steady Viscous Flow in a Triangular Cavity

Steady recirculating viscous flow inside an equilateral triangular cavity is generated by translating one side. The Navier-Stokes equations are solved numerically using finite difference on a transformed geometry. The results show a primary eddy and a series of secondary eddies at the stagnant corner. For high Reynolds numbers the interior of the primary eddy has constant vorticity, but its value cannot be predicted by the mean-squared law

From Cluster to Grid: A Case Study in Scaling-Up a Molecular Electronics Simulation Code

This paper describes an ongoing project whose goal is to significantly improve the performance and applicability of a molecular electronics simulation code. The specific goals are to (1) increase computational performance on the simulation problems currently being solved by our physics collaborators; (2) allow much larger problems to be solved in reasonable time; and (3) expand the set of resources available to the code, from a single homogeneous cluster to a campus-wide computational grid, while maintaining acceptable performance across this larger set of resources. We describe the sequential performance of the code, the performance of two parallel versions, and the benefits of problem-specific load balancing strategies. The grid context motivates the need for runtime algorithm selection; we present a component-based software framework that makes this possible

Analysis of Function Component Complexity for Hypercube Homotopy Algorithms

Probability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that globally convergent from an arbitrary starting point with probability one. The essence of these homotopy algorithms is the construction of a homotopy map p-sub a and the subsequent tracking of a smooth curve y in the zero set p-sub a to the -1 (0) of p-sub a. Tracking the zero curve y requires repeated evaluation of the map p-sub a, its n x (v + 1) Jacobian matrix Dp-sub a and numerical linear algebra for calculating the kernel of Dp-sub a. This paper analyzes parallel homotopy algorithms on a hypercube, considering the numerical algebra, several communications topologies and problem decomposition strategies, functions component complexity, problem size, and the effect of different component complexity distributions. These parameters interact in complicated ways, but some general principles can be inferred based on empirical results

Unit Tangent Vector Computation for Homotopy Curve Tracking on aHypercube

Probability-one homotopy methods are a class of methods for solving nonlinear systems of equations that are globally convergent from an arbitrary starting point. The essence of all such algorithms is the construction of an appropriate homotopy map and subsequent tracking of some smooth curve in the zero set of the homotopy map. Tracking a homotopy curve involves finding the unit tangent vectors at different points along the zero curve. Because of the way a homotopy map is constructed, the unit tangent vector at each point in the zero curve of a homotopy map (symbols) is in the kernel of the Jacobian matrix (symbols). Hence tracking the zero curve of a homotopy map involves finding the kernel of the Jacobian matrix (symbols). The Jacobian matrix (symbols) is a n x (n + 1) matrix with full rank. Since the accuracy of the unit tangent vector is very important, on orthogonal factorization instead of an LU factorization of the Jacobian matrix is computed. Two related factorizations, namely QR and LQ factorization, are considered here. This paper presents computational results showing the performance of several different parallel orthogonal factorization/triangular system solving algorithms on a hypercube. Since the purpose of this study is to find ways to parallelize homotopy algorithms, it is assumed that the matrices are small, dense, and have a special structure such as that of the Jacobian matrix of a homotopy map

Steady Viscous Flow in a Trapezoidal Cavity

The flow in a trapezoidal cavity (including the rectangular and triangular cavities) with one moving wall is studied numerically by finite differences with special treatment in the corners. It is found that streamlines and vorticity distributions are sensitive to geometric changes. The mean square law for core vorticity is valid for the rectangle but ceases to be valid for the triangular cavity

Revisiting Qualitative Data Reuse

Secondary analysis of qualitative data entails reusing data created from previous research projects for new purposes. Reuse provides an opportunity to study the raw materials of past research projects to gain methodological and substantive insights. In the past decade, use of the approach has grown rapidly in the United Kingdom to become sufficiently accepted that it must now be regarded as mainstream. Several factors explain this growth: the open data movement, research funders’ and publishers’ policies supporting data sharing, and researchers seeing benefits from sharing resources, including data. Another factor enabling qualitative data reuse has been improved services and infrastructure that facilitate access to thousands of data collections. The UK Data Service is an example of a well-established facility; more recent has been the proliferation of repositories being established within universities. This article will provide evidence of the growth of data reuse in the United Kingdom and in Finland by presenting both data and case studies of reuse that illustrate the breadth and diversity of this maturing research method. We use two distinct data sources that quantify the scale, types, and trends of reuse of qualitative data: (a) downloads of archived data collections held at data repositories and (b) publication citations. Although the focus of this article is on the United Kingdom, some discussion of the international environment is provided, together with data and examples of reuse at the Finnish Social Science Data Archive. The conclusion summarizes the major findings, including some conjectures regarding what makes qualitative data attractive for reuse and sharing. </jats:p

Visions in monochrome: Families, marriage and the individualisation thesis

This paper takes issue with the way in which the individualisation thesis – in which it is assumed that close relationships have become tenuous and fragile - has become so dominant in ‘new’ sociological theorising about family life. Although others have criticised this thesis, in this paper the main criticism derives from empirical research findings carried out with members of transnational families living in Britain whose values and practices do not fit easily with ideas of individualisation. It is argued that we need a much more complex and less linear notion of how families change across generations and in time

Vorticity Induced by a Moving Elliptic Belt

The viscous flow inside an elliptic moving belt is studied using Newton's method on a Hermite collocation approximation. The streamlines and especially the vorticity distribution are found for Reynolds number up to 1000 and aspect ratio up to five. For low Reynolds numbers vorticity diffuses from regions of high curvature. For high Reynolds numbers there exists a closed boundary layer and a core of constant vorticity. The core vorticity compares well with the estimation from the mean square law

High Dimensional Homotopy Curve Tracking on a Shared Memory Multiprocessor

Results are reported for a series of experiments involving numerical curve tracking on a shared memory parallel computer. Several algorithms exist for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then the tracking of some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. A parallel version of HOMPACK is implemented on a shared memory parallel computer with various levels and degrees of parallelism (e.g., linear algebra, function and Jacobian matrix evaluation), and a detailed study is presented for each of these levels with respect to the speedup in execution time obtained with the parallelism, the time spent implementing the parallel code and the extra memory allocated by the parallel algorithm

Exploring pig trade patterns to inform the design of risk-based disease surveillance and control strategies

An understanding of the patterns of animal contact networks provides essential information for the design of risk-based animal disease surveillance and control strategies. This study characterises pig movements throughout England and Wales between 2009 and 2013 with a view to characterising spatial and temporal patterns, network topology and trade communities. Data were extracted from the Animal and Plant Health Agency (APHA)’s RADAR (Rapid Analysis and Detection of Animal-related Risks) database, and analysed using descriptive and network approaches. A total of 61,937,855 pigs were moved through 872,493 movements of batches in England and Wales during the 5-year study period. Results show that the network exhibited scale-free and small-world topologies, indicating the potential for diseases to quickly spread within the pig industry. The findings also provide suggestions for how risk-based surveillance strategies could be optimised in the country by taking account of highly connected holdings, geographical regions and time periods with the greatest number of movements and pigs moved, as these are likely to be at higher risk for disease introduction. This study is also the first attempt to identify trade communities in the country, information which could be used to facilitate the pig trade and maintain disease-free status across the country in the event of an outbreak