Conservative semi-Lagrangian finite volume schemes

Semi-Lagrangian finite volume schemes for the numerical approximation of linear advection equations are presented. These schemes are constructed so that the conservation properties are preserved by the numerical approximation. This is achieved using an interpolation procedure based on area-weighting. Numerical results are presented illustrating some of the features of these schemes.

Exploitation of symbolic information in interprocedural dependence analysis

The requirement for a very accurate dependence analysis to underpin software tools to aid the generation of efficient parallel implementations of scalar code is argued. The current status of dependence analysis is shown to be inadequate for the generation of efficient parallel code, causing too many conservative assumptions to be made. This paper summarises the limitations of conventional dependence analysis techniques, and then describes a series of extensions which enable the production of a much more accurate dependence graph. The extensions include analysis of symbolic variables, the development of a symbolic inequality disproof algorithm and its exploitation in a symbolic Banerjee inequality test; the use of inference engine proofs; the exploitation of exact dependence and dependence pre-domination attributes; interprocedural array analysis; conditional variable definition tracing; integer array tracing and division calculations. Analysis case studies on typical numerical code is shown to reduce the total dependencies estimated from conventional analysis by up to 50%. The techniques described in this paper have been embedded within a suite of tools, CAPTools, which combines analysis with user knowledge to produce efficient parallel implementations of numerical mesh based codes.

Tree species-area and species-diameter relationships at three lowland rain forest sites in Sumatra

Data from three forest sites in Sumatra (Batang Ule, Pasirmayang and Tebopandak) have been analysed and compared for the effects of sample area cut-off, and tree diameter cut-off. An 'extended inverted exponential model' is shown to be well suited to fitting tree-species-area curves. The model yields species carrying capacities of 680 for Batang Ule, 380 species for Pasirmayang, and 35 for Tebopandak (tree diameter >10cm). It would seem that in terms of species carrying capacity, Tebopandak and Pasirmayang are rather similar, and both less diverse than the hilly Batang Ule site. In terms of conservation policy, this would mean that rather more emphasis should be put on conserving hilly sites on a granite substratum. For Pasirmayang with tree diameter >3cm, the asymptotic species number estimate is 567, considerably higher than the estimate of 387 species for trees with diameter >10cm. It is clear that the diameter cut-off has a major impact on the estimate of the species carrying capacity. A conservative estimate of the total number of tree species in the Pasirmayang region is 632 species! In sampling exercises, the diameter cut-off should not be chosen lightly, and it may be worth adopting field sampling procedures which involve some subsampling of the primary sample area, where the diameter cut-off is set much lower than in the primary plots.

Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Existence, uniqueness and constructions for stochastically monotone Q-processes

The key problems in discussing duality and monotonicity for continuous-time Markov chains are to find conditions for existence and uniqueness and then to construct corresponding processes in terms of infinitesimal characteristics, i.e., q-matrices. Such problems are solved in this paper under the assumption that the given q-matrix is conservative. Some general properties of stochastically monotone Q-process ( Q is not necessarily conservative) are also discussed.

Computational modeling techniques for reliability of electronic components on printed circuit boards

This paper describes modeling technology and its use in providing data governing the assembly and subsequent reliability of electronic chip components on printed circuit boards (PCBs). Products, such as mobile phones, camcorders, intelligent displays, etc., are changing at a tremendous rate where newer technologies are being applied to satisfy the demands for smaller products with increased functionality. At ever decreasing dimensions, and increasing number of input/output connections, the design of these components, in terms of dimensions and materials used, is playing a key role in determining the reliability of the final assembly. Multiphysics modeling techniques are being adopted to predict a range of interacting physics-based phenomena associated with the manufacturing process. For example, heat transfer, solidification, marangoni fluid flow, void movement, and thermal-stress. The modeling techniques used are based on finite volume methods that are conservative and take advantage of being able to represent the physical domain using an unstructured mesh. These techniques are also used to provide data on thermal induced fatigue which is then mapped into product lifetime predictions.