A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

Researching crime and violence: Untold stories from the field

Undertaking empirical research on crime and violence can be a tricky enterprise fraught with ethical, methodological, intellectual and legal implications. This chapter takes readers on a reflective journey through the qualitative methodologies I used to research sex work in Kings Cross, miscarriages of justice, female delinquency, sexual violence, and violence in rural and regional settings over a period of nearly 30 years. Reflecting on these experiences, the chapter explores and analyses the reality of doing qualitative field research, the role of the researcher, the politics of subjectivity, the exercise of power, and the ‘muddiness’ of the research process, which is often overlooked in sanitised accounts of the research process (Byrne-Armstrong, Higgs and Horsfall, 2001; Davies, 2000).

Nitrogen fertilizer rate management as a nitrous oxide mitigation strategy: Development of a nitrous oxide emission reduction protocol (NERP)

Nitrous oxide (N2O) is a potent agricultural greenhouse gas (GHG). More than 50% of the global anthropogenic N2O flux is attributable to emissions from soil, primarily due to large fertilizer nitrogen (N) applications to corn and other non-leguminous crops. Quantification of the trade–offs between N2O emissions, fertilizer N rate, and crop yield is an essential requirement for informing management strategies aiming to reduce the agricultural sector GHG burden, without compromising productivity and producer livelihood. There is currently great interest in developing and implementing agricultural GHG reduction offset projects for inclusion within carbon offset markets. Nitrous oxide, with a global warming potential (GWP) of 298, is a major target for these endeavours due to the high payback associated with its emission prevention. In this paper we use robust quantitative relationships between fertilizer N rate and N2O emissions, along with a recently developed approach for determining economically profitable N rates for optimized crop yield, to propose a simple, transparent, and robust N2O emission reduction protocol (NERP) for generating agricultural GHG emission reduction credits. This NERP has the advantage of providing an economic and environmental incentive for producers and other stakeholders, necessary requirements in the implementation of agricultural offset projects.