Topological Optimization of the Evaluation of Finite Element Matrices

We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on phrasing the computation on each element as the contraction of each collection of reference element tensors with an element-specific geometric tensor. We then present a new concept of complexity-reducing relations that serve as distance relations between these reference element tensors. This notion sets up a graph-theoretic context in which we may find an optimized algorithm by computing a minimum spanning tree. We present experimental results for some common multilinear forms showing significant reductions in operation count and also discuss some efficient algorithms for building the graph we use for the optimization

Moisture sensitivity examination of asphalt mixtures using thermodynamic, direct adhesion peel and compacted mixture mechanical tests

Moisture damage in asphalt mixtures is a complicated mode of pavement distress that results in the loss of stiffness and structural strength of the asphalt pavement layers. This paper evaluated the moisture sensitivity of different aggregate–bitumen combinations through three different approaches: surface energy, peel adhesion and the Saturation Ageing Tensile Stiffness (SATS) tests. In addition, the results obtained from these three tests were compared so as to characterise the relationship between the thermodynamic and the mechanical tests. The surface energy tests showed that the work of adhesion in dry conditions was bitumen type dependent, which is in agreement with the peel test. After moisture damage, all of these three tests found that the moisture sensitivity of aggregate–bitumen combinations were mainly aggregate type dependent. Based on the peel test, the moisture absorption and mineralogical compositions of aggregate were considered as two important factors to moisture sensitivity. This phenomenon suggests that in a susceptible asphalt mixture, the effect of aggregate may be more influential than the effect of bitumen. The SATS test and the peel test showed similar moisture sensitivity results demonstrating the good correlation between these two mechanical tests. However, the surface energy tests and the mechanical tests cannot correlate in terms of moisture sensitivity evaluation

Wildfire selectivity for land cover type: does size matter ?

Previous research has shown that fires burn certain land cover types disproportionally to their abundance. We used quantile regression to study land cover proneness to fire as a function of fire size, under the hypothesis that they are inversely related, for all land cover types. Using five years of fire perimeters, we estimated conditional quantile functions for lower (avoidance) and upper (preference) quantiles of fire selectivity for five land cover types - annual crops, evergreen oak woodlands, eucalypt forests, pine forests and shrublands. The slope of significant regression quantiles describes the rate of change in fire selectivity (avoidance or preference) as a function of fire size. We used Monte-Carlo methods to randomly permutate fires in order to obtain a distribution of fire selectivity due to chance. This distribution was used to test the null hypotheses that 1) mean fire selectivity does not differ from that obtained by randomly relocating observed fire perimeters; 2) that land cover proneness to fire does not vary with fire size. Our results show that land cover proneness to fire is higher for shrublands and pine forests than for annual crops and evergreen oak woodlands. As fire size increases, selectivity decreases for all land cover types tested. Moreover, the rate of change in selectivity with fire size is higher for preference than for avoidance. Comparison between observed and randomized data led us to reject both null hypotheses tested (a = 0.05) and to conclude it is very unlikely the observed values of fire selectivity and change in selectivity with fire size are due to chance.Funding: This paper was supported by the Fundação para a Ciência e Tecnologia Ph.D. Grant SFRH/BD/40398/2007. JMCP participated in this research under the framework of research projects ‘‘Forest fire under climate, social and economic changes in Europe, the Mediterranean and other fire-affected areas of the world (FUME)’’, EC FP7 Grant Agreement No. 243888. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscrip

Disequilibrium, adaptation and the Norse settlement of Greenland

This research was supported by the University of Edinburgh ExEDE Doctoral Training Studentship and NSF grant numbers 1202692 and 1140106.There is increasing evidence to suggest that arctic cultures and ecosystems have followed non-linear responses to climate change. Norse Scandinavian farmers introduced agriculture to sub-arctic Greenland in the late tenth century, creating synanthropic landscapes and utilising seasonally abundant marine and terrestrial resources. Using a niche-construction framework and data from recent survey work, studies of diet, and regional-scale climate proxies we examine the potential mismatch between this imported agricultural niche and the constraints of the environment from the tenth to the fifteenth centuries. We argue that landscape modification conformed the Norse to a Scandinavian style of agriculture throughout settlement, structuring and limiting the efficacy of seasonal hunting strategies. Recent climate data provide evidence of sustained cooling from the mid thirteenth century and climate variation from the early fifteenth century. Archaeological evidence suggests that the Norse made incremental adjustments to the changing sub-arctic environment, but were limited by cultural adaptations made in past environments.Publisher PDFPeer reviewe

Discrete Optimization of Finite Element Matrix Evaluation

The tensor contraction structure for the computation of the element tensor AT obtained in Chapter 8,enables not only the construction of a compiler for variational forms,but an optimizing compiler.For typical variational forms,the reference tensor A0 has significant structure that allows the element tensor AT to be computed on an arbitrary cell T at a lower computational cost