Certain necessary conditions for energy-minimizing states of fluid systems consisting of bulk, surface, and line phases are discussed. These include generalizations of the Laplace and Young equations of equilibrium, together with a demonstration that the line tension associated with a three-phase contact curve must be nonnegative.
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The concern over climate change has motivated a search for low-carbon transportation fuels. One approach to low-carbon fuels is to exploit photosynthesis, which stores solar energy in plant biomass. I review here some aspects of the potential for making liquid fuels from biomasss. There appear to be significant amounts of currently un- or underutilized land available to raise biomass for liquid fuels. Rather than compete with feed crops, we have explored the potential of energy crops such as perennial grasses. Processes have been developed for efficient production of fuels from biomass. Lots of progress has been made but lessons are still being learned.
Aging disrupts sleep. Moreover, these sleep impairments are exaggerated in Alzheimer's disease, and are proposed to contribute to cognitive decline. Recent human studies have linked β-amyloid with non-rapid eye-movement (NREM) sleep disruption. However, the impact of tau pathology on human sleep oscillations and cognition remains uninvestigated. Here, we tested the hypothesis that tau burden within medial temporal lobe (MTL) impairs the coupled relationship between the two key NREM sleep oscillations—sleep spindles and slow waves, and their known support of hippocampal memory. In vivo tau was measured with [18F]AV1451 PET in cognitively normal older adults (n=19, mean age=75.8), together with overnight, dense-array sleep EEG recordings. A validated associative recognition task was used to measure hippocampal memory function. Analyses focused on relationships between three measurements: (i) AV1451 tau PET binding in MTL measured as the mean (L+R) standardized uptake value ratio of tracer relative to inferior cerebellar gray matter (SUVR), (ii) EEG phase-amplitude coupling between NREM spindles and slow wave oscillations, and (iii) hippocampus-dependent memory. Worse memory performance was related to greater tau burden in MTL (AV1451 SUVR; p=0.03; Fig. 1). MTL tau burden additionally predicted the severity of impaired sleep spindle-slow wave oscillation coupling over the prefrontal cortex (p=0.03; Fig. 2, top). Moreover, this tau-related sleep disruption of spindle-slow wave coupling predicted the degree of memory impairment (p=0.05; Fig. 2, bottom).
One of the many benefits of multicast, when compared to traditional unicast, is that multicast reduces the overall network load. While the importance of multicast is beyond dispute, there have been surprisingly few attempts to quantify multicast's reduction in overall network load. The only substantial and quantitative effort we are aware of is that of Chuang and Sirbu [3]. They calculate the number of links L in a multicast delivery tree connecting a random source to m random and distinct network sites; extensive simulations over a range of networks suggest that L(m) ∝ m 0.8 . In this paper we examine the function L(m) in more detail and derive the asymptotic form for L(m) in k-ary trees. These results suggest one possible explanation for the universality of the Chuang-Sirbu scaling behavior.