Observation of surface and bulk phase transitions in nematic liquid crystals

The behaviour of liquid crystal (LC) molecules near a surface is of both fundamental and technological interest: it gives rise to various surface phase-transition and wetting phenomena, and surface-induced ordering of the LC molecules is integral to the operation of LC displays. Here we report the observation of a pure isotropic-nematic (IN) surface phase transition-clearly separated from the bulk IN transition-in a nematic LC on a substrate. Differences in phase behaviour between surface and bulk are expected, but have hitherto proved difficult to distinguish, owing in part to the close proximity of their transition temperatures. We have overcome these difficulties by using a mixture of nematic LCs: small, surface-induced composition variations lead to complete separation of the surface and bulk transitions, which we then study independently as a function of substrate and applied magnetic field. We find the surface IN transition to be of first order on surfaces with a weak anchoring energy and continuous on surfaces with a strong anchoring. We show that the presence of high magnetic fields does not change the surface IN transition temperature, whereas the bulk IN transition temperature increases with field. We attribute this to the interaction energy between the surface and bulk phases, which is tuned by magnetic-field-induced order in the surface-wetting layer.     

Speciation through sensory drive in cichlid fish

Theoretically, divergent selection on sensory systems can cause speciation through sensory drive. However, empirical evidence is rare and incomplete. Here we demonstrate sensory drive speciation within island populations of cichlid fish. We identify the ecological and molecular basis of divergent evolution in the cichlid visual system, demonstrate associated divergence in male colouration and female preferences, and show subsequent differentiation at neutral loci, indicating reproductive isolation. Evidence is replicated in several pairs of sympatric populations and species. Variation in the slope of the environmental gradients explains variation in the progress towards speciation: speciation occurs on all but the steepest gradients. This is the most complete demonstration so far of speciation through sensory drive without geographical isolation. Our results also provide a mechanistic explanation for the collapse of cichlid fish species diversity during the anthropogenic eutrophication of Lake Victoria.     

多项式微分系统的不变直线的不同斜率的最大个数

本文证明了公式β（ｎ）＝σ（ｎ－１）＋１其中α（ｎ－１）是ｎ－１次多项式微分系统的不为直线的最多条数，βｎ）是ｎ次多项式微分系统的不变直线的不同斜率的最大个数。这里假设所讨论的多项式系统只有限条不变直线。