Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature

We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and various bicontinuous cubic phases. For the latter case we consider both single structures (one monolayer) and double structures (two monolayers). Their interfaces are modeled by the triply periodic surfaces of constant mean curvature of the families G, D, P, C(P), I-WP and F-RD. The stability of the different bicontinuous cubic phases can be explained by the way in which their universal geometrical properties conspire with the concentration constraints. For vanishing saddle-splay modulus $\bar \kappa$, almost every phase considered has some region of stability in the Gibbs triangle. Although bicontinuous cubic phases are suppressed by sufficiently negative values of the saddle-splay modulus $\bar \kappa$, we find that they can exist for considerably lower values than obtained previously. The most stable bicontinuous cubic phases with decreasing $\bar \kappa < 0$ are the single and double gyroid structures since they combine favorable topological properties with extreme volume fractions.Comment: Revtex, 23 pages with 10 Postscript files included, to appear in J. Chem. Phys. 112 (6) (February 2000

Morphological and behavioural adaptations to feed on nectar: how feeding ecology determines the diversity and composition of hummingbird assemblages

Hummingbirds are the most specialised nectarivorous birds and show close ecological relationships to their food plants. Their small body size, bright colors, and unique behaviour have fascinated generations of naturalists. In this review, we investigate the morphological and behavioural adaptations of hummingbirds to feed on nectar and arthropods, and explore their diffuse co-evolution with their food plant species. Further, a list of plant genera including species mainly pollinated by hummingbirds is presented. Summarising the existing knowledge on hummingbird feeding ecology, we find that much of the variability in morphology and behaviour of hummingbirds is determined by their unique feeding mode and the constraints set by their food plants. Based on the existing literature, we developed a hierarchical system explaining how different environmental factors have shaped the current richness of hummingbirds, and their morphological and behavioural diversity. We propose that climatic stability within and between seasons and days determines the constancy of food availability, which in turn is the most important factor for species richness in hummingbird assemblages. However, the assemblage composition of hummingbirds is also influenced by phylogenetic factors, especially under harsh environmental conditions. Unsurprisingly, the highest morphological and behavioural diversity is observed in the most species-rich assemblages. This diversity may have at least partly evolved to reduce inter- and intraspecific competition. Independently of which morphological character we consider, the 360 different hummingbird species have evolved a large morphological variability to adapt to their individual feeding niches