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

Photonic band gaps in materials with triply periodic surfaces and related tubular structures

We calculate the photonic band gap of triply periodic bicontinuous cubic structures and of tubular structures constructed from the skeletal graphs of triply periodic minimal surfaces. The effect of the symmetry and topology of the periodic dielectric structures on the existence and the characteristics of the gaps is discussed. We find that the C(I2-Y**) structure with Ia3d symmetry, a symmetry which is often seen in experimentally realized bicontinuous structures, has a photonic band gap with interesting characteristics. For a dielectric contrast of 11.9 the largest gap is approximately 20% for a volume fraction of the high dielectric material of 25%. The midgap frequency is a factor of 1.5 higher than the one for the (tubular) D and G structures

Changes to the Fossil Record of Insects through Fifteen Years of Discovery

The first and last occurrences of hexapod families in the fossil record are compiled from publications up to end-2009. The major features of these data are compared with those of previous datasets (1993 and 1994). About a third of families (>400) are new to the fossil record since 1994, over half of the earlier, existing families have experienced changes in their known stratigraphic range and only about ten percent have unchanged ranges. Despite these significant additions to knowledge, the broad pattern of described richness through time remains similar, with described richness increasing steadily through geological history and a shift in dominant taxa, from Palaeoptera and Polyneoptera to Paraneoptera and Holometabola, after the Palaeozoic. However, after detrending, described richness is not well correlated with the earlier datasets, indicating significant changes in shorter-term patterns. There is reduced Palaeozoic richness, peaking at a different time, and a less pronounced Permian decline. A pronounced Triassic peak and decline is shown, and the plateau from the mid Early Cretaceous to the end of the period remains, albeit at substantially higher richness compared to earlier datasets. Origination and extinction rates are broadly similar to before, with a broad decline in both through time but episodic peaks, including end-Permian turnover. Origination more consistently exceeds extinction compared to previous datasets and exceptions are mainly in the Palaeozoic. These changes suggest that some inferences about causal mechanisms in insect macroevolution are likely to differ as well