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The family Nymphaeaceae includes most of the diversity among the ANA‐grade angiosperms. Among the species of this family, floral structures and pollination strategies are quite varied. The genus Victoria, as well as subgenera Lotos and Hydrocallis in Nymphaea, presents night‐blooming, scented flowers pollinated by scarab beetles. Such similar pollination strategies have led to macromorphological similarities among the flowers of these species, which could be interpreted as homologies or convergences based on different phylogenetic hypotheses about the relationships of these groups. We employed SEM of floral epidermis for seven species of the Nymphaeaceae with contrasting pollination biology to identify the main characters of the floral organs and the potential homologous nature of the structures involved in pollinator attraction. Moreover, we used TEM to observe ultrastructure of papillate‐conical epidermis in the stamen of Victoria cruziana. We then tested the phylogenetic or ecological distribution of these traits using both consensus network approaches and ancestral state reconstruction on fixed phylogenies. Our results show that the night‐blooming flowers present different specializations in their epidermis, with Victoria cruziana presenting the most elaborate floral anatomy. We also identify for the first time the presence of conical‐papillate cells in the order Nymphaeales. The epidermal characters tend to reflect phylogenetic relationships more than convergence due to pollinator selection. These results point to an independent and parallel evolution of scarab pollination in Nymphaeaceae, and show the promise of floral anatomy as a phylogenetic marker. Moreover, they indicate a degree of sophistication in the anatomical basis of cantharophilous flowers in the Nymphaeales that diverges from the most simplistic views of floral evolution in the angiosperms. This article is protected by copyright. All rights reserved.

† Background and Aims In the sexually deceptive Ophrys genus, species isolation is generally considered ethological and occurs via different, specific pollinators, but there are cases in which Ophrys species can share a common pollinator and differ in pollen placement on the body of the insect. In that condition, species are expected to be reproductively isolated through a pre-mating mechanical barrier. Here, the relative contribution of pre- vs. post-mating barriers to gene flow among two Ophrys species that share a common pollinator and can occur in sympatry is studied. † Methods A natural hybrid zone on Sardinia between O. iricolor and O. incubacea, sharing Andrena morio as pollinator, was investigated by analysing floral traits involved in pollinator attraction as odour extracts both for non-active and active compounds and for labellum morphology. The genetic architecture of the hybrid zone was also estimated with amplified fragment length polymorphism (AFLP) markers, and pollination fitness and seed set of both parental species and their hybrids in the sympatric zone were estimated by controlled crosses. † Key Results Although hybrids were intermediate between parental species in labellum morphology and nonactive odour compounds, both parental species and hybrids produced a similar odour bouquet for active compounds. However, hybrids produced significantly lower fruit and seed set than parental species, and the genetic architecture of the hybrid zone suggests that they were mostly first-generation hybrids. † Conclusions The two parental species hybridize in sympatry as a consequence of pollinator overlap and weak mechanical isolation, but post-zygotic barriers reduce hybrid frequency and fitness, and prevent extensive introgression. These results highlight a significant contribution of late post-mating barriers, such as chromosomal divergence, for maintaining reproductive isolation, in an orchid group for which pre-mating barriers are often considered predominant.

• Background and Aims Pollen characters have been widely used in defining evolutionary trends in orchids. In recent years, information on pollination biology and phylogenetic patterns within Orchidinae has become available. Hence, the aim of the presented work is to re-evaluate exine micromorphology of Orchidinae in light of recent phylogenetic studies and to test whether pollen micromorphology strictly depends on phylogenetic relationships among species or whether it is influenced by the marked differences in pollination ecology also reported among closely related species. • Methods Pollen sculpturing of 45 species of Orchidinae and related taxa was investigated using scanning electron microscopy. To cover potential intraspecific variation, several accessions of the same species were examined. • Key Results Orchidinae show remarkable variation in exine sculpturing, with a different level of variation within species groups. In some genera, such as Serapias (rugulate) and Ophrys (psilate to verrucate), intrageneric uniformity corresponds well to a common pollination strategy and close relationships among species. However, little exine variability (psilate–scabrate and scabrate–rugulate) was also found in the genus Anacamptis in spite of striking differences in floral architecture and pollination strategies. A larger variety of exine conditions was found in genera Dactylorhiza (psilate, psilate–scabrate and reticulate) and Orchis s.s. (psilate, reticulate, perforate–rugulate and baculate) where no unequivocal correspondence can be found to either phylogenetic patterns or pollination strategies. • Conclusions Changes in pollen characteristics do not consistently reflect shifts in pollination strategy. A unique trend of exine evolution within Orchidinae is difficult to trace. However, the clades comprising Anacamptis, Neotinea, Ophrys and Serapias show psilate to rugulate or scabrate pollen, while that of the clade comprising Chamorchis, Dactylorhiza, Gymnadenia, Orchis s.s., Platanthera, Pseudorchis and Traunsteinera ranges from psilate to reticulate. Comparison of the data with exine micromorphology from members of the tribe Orchidieae and related tribes suggests a possible general trend from reticulate to psilate.

A model is developed for heat transfer, polymer vaporization, and gas diffusion at the interface between the advancing liquid metal and the receding foam pattern during mold filling in lost foam casting of aluminum. Most of the pattern interior decomposes by ablation, but the boundary cells decompose by a collapse mechanism, which creates an undercut in the pattern next to the coating. By regulating how much of the pattern coating is exposed to gas diffusion, the undercut controls the overall filling speed of the metal through the mold. Computed values for the foam decomposition energy from this model compare very well with experimental data on foam pyrolysis, and predicted filling speeds are consistent with observations in published experiments. In addition, the model explains several unusual observations about mold filling that until now have not been understood.

A method has been developed for calculating hydraulic pressures induced by thermal expansion of liquid binders early in the removal cycle, when evaporative losses are negligible and fully saturated conditions prevail. Specific results were obtained for flat compacts containing a common wax binder, mixed with varying amounts of low-density polyethylne. In general, these results show how the risk of hydraulic fracture increases with heating rate and compact thickness. Although pressures are minimal when the binder consists entirely of wax, the continual addition of polyethylene eventually gives rise to unacceptable risk levels, even for relatively thin compacts. Binder removal at elevated temperatures is considered subsequently. In this case, vapor pressures eventually approach a critical level, thereby allowing mass removal by evaporation to overcome the effect of thermal expansion in maintaining full saturation. With the onset of void formation, the developing capillary pressure supersedes hydraulic pressure as the driving force in liquid transport. Besides representing capillary flow, the present formulation also accounts for thermal degradation of the binder during removal. The resulting system of equations was solved numerically for a variety of representative debinding conditions. Predictions for flat compact containing a balanced wax/polyethylene binder indicate that thermal degradation of the polyethylene can give rise to a marked improvement in debinding rates. It turns out, however, that this enhancement is far more effective in thinner compacts.

A new formulation for obtaining design sensitivities in shape optimization has been developed. The formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid. As a check on accuracy, the approach was applied to a uniformly loaded infinite plate containing an elliptical hole. In this case, the availability of an analytical solution made it possible to calculate errors exactly. Furthermore, a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole. For convenience, the design sensitivities were calculated with respect to changes in the major axis. Numerical convergence was established by comparing results based on four successive boundary meshes. In general, the predictions for both displacement and stress sensitivities were remarkably accurate.

A boundary element formulation for design sensitivities has been developed for application in three-dimensional shape optimization of elastic solids. Both displacement and stress sensitivities can be determined, at any stage of the design process, by relatively straightforward numerical integration procedures. Further simplification in calculating displacement sensitivities is accomplished by using a special rigid-body integral identity to remove singularities. The issue of accuracy was addressed by analyzing the problem of an infinite elastic solid with a triaxial ellipsoidal cavity. It turns out that this test case is considerably more general than the usual axisymmetric examples employed in prior elastostatic error analyses. Furthermore, the stress concentration can be increased indefinitely by decreasing the two aspect ratios that define the cavity surface. More importantly, the availability of an analytical solution makes it possible to obtain an exact measure of error. For completeness, stresses and stress sensitivities were obtained for three progressively eccentric cavity shapes, using three different singular integration schemes. Generally, the numerical predictions and exact results were in excellent agreement. In the worst case, with a stress concentration of about 4.1, the best stress sensitivity prediction was within 2 percent of the exact value. This is remarkably accurate, given that the corresponding cavity model consisted of only twelve elements per octant.

This paper concerns heat conduction in a chopped-fiber reinforced polyester resin during compression molding of thin sheet-like parts. Since the resin generates heat as it cures, the general boundary value problem involves a deforming heat conductor which reacts chemically. The randomly woven fiber structure in the sheet molding compound (SMC) motivates a kinematical assumption on the material deformation in the mold cavity. The resulting description of the deformation field is then used to formulate a boundary value problem for the temperature distribution in the deforming SMC in terms of coordinates that move with the material. From the solution to this problem we derive a general expression in closed form for the nonuniform distribution of heat energy absorbed from the mold surface as each part is molded. The exothermic cure reaction in the polyester resin, which begins after the mold closes, is characterized in terms of heat generated in the SMC. Numerical analysis of the transient distribution of temperature and cure shows how the degree of coupling between heat conduction and cure depends on the thickness of the molded sheet. The results of the analysis also determine the effect of sheet thickness and mold temperature on cure time, subject to limitations of thermal degradation.

Since the cure rate of injection molded thermosets is usually very sensitive to cavity surface temperature, spatial variations in these temperatures can lengthen the necessary cure time for the entire part and cause distortion and residual stress in the molded article. This problem is addressed in the present paper by combining an optimization algorithm with a quasi-steady heat conduction analysis in the mold to determine the heating line positions and operating temperatures that minimize the spatial variation in cavity surface temperature. The method is applied to an example mold for a flat panel of uniform thickness, using two different gate locations. At a one-minute cycle, the optimal designs for each gate location dramatically reduce the variation in cavity surface temperature compared with corresponding results using a conventional heating system. These results are made more significant by the fact that the optimal designs use considerably fewer heating lines. In spite of their simplicity, the optimal designs still have enough flexibility to adjust to a changing cycle without sacrificing uniformity in cavity surface temperature.