Wire mesh design

We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods

Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

Flower heating following anthesis and the evolution of gall midge pollination in Schisandraceae

Premise of the study: Flower heating is known from a few species in 11 of the c. 450 families of flowering plants. Flowers in these families produce heat metabolically and are adapted to beetles or flies as pollinators. Here, we focus on the Schisandraceae, an American/Asian plant family known to exhibit flower heating in some species, but not others, raising the question of the adaptive function of heat production. Methods: We used field observations, experiments, and ancestral trait reconstruction on a molecular phylogeny for Schisandraceae that includes the investigated species. Key results: At least two Chinese species of Illicium are exclusively pollinated by gall midges that use the flowers as brood sites (not for pollen feeding). Continuous monitoring of flower temperatures revealed that the highest temperatures were attained after the flowers’ sexual functions were over, and experiments showed that post-anthetic warming benefited larval development, not fruit development. Midge larvae in flowers with trimmed tepals (and hence a lower temperature) died, but fruit set ratios remained unchanged. Based on the DNA phylogeny, gall midge pollination evolved from general fly/beetle pollination several times in Schisandraceae, with some species adapted to flower-breeding midges, others to pollen-feeding midges. Conclusions: Flower heating may be an ancestral trait in Schisandraceae that became co-opted in species pollinated by flower-breeding midges requiring long-persistent warm chambers for larval development