Fluid-structure Interactions of Inverted Leaves and Flags

Interactions between fluid flows and elastic bodies are ubiquitous in nature. One such phenomena that is encountered on a daily basis is the flapping and fluttering of leaves in the wind. The fluid-structure interaction that governs the physics of a leaf in the wind is poorly understood at best and has potential applications in biomechanics, vehicle design, and energy conversion. We build upon previous work on the flapping dynamics of inverted flags, which are cantilevered elastic sheets with free leading edge and fixed trailing edge that display unique large amplitude oscillatory behaviors. We model a leaf in the laboratory using modified inverted flags, experimentally probing the governing parameters behind leaf fluttering as well as shedding light on the physics behind the inverted flag phenomena. The behavior of these "inverted leaves" studied here display sensitive dependence on two biomechanically relevant parameters, stem-to-leaf rigidity and stem-to-leaf length. In addition, leaves on a tree are not often found alone. We seek to understand the complex interactions of multiple fluttering and flapping leaves by way of examining the interactions between pairs of inverted flags. Coupling through their flow fields, pairs of inverted flags exhibit striking emergent phenomena. We report these observed dynamical behaviors and the conditions upon which they arise.

Morphogenesis of the Arabidopsis Shoot Apical Meristem

Phyllotaxis patterns in plants, or the arrangement of leaves and flowers radially around the shoot, have fascinated both biologists and mathematicians for centuries. The current model of this process involves the lateral transport of the hormone auxin through the first layer of cells in the shoot apical meristem via the auxin efflux carrier protein PIN1. Locations around the meristem with high auxin concentration are sites of organ formation and differentiation. Many of the molecular players in this process are well known and characterized. Computer models composed of all these components are able to produce many of the observed phyllotaxis patterns. To understand which parts of this model have a large effect on the phenotype I automated parameter testing and tried many different parameter combinations. Results of this showed that cell size and meristem size should have the largest effect on phyllotaxis. This lead to three questions: (1) How is cell geometry regulated? (2) Does cell size affect auxin distribution? (3) Does meristem size affect phyllotaxis? To answer the first question I tracked cell divisions in live meristems and quantified the geometry of the cells and the division planes using advanced image processing techniques. The results show that cell shape is maintained by minimizing the length of the new wall and by minimizing the difference in area of the daughter cells. To answer the second question I observed auxin patterning in the meristem, shoot, leaves, and roots of Arabidopsis mutants with larger and smaller cell sizes. In the meristem and shoot, cell size plays an important role in determining the distribution of auxin. Observations of auxin in the root and leaves are less definitive. To answer the third question I measured meristem sizes and phyllotaxis patterns in mutants with altered meristem sizes. These results show that there is no correlation between meristem size and average divergence angle. But in an extreme case, making the meristem very small does lead to a switch on observed phyllotaxis in accordance with the model.