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Current theories and models of the formation of phyllotactic patterns at plant apical meristems center on either transport of the growth hormone auxin or the mechanical buckling of the plant tunica. By deriving a continuum approximation of an existing discrete biochemical model and comparing it with a mechanical model, we show that the model partial(More)
We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the deformation configurations seen on plant surfaces may be understood as the energy-minimizing buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is that the strain energy is minimized by configurations consisting of special triads(More)
Many data sets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a data set. A useful representation of this homological(More)
We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special(More)
Phyllotaxis, the arrangement of a plant's phylla (flowers, bracts, stickers) near its shoot apical meristem (SAM), has intrigued natural scientists for centuries. Even today, the reasons for the observed patterns and their special properties, the physical and chemical mechanisms which give rise to strikingly similar configurations in a wide variety of(More)
A theory is developed that explains the genesis of the strikingly regular hexagonal arrays of nanoscale mounds that can form when a flat surface of a binary compound is subjected to normal-incidence ion bombardment. We find that the species with the higher sputter yield is concentrated at the peaks of the nanodots and that hysteretic switching between the(More)
Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by(More)
We use a simple mathematical model to estimate the probability and its time dependence that one or more HIV virions successfully infect target cells. For the transfer of a given number of virions to target cells we derive expressions for the probability P(inf), of infection. Thus, in the case of needlestick transfer we determine P(inf) and an approximate(More)