Patrick D. Shipman

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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 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)
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 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)
The dynamics of inertial elastic helical thin rods with non-circular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis and the dispersion relation for helical strips is derived and analyzed. It is shown that all(More)
Predicting the probability of persistence of HIV infection with the standard model Abstract It is not well understood why the transmission of HIV may have a small probability of occurrence despite frequent high risk exposures or ongoing contact between members of a discordant couple. We explore the possible contributions made by distributions of system(More)
The snow surface is very dynamic, and the roughness of the snowpack surface varies spatially and temporally. The snow surface roughness influences the movement of air across the snow surface as well as the resulting transfers of energy, and is used to estimate the sensible and latent heat fluxes to and/or from the snow surface to the atmosphere. In the(More)