@article{may_shearer_daniels_2010, title={Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow}, volume={20}, ISSN={0938-8974 1432-1467}, url={http://dx.doi.org/10.1007/s00332-010-9069-7}, DOI={10.1007/s00332-010-9069-7}, abstractNote={Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is nonstandard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case.}, number={6}, journal={Journal of Nonlinear Science}, publisher={Springer Science and Business Media LLC}, author={May, Lindsay B. H. and Shearer, Michael and Daniels, Karen E.}, year={2010}, month={May}, pages={689–707} }
 @article{may_golick_phillips_shearer_daniels_2010, title={Shear-driven size segregation of granular materials: Modeling and experiment}, volume={81}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.81.051301}, abstractNote={Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential shear profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then resegregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we map the local concentration (from the model) to changes in packing fraction; this provides a way to make a semiquantitative comparison with the measured global dilation. We observe that the resulting model successfully captures the presence of a fast mixing process and relatively slower resegregation process, but the model predicts a finite resegregation time, while in the experiment resegregation occurs only exponentially in time.}, number={5}, journal={PHYSICAL REVIEW E}, publisher={American Physical Society (APS)}, author={May, Lindsay B. H. and Golick, Laura A. and Phillips, Katherine C. and Shearer, Michael and Daniels, Karen E.}, year={2010}, month={May} }
 @article{crannell_may_hilbert_2007, title={Shifts of finite type and Fibonacci Harps}, volume={20}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2006.03.007}, abstractNote={We make an explicit connection between the Fibonacci Harp (or Fibonacci String) and two well-known dynamical systems: subshifts of finite type and the baker’s map on the unit interval. In particular, we show that the boundary of the Fibonacci Harp is an embedding of a commonly studied shift of finite type in the unit interval. Moreover, every shift of finite type embeds as the boundary of a lattice harp.}, number={2}, journal={APPLIED MATHEMATICS LETTERS}, author={Crannell, Annalisa and May, Stephen and Hilbert, Lindsay}, year={2007}, month={Feb}, pages={138–141} }