Chen, Bryan Gin-ge
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Publication Minimal Resonances in Annular Non-Euclidean Strips(2010-11-02) Chen, Bryan Gin-ge; Santangelo, Christian D.Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of “conical” closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. We derive and test a surprising resonance condition for strips with minimal bending energy along the strip center line to exist.Publication Helical Packings and Phase Transformations of Soft Spheres in Cylinders(2010-04-13) Lohr, Matthew A; Chen, Bryan G; Alsayed, A. M; Kamien, Randall D; Zhang, Zheng; Yodh, Arjun GThe phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of the volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as the particle volume fraction is reduced, consistent with recent hard-sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter 6. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase-transition-like behavior in quasi-one-dimensional systems.