Shiuan-Fan Liou, Chun-Chao Lo, Ming-Han Chou, Pai-Yi Hsiao, Tzay-Ming Hong
Our primary goal was to study whether or how the scaling relations based on the energy optimization of a single ridge would be revised on an actual crumpled sheet; namely, when ridge-ridge interactions were important. Molecular Dynamics Simulation was employed for this purpose. In order to obtain better quantitative results, we introduced several revisions to the existent proctocols which made use of a triangular lattice of beads and springs to record the distribution of stretching and bending energies due to a collapsing spherical wall. We proposed that cautions be taken at remedizing three deficiencies of the model, including interstitial holes, a growing number of beads that wedged in these holes, and the convenient but error-prone use of wall radius to denote the crumpled ball size. We found after refinements that, only when the ball density was very low, Witten was correct at predicting (1) the energy stored in a single ridge was proportional to 1/3-power of its length and (2) the ratio between bending and stretching energies equaled 5. But soon as the density and ridge number increased, the ridge-ridge interactions swarmed and altered these scalings. In the mean time, we (3) succeeded at resolving the crucial discrepancies between previous simulations and experiments in the power-law regime, (4) completed the measurement of related properties such as averaged ridge length, ridge number, and energy cost per unit length of ridge as a function of density, (5) provided heuristic derivations for these properties via a mean-field model, (6) extended the existent simulations to the vast untapped regime of high pressures and (7) verified the existence of a scaling relation that was more general than the familiar power law at covering the whole density range.
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http://arxiv.org/abs/1303.2180
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