TY - JOUR
T1 - Intrinsically anomalous self-similarity of randomly folded matter
AU - Balankin, Alexander S.
AU - De Oca, Rolando Cortes Montes
AU - Ochoa, Didier Samayoa
PY - 2007/9/10
Y1 - 2007/9/10
N2 - We found that randomly folded thin sheets exhibit unconventional scale invariance, which we termed as an intrinsically anomalous self-similarity, because the self-similarity of the folded configurations and of the set of folded sheets are characterized by different fractal dimensions. Besides, we found that self-avoidance does not affect the scaling properties of folded patterns, because the self-intersections of sheets with finite bending rigidity are restricted by the finite size of crumpling creases, rather than by the condition of self-avoidance. Accordingly, the local fractal dimension of folding structures is found to be universal (Dl =2.64±0.05) and close to expected for a randomly folded phantom sheet with finite bending rigidity. At the same time, self-avoidance is found to play an important role in the scaling properties of the set of randomly folded sheets of different sizes, characterized by the material-dependent global fractal dimension D< Dl. So intrinsically anomalous self-similarity is expected to be an essential feature of randomly folded thin matter.
AB - We found that randomly folded thin sheets exhibit unconventional scale invariance, which we termed as an intrinsically anomalous self-similarity, because the self-similarity of the folded configurations and of the set of folded sheets are characterized by different fractal dimensions. Besides, we found that self-avoidance does not affect the scaling properties of folded patterns, because the self-intersections of sheets with finite bending rigidity are restricted by the finite size of crumpling creases, rather than by the condition of self-avoidance. Accordingly, the local fractal dimension of folding structures is found to be universal (Dl =2.64±0.05) and close to expected for a randomly folded phantom sheet with finite bending rigidity. At the same time, self-avoidance is found to play an important role in the scaling properties of the set of randomly folded sheets of different sizes, characterized by the material-dependent global fractal dimension D< Dl. So intrinsically anomalous self-similarity is expected to be an essential feature of randomly folded thin matter.
UR - http://www.scopus.com/inward/record.url?scp=34548819393&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.76.032101
DO - 10.1103/PhysRevE.76.032101
M3 - Artículo
SN - 1539-3755
VL - 76
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 032101
ER -