We study the statistical topology of folding configurations of hand folded paper balls. Specifically, we are studying the distribution of two sides of the sheet along the ball surface and the distribution of sheet fragments when the ball is cut in half. We found that patterns obtained by mapping of ball surface into unfolded flat sheet exhibit the fractal properties characterized by two fractal dimensions which are independent on the sheet size and the ball diameter. The mosaic patterns obtained by sheet reconstruction from fragments of two parts (painted in two different colors) of the ball cut in half also possess a fractal scale invariance characterized by the box fractal dimension DBF=1.68 ± 0.04 , which is independent on the sheet size. Furthermore, we noted that DBF, at least numerically, coincide with the universal fractal dimension of the intersection of hand folded paper ball with a plane. Some other fractal properties of folding configurations are recognized.

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Stress and strain relaxation in randomly folded paper sheets under axial compression is studied both experimentally and theoretically. Equations providing the best fit to the experimental data are found. Our findings suggest that, in an axially compressed ball folded from an elastic or elasto-plastic material, the relaxation dynamics is ruled by activated processes of an energy foci rearrangement in the crumpling network. The dynamics of relaxation is discussed within a framework of Edwards's statistical mechanics. The functional forms of the activation barrier between admissible jammed folding configurations of the crumpling network under axial compression are derived. It is shown that relaxation kinetics can be mapped to activated dynamics of depinning and creep of elastic interface in a disordered medium.

Cerium oxide nanomaterials are known to absorb ionizing radiation energy, as well as to neutralize free radicals in solution, by undergoing redox changes. We, therefore, proposed that ceria nanoparticles could be used in biomedical applications as an injectable, radio-protectant material. In this study, we examine the effectiveness of engineered nanoparticles in protecting germ cells from the damaging effects of irradiation-induced cell death, in vivo. C57BL/6J male mice were used as a model and irradiation was localized to the scrotal region at 2.5, 5, and/or 10 Gy intensities. Ceria nanoparticles were introduced as 100 μL injections at 100 nM and 100 μM via tail vein injections, weekly, for one month. Following this, the animals were sacrificed and their organs (heart, brain, kidneys) were harvested. Tissues were fixed, sectioned, and stained for instances of cell death, DNA damage (TUNEL assay), and ROS (nitro-tyrosine evolution). Tissues from mice treated with ceria nanoparticles showed significantly less (∼13% decrease; *P < 0.05) tissue damage (per immunohistochemistry) over controls at up to 5 Gy radiation. DNA damage and ROS also decrease substantially with ceria treatment, confirming ceria's capacity as an injectable, radio-protectant material. The study also highlights the ability of ceria nanoparticles to protect cells/tissues from both direct and indirect effects of ionizing radiation.