Statistical properties for directional alignment and chasing of players in football games

Focusing on motion of two interacting players in football games, two velocity vectors for the pair of one player and the nearest opponent player exhibit strong alignment. Especially, we find that there exists a characteristic interpersonal distance $r\simeq 500$ cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter $\phi(t)$ in order to measure degree of alignment of players' velocity vectors, we also find that the angle distribution between the nearest players' velocity vectors becomes wrapped Cauchy ($\phi \lesssim 0.7$) and the mixture of von Mises and wrapped Cauchy distributions ($\phi \gtrsim 0.7$), respectively. To understand these findings, we construct a simple model for the motion of the two interacting players with the following rules: chasing between the players and the reset of the chasing. We numerically show that our model successfully reproduce the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance $r\simeq 1000$ cm below which player's chasing starts.Comment: 16pages, 12 figures, 3 table

Bouncing gel balls: impact of soft gels onto rigid surface

After thrown onto a solid substrate, very soft spherical gels bounce repeatedly. Separate rheological measurements suggest that these balls can be treated as nearly elastic. The Hertz contact deformation expected in the static (elastic) limit was observed only at very small impact velocities. For larger velocities, the gel ball deformed into flattened forms like a pancake. We measured the size of the gel balls at the maximal deformation and the contact time as a function of velocities for the samples different in the original spherical radius and the Young modulus. The experimental results revealed a number of scaling relations. To interpret these relations, we developed scaling arguments to propose a physical picture.Comment: 7 pages, 4 figures (minor revisions, To appear in Europhys. Lett.

Solar-driven thermochemical CO2 reduction using nonstoichiometric perovskite

The solar energy is, by far, the most abundant renewable energy source. Thus, our challenge is to capture the vast, yet intermittent solar energy for on-demand usage. To address this issue, we pursue solar thermochemical fuel production using nonstoichiometric perovskite oxides. It relies on the redox reaction in which the nonstoichiometric perovskite strips oxygen atoms from carbon dioxides and water vapors. As a result, syngas, carbon monoxide and hydrogen fuels can be produced, reaching to the thermodynamic efficiency of 13~75% depending on materials and operation condition. Ceria has produced large amount of carbon monoxide and hydrogen in a solar-thermochemical cycle, showing the record solar-fuel conversion efficiency of ~1%. However, the operation temperature is extremely high, over 1500 °C, challenging reactor design. To moderate reaction condition with enhanced fuel productivity, we focus on the structure-thermochemistry relation in the Mn-based perovskite oxides, specifically Sr-doped LaMnO3-δ. Lower thermochemical temperature cycle, 1400-800 °C, was chosen. The hydrogen yield from water vapor increases with increasing the Sr content. It is mainly due to lower redox enthalpy rather than the entropy contribution. Carbon monoxide was also produced from CO2, with the amount exceeding 5 ml/g. In situ X-ray absorption spectroscopy shows that the mean Mn valence increases from 3.12 to 3.41 while the Mn-O length decreases during CO2 reduction. These results suggest that Mn redox in the MnO6 octahedron is a key to improve thermochemical fuel productivity using the nonstoichiometric perovskite compound