Stability of twisted states in power-law-coupled Kuramoto oscillators on a circle with and without time delay.

Other than the fully synchronized state, a twisted state can also be an equilibrium solution in the Kuramoto model and its variations. In the present work, we explore the stability of the twisted state in Kuramoto oscillators put on a rim of a planar circle in the two-dimensional space in the presence of power-law decaying interaction strength (∼r^{-α} with the distance r) and time delays due to a finite speed of information transfer. For example, our model can phenomenologically mimic a large sports stadium where many people try to sing or clap their hands in unison; the sound intensity decays with the distance and there can exist a time delay proportional to the distance due to the finiteness of sound speed. We first consider the case without the time delay effect and numerically find that stable twisted states emerge when the exponent α exceeds a critical value of α_{c}≈2. In other words, for α<α_{c}, the fully synchronized state, not the twisted state, is the only stable fixed point of the dynamics. In our analytic approach, we also derive an equation for α_{c} and discuss its solutions. In the presence of time delay, we find that it is possible that the synchronized state becomes unstable while twisted states are stable.

Enhancement of the protein loading density by a pre-cleaning process of a gold substrate: confocal laser scanning microscopic study.

The immobilization of glucose oxidase (GOx), using self assembled monolayers (SAMs) on gold surfaces, was investigated by grazing angle FT-IR spectroscopy, surface plasmon resonance (SPR) spectroscopy, and atomic force microscopy (AFM) in conjunction with confocal laser scanning microscopy (CLSM). To find an optimum condition for the maximum GOx loading density on gold surfaces, different cleaning protocols were examined. The loading density of GOx on surfaces was investigated by AFM and CLSM. In particular, CLSM was more effective for identifying the GOx density than AFM, since its scanning speed is much faster and it covers a larger area. Based on CLSM images of the GOx immobilized on the surfaces, it was concluded that the pre-cleaning process of gold substrates using different solvents, such as acetone, ethanol and 2-propanol, is very important for enhancing the GOx loading density. This result enables us to investigate an effective fabrication process in fabricating biosensors.