Strong spectral lines in the visible range are obtained from luminescence generated by low-pressure gas discharge tubes of hydrogen, neon, helium, and mercury. Although the spectrum of neon is complicated at first glance, the energy levels are degenerate and clustered; this means that the level statistics differ from the Wigner surmise, which is closely related to level repulsion and quantum chaos. We present a visualization of the lower 99 energy levels of each atom in a barcode-like periodic table.

We derived the Stokes equations and velocity potential around a hyperspherical obstacle in n-dimensional space. The objectives of this study were to understand the hyperspace through the physics in the space and to bring the analytical solution of fluid flow in hyperspace for numerical simulation. The equations were obtained from the n-dimensional Navier-Stokes equation assuming the low Reynolds number flow. These were generalized formulae from a 3-dimensional system to an n-dimensional one. Our results show that the effect of the hyperspherical obstacle on the uniform flow is localized in higher dimensional spaces. We visualized the flow using the collections of hypersections.

The nonlinearity of the mathematical model describing the cerebral blood flow dynamics and the body sway in the prefrontal cortex was investigated experimentally. The measured bio-signal data were smoothed with each low-pass filter. The signal was set to 0.1-2 Hz for the cerebral blood flow dynamics and to 0.1-20 Hz for the body sway. Nonlinearity was observed in the biological signal when the cut-off frequency of the low-pass filtering was 0.2 Hz or less, and while the body sway was 0.5 Hz or less, and was considered as a stochastic differential equations.