Yu Kurokawa

Multi-dimensional pyramidal travelling fronts in the Allen-Cahn equations

We study travelling-front solutions of pyramidal shapes in the Allen–Cahn equation in RN with N 3. It is well known that two-dimensional V-form travelling fronts and three-dimensional pyramidal travelling fronts exist and are stable. The aim of this paper is to show that for N 4 there exist N -dimensional pyramidal travelling fronts. We construct a supersolution and a subsolution, and find a pyramidal travelling-front solution between them. For the construction of a supersolution we use a multi-scale method.

Wavelet Analysis of Flexural Wave Fronts in Water/Slurry Hammer

The present study experimentally analyzes flexural wave fronts in water hammer and slurry hammer with polycarbonate tubes by wavelet analysis. The water/slurry hammer was initiated by the impact between the free-falling projectile and the water/slurry in the vertical mounting tube. We measured hoop strain histories of flexural wave fronts at several locations by strain gages and analyzed the histories, using the wavelet transform method. The wavelet power spectrum near the flexural wave fronts and dispersion behaviors in water/slurry hammer were examined. In the water hammer experiments, by tracing the dispersion curve from the time-frequency signal, it is revealed that the water hammer front have a dispersion tendency. Moreover, the measured frequencies indicate a reasonable agreement with the Skalak’s theory [1, 2]. As for slurry, we mixed water and alumina balls or polystyrene (PS) balls. Wave speeds with Alumina or PS balls were compared with theoretical estimations by Han et al. [3, 4]. It is confirmed that the particles enhance slurry hammer’s dispersion and the oscillation frequency of the slurry hammer becomes lower than that of the water hammer. Additionally, the oscillation frequency corresponds to the theoretical value estimated from wave speed assuming particles as rigid-body particles.Copyright