Narrow Results

The drift of rigidly rotating spiral waves in an excitable medium induced by synchronous and asynchronous mechanical deformation is investigated numerically and analytically. The resonant drift of spiral waves induced by a mechanical deformation with ω = ω₀ and ω = 3ω₀ is observed. At ω = ω₀, synchronous and greatest degree of asynchronous mechanical deformations are specially investigated. For the case ω = 3ω₀, synchronous mechanism deformation locks the spiral while decreasing of degree of synchronization increases the drift velocity. We derive an approximate but explicit formula of the spiral drift velocity and direction which is consistent with the numerical results.

In this paper, the stress intensity factor (SIF) formula $F_{\mathrm{\text{ISE}}}$ along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution $F_{\mathrm{\text{ISE}}}$ is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio $F_{\mathrm{\text{ISE}}}$/$F_{\mathrm{\text{IE}}}$ is focused considering the exact solution $F_{\mathrm{\text{IE}}}$ of an elliptical crack. By applying the least squares method to the ratio $F_{\mathrm{\text{ISE}}}$/$F_{\mathrm{\text{IE}}}$, accurate and convenient formula is proposed. The proposed formulas may provide the accurate SIF distributions for the aspect ratio $a/b=1$–4 better than 0.2% accuracy.