Fig. 6: Scaling between characteristic size and propagating wave speed obtained by response function method.

The characteristic size l = 2R is quantified by the radius R of the circle on which inputs are located (see Fig. 2-(3)). a, c MC and b, d IPC as a function of the characteristic length scale between physical nodes R and the speed of wave propagation v with θ = 0.04 ns and α = 5.0 × 10⁻⁴. The results with the response function for the dipole interactions Eqs. (16) and (17) a, b and for the Gaussian function Eq. (19) c, d are shown. Open circle symbols in a–d corresponds to wave speed (v = 200 m⋅s⁻¹) and length (l = 2R = 500 nm) used in micromagnetic simulation. The damping time shown in a, b expresses the length scale obtained from the wave speed multiplied by the time scale of damping associated with α. e Schematic illustration of the response function and its relation to wave propagation between physical nodes. When the speed of the wave is too fast, all the response functions are overlapped (dense regime), while the response functions cannot cover the time windows when the speed of the wave is too slow (sparse regime).