Parameter Correlation Analysis Between the Equal Expansion Rate Evolving Envelope Surface and Its Sub-Envelope Surfaces

Based on the Equal Expansion Rate Evolving Envelope Surface, this paper discusses the parameter correlations between the parent envelope surface and its nested sub-envelope surfaces. The minimum length unit of the parent layer is taken as the parent initial radius r0; the minimum length unit of the child layer is taken as the child minimum length l_min. The two layers share the same maximum frequency f_max, and the frequency does not change across layers. After normalizing both minimum units to 1, the parent layer and the child layer are connected by a bridge variable Lambda(t): Lambda(t) = exp( b * integral(omega(tau) dtau, 0, t) ) where b is the growth rate and omega(t) is the phase advance angular speed. This variable explicitly contains b and omega(t), and is therefore a time-varying correlation factor, not a constant. Within the child layer, because the ruler and space scale synchronously by the same proportion, Lambda(t) is absorbed and thus b and omega(t) are not readable; the child layer retains only its own constant reading c = f_max * l_min. Keywords: Equal Expansion Rate Evolving Envelope Surface; sub-envelope surface; minimum length unit; parameter correlation; bridge variable