Figure 5
Generation of random distributions of modiolus porosity using regionally kinetic porosity equations and their associated electrical conditions. (a) Random pattern distribution of the state variable u defined by two coupled reaction–diffusion equations (“Methods”, Eq. (5)) for six time steps, generating six modiolus samples labelled M1–M6. For a given modiolus sample, the set of u values simulate the pixels of a colour image of the modiolus during the time stepping whilst solving the reaction–diffusion Eq. (5) (“Methods”). (b) Random distributions of electrically conducting pores (black regions) for M1–M6 based on the binary conditional Eq. (7) (“Methods”), with control parameter \(\upgamma = 0.6\). Values in brackets are the effective conductivities (S m−1) calculated with Eq. (4) using the Wiener upper bound. Notice that the five samples M2–M6 present different pore patterns (black regions) but all have approximately the same overall porosity (25%) and effective conductivity (0.32 S m−1). (c) Electric field distributions for M1–M6 expressed in natural logarithms relative to 1 V m−1. All subdomains except Rosenthal’s canal (RC) are kept hidden for better visualization. (d) Electric potential distributions in RC for M1–M6. The matrix of SGNs is indicated in each RC. Random distributions of electrical conductivity for M1–M6 having porosity (for M2–M6) of approximately (e) 45%, (f) 64%, and (g) 12%, generated using the control parameter \(\upgamma =0.4\), 0.2, and 0.8 respectively.
