Erratum to: Water sorption hysteresis in wood: II mathematical modeling – functions beyond data fitting

Pattern (d)

Pattern (d) reveals that any point within the major hysteresis loop can be reached more than one way. The same MC means that the integration from the support 𝑆⁺ in the RH_u − RH_l diagram is the same, and different hygroscopic histories indicate different interface lines L. Therefore, the proof of this patterns demands the existence of two different interface lines with appropriate supports 𝑆⁺ that lead to the same integration. As different supports correspond to different weighting functions μ(RH_u, RH_l), the support areas can be different. Figure 5Aa gives such an example where L₁ and L₂ are two interfaces formed from two different RH histories. The differences of the interfaces are indicated by red color for L₁, and blue color, L₂. The differences of the supports are indicated by the shaded rectangular areas ΔR₁ and ΔR₂. As the areas of ΔR₁ can be finely tuned by the final movement of RH_u = RH_f, the equality of integration based on ΔR₁ and ΔR₂ can be satisfied.