Appendix A xA The general

Appendix A. The general solution of the transformed governing Eq. (15) in the coating, substrate and subsystem may be applied to the boundary conditions (16) through (18) to solve for the unknown coefficients. The solution for h˜coatz may be put into the 'GM6001' form ofh˜coatz=exp−ν2/42ν˜coat2−1/Λ2s˜z−1−ℜ1exp−2/Λacoatγcoatv˜coatΛ2exp−v˜coatz+2C1coshv˜coatzThe remaining GM6001 constant can be evaluated fromC1=detd1b12b130d2b22b2300b32b33b340b42b43b44/detb11b12b130b21b22b2300b32b33b340b42b43b44with b11 = 2 cosh(?coat), b21 = − 2acoatγcoat?coat sinh(?coat),b12=−expν˜sub,b22=ν˜subexpν˜sub,b13=−exp−ν˜sub,b23=−ν˜subexp−ν˜sub,b32=1+Rss*ν˜sub/acoatγcoatexpν˜sub1+Zsub,b42=expν˜sub1+Zsub,b33=1−Rss*ν˜sub/acoatγcoatexp−ν˜sub1+Zsub,b43=−exp−ν˜sub1+Zsub,b34=−exp−ν˜ss1+Zsub,b44=assγssν˜ss/ν˜subexp−ν˜ss1+Zsub,and,d1=exp−ν2/42acoatγcoatΛν˜coat2−1/Λ2×exp−v˜coatΛv˜coat1−ℜ1exp−2/Λ−1+ℜ1exp−1/Λ,d2=−exp−ν2/42exp−1/Λ×1−ℜ1+Λ21−ℜ1+ℜ1exp−1/Λ−exp1/Λexp−v˜coatν˜coat2−1/Λ2. PGA (phosphoglycerate)