关键词: liquid-vapor interfacial tension, modal truncation method, eigenvector derivative, asymmetric matrix, repeated eigenvalue, soft substrate, wetting, surface deformation, vertical component, contact angle (CA)

Abstract: An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ₁, λ₂, · · · , λ_r of the matrix satisfy |λ₁| <= · · ·<= |λ_r| and |λ_s| < |λ_s+1| (s <= r−1), then associated with any eigenvalue λ_i (i <=s), the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to |λ_i/λ_s+1|^q+1, where the approximate method only uses the eigenpairs corresponding to λ₁, λ₂, · · · , λ_s. A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.

Key words: vertical component, modal truncation method, eigenvector derivative, asymmetric matrix, repeated eigenvalue, contact angle (CA), surface deformation, liquid-vapor interfacial tension, soft substrate, wetting