Eigenfunctions and eigenvalues for elastica in a shear flow

The data available here are the eigenfunctions Φu(s) and eigenvalues σ for the elastica spectral problem in the simple shear flow, determined and analyzed in Ref. [1]. The parameter −0.5 ≤ s ≤ 0.5 is the arclength coordinate. Φu(s) and σ are solutions of the set of Eqs. (20) and (22) in Ref. [1], dependent on the elastoviscous number η, defined in Eq. (2). The unperturbed fiber is in the plane of the shear flow and the flow gradient. Its shape is straight at an arbitrary inclination angle ϕ with respect to the shear flow direction. The spectral analysis determines the growth (or decay) of a small perturbation as Φu(s) exp(σt).[1] Lujia Liu, Pawel Sznajder, and Maria L. Ekiel-Jezewska, ”Spectral analysis for elastica dynamics in a shear flow”, Phys. Rev. Fluids, 9, 014101, 2024.