A New Method for Q Estimation Based on the Logarithmic Spectral Area-difference

Near equilibrium dynamics and one-dimensional spatial—temporal structures of polar active liquid crystals

“…This is consistent with the linear stability analysis for an inertialess limit. [56] But if we retain the inertia term ∂ 𝑣/∂t in our numerical simulations, the results are different (see Figs. 13(i)-13(l)).…”

“…When the Neumann BC is used, there could exist more bending structures of a 180 • rotation in the polarity vector determined by the wave integer in the initial state at any given, large, activity parameter |ζ |. [56] Figures 13(a)-13(d) depict a simulation with a large |ζ | that can accommodate more such bending structures. Essentially, the initially given wave integer determines the final bending structures in the steady states in long-time simulations.…”

“…This is consistent with the result of a linear stability analysis for an inertialess limit. [56] Secondly, for the initial state 𝑝 = (δ p 1 , 1, δ p 3 ) with the Dirichlet BC 𝑝| y=0,1 = (0, 1, 0) or the Neumann BC ∂ 𝑝/∂ y| y=0,1 = (0, 0, 0); however, the component p 3 may be unstable to perturbations depending on the value of ζ (ν + 1), leading to true 3D spontaneous flows. We use two initial perturbations given by the following: δ p 1 = δ sin(kπy), δ p 3 = δ sin(kπy) for the Dirichlet BC and δ p 1 = δ cos(kπy), δ p 3 = δ cos(kπy) for the Neumann BC, respectively, in our computations.…”

“…In fact, we notice that (β (ν + 1)/2η + ω) 2 controls the p 3 instability in a linear stability analysis of the 1D channel flow in an inertialess model. [56] We will pursue a comprehensive stability analysis on the full model in a sequel.…”