Nonvariational mechanism of front propagation: Theory and experiments

Abstract

Multistable systems exhibit a rich front dynamics between equilibria. In one-dimensional scalar gradient systems, the spread of the fronts is proportional to the energy difference between equilibria. Fronts spreading proportionally to the energetic difference between equilibria is a characteristic of one-dimensional scalar gradient systems. Based on a simple nonvariational bistable model, we show analytically and numerically that the direction and speed of front propagation is led by nonvariational dynamics. We provide experimental evidence of nonvariational front propagation between different molecular orientations in a quasi-one-dimensional liquid-crystal light valve subjected to optical feedback. Free diffraction length allows us to control the variational or nonvariational nature of this system. Numerical simulations of the phenomenological model have quite good agreement with experimental observations.

Continuation for Thin Film Hydrodynamics and Related Scalar Problems

“…Such a term also appears in the Kardar-Parisi-Zhang (KPZ) equation [64] and is also used in a nonvariational version of the SH equation [61]. One also finds µ [5] and SH [72,17] equations. Similar and higher order terms are used in Ref.…”

“…Employing the energy functional (5) in a conserved gradient dynamics [Eq. ( 4) with Q nc = 0] with f being a quartic polynomial gives the Cahn-Hilliard (CH) equation that describes e.g.…”

Bifurcations of front motion in passive and active Allen-Cahn-type equations

“…18, i.e., we incorporate a nonequilibrium chemical potential 15 as also frequently done for massconserving Cahn-Hilliard-type dynamics [19][20][21][22] . Such an amended AC equation may be employed to model, e.g., front propagation in a liquid crystal light valve 18 . Second, we couple the AC equation for the order parameter to an evolution equation of a polarisation field P in a similar spirit as in an active phase-field-crystal (PFC) model [23][24][25] .…”

“…Appendix A: Nonvariational cubic Allen-Cahn equation As in the literature 18 the derivation of Eq. 18 is only sketched, and we find it instructive, here we reproduce it in greater detail.…”

Spontaneous motion of localized structures induced by parity symmetry breaking transition

“…Soon after, it has been considered in a various out of equilibrium systems such as driven liquid crystal [29], coupled oscillators [30], and nonlinear optic cavity [31]. More recently, it has been shown that non-variational terms can induce propagation of fronts in quasi-one-dimensional liquid crystals based devices [32]. Experimental observation of a supercritical transition from stationary to moving localized structures has been realized in two-dimensional planar gas-discharge systems [33].…”