Vector Nematodynamics with Symmetry-driven Energy Exchange

TL;DR

The paper addresses shortcomings of conventional nematodynamic theories that rely on near-equilibrium reciprocity. It develops a symmetry-driven, energy-exchange framework using a vector order parameter with variable modulus, yielding antisymmetric flow–orientation coupling and an elasto-hydrodynamic energy balance. Key contributions include a dynamic equation combining molecular-field drive with rotation by local vorticity, an antisymmetric stress formulation, and a stability analysis for a quiescent ordered state. The work provides a robust, energy-based basis for describing flow-nematic interactions in both passive and active nematic systems, with implications for 2D and 3D applications in active matter.

Abstract

We review inadequacy of existing nematodynamic theories and suggest a novel way of establishing relations between nematic orientation and flow based on the \emph{local} symmetry between simultaneous rotation of nematic alignment and flow, which establishes energy exchange between the the two without reducing the problem to near-equilibrium conditions and invoking Onsager's relations. This approach, applied in the framework of the vector-based theory with a variable modulus, involves antisymmetric interactions between nematic alignment and flow and avoids spurious instabilities in the absence of an active inputs.