Vector Nematodynamics with Symmetry-driven Energy Exchange

TL;DR

This paper introduces a novel vector-based nematodynamic theory emphasizing local symmetry between nematic orientation and flow, enabling energy exchange without near-equilibrium assumptions or Onsager's relations, and avoiding spurious instabilities.

Contribution

It proposes a new symmetry-driven approach to nematodynamics that incorporates antisymmetric interactions and variable modulus, improving upon existing theories.

Findings

Establishes energy exchange based on local symmetry.

Avoids spurious instabilities without active inputs.

Provides a framework for nematodynamics beyond near-equilibrium.

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.