Theory of ferroelectric liquid crystals as micropolar medium in bundle space

Czeslaw Rymarz

doi:10.1117/12.156939

15 October 1993 Theory of ferroelectric liquid crystals as micropolar medium in bundle space

Czeslaw Rymarz

Proceedings Volume 1845, Liquid and Solid State Crystals: Physics, Technology and Applications; (1993) https://doi.org/10.1117/12.156939
Event: Liquid and Solid State Crystals: Physics, Technology, and Applications, 1992, Zakopane, Poland

Abstract

The paper presents the formulation of the theory of ferroelectric liquid crystals (smectic C^*). In this formulation the formalism of bundle space has been applied. The used bundle space has a form of a Cartesian product of the three-dimensional Euclidean space E³ (the base space) and a differentiable manifold M_s with a conical structure. The presentation contains: the formulation of the kinematics of the continuous micropolar model, the local form of the conservation laws (the equations of the evolution of the medium), and the constitutive relations for chiral smectic C^*. The kinematic of the medium is described by two vector fields: the director, d, and the normal to the smectic layers, k. The vector d rotates around the vector k, the axis of instantaneous rotation. From the integral principle of the energy conservation law the equations of evolution of the mass, momentum and angular momentum densities are derived. The set of the constitutive arguments is established and the integrity base or the set of invariants of the group of material symmetry is obtained. The constitutive relations for stresses and internal forces are presented.

Citation Download Citation

Czeslaw Rymarz "Theory of ferroelectric liquid crystals as micropolar medium in bundle space", Proc. SPIE 1845, Liquid and Solid State Crystals: Physics, Technology and Applications, (15 October 1993); https://doi.org/10.1117/12.156939

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