101,918 research outputs found
Swelling and tilting in smectic layers
No full textAbstractSmectic liquid crystals are quasi-solid materials, in that they possess microstructure both of the material and the local type (the nematic microstructure and the lamellae). In the standard approach, the rod-like molecules are supposed to be strictly normal to the layers; here we abandon this constraint and admit the possibility for the molecules to change orientation with respect to the layers, paying in energy. As a consequence, we obtain two equations: one expresses the balance of micromomentum, the other is Cauchy's equation. We derive also their form in the linear approximation and solve two typical problems
Manifolds in a theory of microstructures
No full textA synopsis, broadly based on contributions by Capriz and co-workers, is presented of a model for a body with microstructure that employs the Cartesian product of a Euclidean space (a fit set part of which is instantaneously occupied by the gross image of the body) and a Riemannian manifold each of whose members specifies a microstructure. Motivation is provided by known special theories. Macro and micro kinetic energy, kinetic coenergy, and inertia are discussed preparatory to the derivation of the governing nonlinear partial differential equations from the Lagrangian action principle, Noether’a theorem, and a Hamiltonian formulation. Precise mathematical specification of initial and boundary conditions remains fragmentary.</p
On Surface Biaxiality
No full textWe propose the following: on the boundary of a nematic liquid crystal, the function which describes the molecular orientation is subject to a further symmetry condition, besides that reflecting apolarity. This additional symmetry delimits a class of biaxial states; within that class we study a model problem for a thin layer in which the anchoring energy prevails over the elastic energy in the presence of an electric field. We show that, when the anchoring and electric energies favour uniaxial states with optic axes at right angles, the equilibrium configuration migrates from one state to the other, traversing a whole family of biaxial states as the strength of the electric field increases
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