Critical exponents for Fréedericskz transition in nematics between concentric cylinders

Souza, R. Teixeira de; Dias, João-Paulo; Mendes, R. S.; Evangelista, L. R.

doi:10.1016/j.physa.2009.11.006

Cited by 11 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…No generality is lost by assuming that

U > 0

for

t \in (0, - log ρ)

and thus that U achieves its maximum value, A say, at

t = (- log ρ) / 2

. Then may be integrated twice to yield the implicit solution

\int_{0}^{U (t; δ)} \sqrt{\frac{1 - δ {cos}^{2} u}{δ {cos}^{2} u - δ {cos}^{2} A}} d u = t

for

0 < t < (- log ρ) / 2

, where the amplitude A is related to ρ and δ by

\int_{0}^{A} \sqrt{\frac{1 - δ {cos}^{2} u}{δ {cos}^{2} u - δ {cos}^{2} A}} d u = \frac{- log ρ}{2} .

An analogous solution was obtained in to describe the Fréedricksz transition in an annulus with strong perpendicular anchoring. For the special limiting case

δ = 1

, we can solve exactly to find

U false(1; t false) = {prefixcos}^{- 1} (\frac{ρ e^{t}}{ρ + 1} + \frac{{normale}^{- t}}{ρ + 1}),

with associated amplitude

A = {prefixcos}^{- 1} (\frac{2 \sqrt{ρ}}{1 + ρ}) .

…”

Section: The Defect‐free State In Of Theorymentioning

confidence: 99%

Nematic Equilibria on a Two‐Dimensional Annulus

et al. 2017

View full text Add to dashboard Cite

We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen-Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defectfree state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.

show abstract

“…No generality is lost by assuming that

U > 0

for

t \in (0, - log ρ)

and thus that U achieves its maximum value, A say, at

t = (- log ρ) / 2

. Then may be integrated twice to yield the implicit solution

\int_{0}^{U (t; δ)} \sqrt{\frac{1 - δ {cos}^{2} u}{δ {cos}^{2} u - δ {cos}^{2} A}} d u = t

for

0 < t < (- log ρ) / 2

, where the amplitude A is related to ρ and δ by

\int_{0}^{A} \sqrt{\frac{1 - δ {cos}^{2} u}{δ {cos}^{2} u - δ {cos}^{2} A}} d u = \frac{- log ρ}{2} .

An analogous solution was obtained in to describe the Fréedricksz transition in an annulus with strong perpendicular anchoring. For the special limiting case