کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
839621 | 1470481 | 2015 | 24 صفحه PDF | دانلود رایگان |
We study the weak anchoring condition for nematic liquid crystals in the context of the Landau–De Gennes model. We restrict our attention to two dimensional samples and to nematic director fields lying in the plane, for which the Landau–De Gennes energy reduces to the Ginzburg–Landau functional, and the weak anchoring condition is realized via a penalized boundary term in the energy. We study the singular limit as the length scale parameter ε→0ε→0, assuming the weak anchoring parameter λ=λ(ε)→∞λ=λ(ε)→∞ at a prescribed rate. We also consider a specific example of a bulk nematic liquid crystal with an included oil droplet and derive a precise description of the defect locations for this situation, for λ(ε)=Kε−αλ(ε)=Kε−α with α∈(0,1]α∈(0,1]. We show that defects lie on the weak anchoring boundary for α∈(0,12), or for α=12 and KK small, but they occur inside the bulk domain ΩΩ for α>12 or α=12 with KK large.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 119, June 2015, Pages 74–97