In this work we recover the Oseen-Frank theory of nematic liquid crystals as\na $\\Gamma$-limit of a particular mean-field free energy as the sample size\nbecomes infinitely large. The Frank constants are not necessarily all equal.\nOur analysis takes place in a broader framework however, ...
We investigate the Ericksen–Leslie system with the Oseen–Frank energy for unequal Frank elastic constants in \({\mathbb R}^3\). Motivated by the results of Kato (Math Z 187:471–480, 1984) and Hineman–Wang (Arch Ration Mech Anal 210:177–218, 2013), we prove existence of solutions...
These 12 arguments are independent variables in the Frank-Oseen energy density FF. The independence of n⃗ n→ and TT in F(n⃗ ,T)F(n→,T) is similar to the independence of qq and vv in the Lagrangian L(q,v,t)L(q,v,t) for point mechanics. It may seem a bit pedantic to...
在这篇文章中,我们研究的是来自于相变理论中的二阶能量模型.在薄膜外壳和近晶型液晶的研究中,它被称为简化的Oseen-Frank能量:其中G是欧式空间中有界光滑单连通区域,ε... 夏玲茹 - 南京师范大学 被引量: 0发表: 2015年 瞬态Oseen方程的全离散局部投影稳定化方法 研究了非定常的Oseen方程的局部投影全离散有限元...
arXiv:1703.02214v1 [math.AP] 7 Mar 2017WELL-POSEDNESS OF THE ERICKSEN-LESLIE SYSTEM FORTHE OSEEN-FRANK MODEL IN L 3uloc (R3 )MIN-CHUN HONG AND YU MEIAbstract. We investigate the Ericksen-Leslie system for the Oseen-Frankmodel with unequal Frank elastic constants in R 3 . To generalize ...
Frank M. Neubrander (4) Serge Nicaise (5) Joachim von Below (6) Editor Affiliations 1. Institut für Mathematik, Universität Zürich 2. Abteilung Angewandte Analysis, Universität Ulm 3. Fachbereich Mathematik, Technische Universität Darmstadt 4. Department of Mathematics, Louisiana ...
Dimensional reduction and emergence of defects in the Oseen-Frank model for nematic liquid crystals In this paper we discuss the behavior of the Oseen-Frank model for nematic liquid crystals in the limit of vanishing thickness. More precisely, in a thin s... G Canevari,A Segatti - Discrete...
网络形变理论是由欧森;奥森 网络释义
The Oseen–Frank energyPartial regularityWe observe that for a unit tangent vector field u ∈ TM on a 3-dimensional Riemannian manifold M, there is a unique unit cotangent vector field A ∈ TM associated to u such that we can define the curl of u by dA. Through a unit cotangent vector...
Moreover, the convergence is\nuniform in the interior of the domain, away from the singularities of the\nlimiting Oseen-Frank global minimizer. We obtain results on the rate of\nconvergence of the eigenvalues and the regularity of the eigenvectors of the\nLandau-De Gennes global minimizer.\nW...