Blowup Rate Estimates of a Singular Potential and Its Gradient in the Landau-de Gennes Theory

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Xin Yang Lu ◽  
Xiang Xu ◽  
Wujun Zhang
Keyword(s):  
Singular Potential ◽  
Blowup Rate ◽  
Gennes Theory

New structure induced by elastic anisotropy in cylindrical nematic liquid crystal

2017 ◽  
Vol 13 (2) ◽  
pp. 4705-4717
Author(s):  
Zhang Qian ◽  
Zhou Xuan ◽  
Zhang Zhidong
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nematic Liquid Crystal ◽  
Elastic Anisotropy ◽  
Nematic Liquid Crystals ◽  
Gennes Theory

Basing on Landau–de Gennes theory, this study investigated the chiral configurations of nematic liquid crystals confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls. When the elastic anisotropy (L2/L1) is large enough, a new structure results from the convergence of two opposite escape directions of the heterochiral twist and escape radial (TER) configurations. The new defect presents when L2/L1≥7 and disappears when L2/L1<7. The new structure possesses a heterochiral hyperbolic defect at the center and two homochiral radial defects on both sides. The two radial defects show different chiralities.

scholarly journals On Scattering and Bound States for a Singular Potential

1970 ◽  
Vol 43 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Erasmo Ferreira ◽  
Javier Sesma ◽  
Pedro L. Torres
Keyword(s):  
Bound States ◽  
Singular Potential

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

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