Nonlinear generalization of the Maslov index

Author(s):  
A. Givental
2008 ◽  
Vol 35 (5) ◽  
Author(s):  
Miguel Javaloyes ◽  
Paolo Piccione

2018 ◽  
Vol 60 (2) ◽  
pp. 405
Author(s):  
А.В. Захаров

AbstractA numerical study of new regimes of reorientation of director field n̂ , velocity v , and components of stress tensor σ_ ij ( ij = x , y , z ) of nematic liquid crystal (LC) encapsulated in a rectangular channel under the action of a strong electric field E directed at angle $$\alpha \left( {\sim\frac{\pi } {2}} \right)$$ α ( ∼ π 2 ) to the horizontal surfaces bounding the LC channel is proposed. The numerical calculations performed in the framework of nonlinear generalization of the classical Eriksen-Leslie theory have shown that at certain relations between the torques and momenta affecting the unit LC volume and E ≫ E _th, transition periodic structures can emerge during reorientation of n̂ , if the corresponding distortion mode has the fastest response, and, thus, suppress all other modes. Rotating domains originating within this process decrease the energy dissipation rate and create more favorable regimes of the director field reorientation, as compared with the uniform rotational displacement.


2004 ◽  
Vol 338 (5) ◽  
pp. 397-402 ◽  
Author(s):  
Roberto Giambò ◽  
Paolo Piccione ◽  
Alessandro Portaluri
Keyword(s):  

Author(s):  
Yunhyung Cho ◽  
Yoosik Kim

Abstract In this paper, we give a formula for the Maslov index of a gradient holomorphic disk, which is a relative version of the Chern number formula of a gradient holomorphic sphere for a Hamiltonian $S^1$-action. Using the formula, we classify all monotone Lagrangian fibers of Gelfand–Cetlin systems on partial flag manifolds.


1998 ◽  
Vol 21 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Bernhelm BOOSS-BAVNBEK ◽  
Kenro FURUTANI
Keyword(s):  

2017 ◽  
Vol 164 (3) ◽  
pp. 493-530 ◽  
Author(s):  
DAVID CIMASONI ◽  
ANTHONY CONWAY

AbstractTaking the signature of the closure of a braid defines a map from the braid group to the integers. In 2005, Gambaudo and Ghys expressed the homomorphism defect of this map in terms of the Meyer cocycle and the Burau representation. In the present paper, we simultaneously extend this result in two directions, considering the multivariable signature of the closure of a coloured tangle. The corresponding defect is expressed in terms of the Maslov index and of the Lagrangian functor defined by Turaev and the first-named author.


1990 ◽  
Vol 42 (8) ◽  
pp. 2763-2778 ◽  
Author(s):  
M. Reuter

Sign in / Sign up

Export Citation Format

Share Document