Nonlinear generalization of the Maslov index

1990 ◽  
pp. 71-104 ◽  
Author(s):  
A. Givental
Keyword(s):  
Maslov Index ◽  
Nonlinear Generalization

On the Isotropic Reduction Method and the Maslov Index

2008 ◽  
Vol 35 (5) ◽  
Author(s):  
Miguel Javaloyes ◽  
Paolo Piccione
Keyword(s):  
Reduction Method ◽  
Maslov Index

scholarly journals Особенности релаксации тензора напряжения в микроскопическом объеме нематической фазы под действием сильного электрического поля

2018 ◽  
Vol 60 (2) ◽  
pp. 405
Author(s):  
А.В. Захаров
Keyword(s):  
Dissipation Rate ◽  
Periodic Structures ◽  
Numerical Study ◽  
Strong Electric Field ◽  
Rectangular Channel ◽  
Energy Dissipation Rate ◽  
Director Field ◽  
Rotational Displacement ◽  
Nonlinear Generalization ◽  
Angle Alpha

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.

scholarly journals Computation of the Maslov index and the spectral flow via partial signatures

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

scholarly journals Monotone Lagrangians in Flag Varieties

2019 ◽  
Author(s):  
Yunhyung Cho ◽  
Yoosik Kim
Keyword(s):  
Maslov Index ◽  
Chern Number ◽  
Flag Manifolds ◽  
Flag Varieties ◽  
Holomorphic Disk ◽  
Relative Version ◽  
Number Formula

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.

scholarly journals The Maslov Index: a Functional Analytical Definition and the Spectral Flow Formula

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

Coloured tangles and signatures

2017 ◽  
Vol 164 (3) ◽  
pp. 493-530 ◽  
Author(s):  
DAVID CIMASONI ◽  
ANTHONY CONWAY
Keyword(s):  
Braid Group ◽  
Maslov Index ◽  
Burau Representation

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.

Maslov index in Chern-Simons quantum mechanics

1990 ◽  
Vol 42 (8) ◽  
pp. 2763-2778 ◽  
Author(s):  
M. Reuter
Keyword(s):  
Quantum Mechanics ◽  
Maslov Index ◽  
Chern Simons
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