Vector order parameter for an unpolarized laser and its vectorial topological defects

1993 ◽  
Vol 70 (2) ◽  
pp. 162-165 ◽  
Author(s):  
L. Gil
Keyword(s):  
Order Parameter ◽  
Topological Defects

scholarly journals VORTEX NUCLEATION IN ROTATING BOSE–EINSTEIN CONDENSATE: THE ROLE OF THE BOUNDARY CONDITION FOR THE ORDER PARAMETER

2006 ◽  
Vol 20 (15) ◽  
pp. 2147-2158
Author(s):  
W. V. POGOSOV ◽  
K. MACHIDA
Keyword(s):  
Boundary Condition ◽  
Order Parameter ◽  
Topological Defects ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Surface Modes ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Vortex Nucleation

We study the problem of vortex nucleation in rotating two-dimensional Bose–Einstein condensate confined in a harmonic trap. We show that, within the Gross–Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then vortices move toward the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes.

scholarly journals Nematic topological defects positionally controlled by geometry and external fields

2018 ◽  
Vol 9 ◽  
pp. 109-118 ◽  
Author(s):  
Pavlo Kurioz ◽  
Marko Kralj ◽  
Bryce S Murray ◽  
Charles Rosenblatt ◽  
Samo Kralj
Keyword(s):  
Electric Field ◽  
Topological Charge ◽  
Order Parameter ◽  
Topological Defects ◽  
Two Dimensional ◽  
External Fields ◽  
Nematic Ordering ◽  
Spatial Positioning ◽  
A Charge ◽  
The Impact

Using a Landau–de Gennes approach, we study the impact of confinement topology, geometry and external fields on the spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that a confinement-enforced total topological charge of m > 1/2 decays into elementary TDs bearing a charge of m = 1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. We observe that in certain confinement geometries, varying the correlation length size of the order parameter could trigger a global rotation of an assembly of TDs. Finally, we show that an external electric field could be used to drag the boojum fingertip towards the interior of the confinement cell. Assemblies of TDs could be exploited as traps for appropriate nanoparticles, opening several opportunities for the development of functional nanodevices.

scholarly journals A Bidimensional Gay-Berne Calamitic Fluid: Structure and Phase Behavior in Bulk and Strongly Confined Systems

2021 ◽  
Vol 8 ◽  
Author(s):  
A. Calderón-Alcaraz ◽  
J. Munguía-Valadez ◽  
S. I. Hernández ◽  
A. Ramírez-Hernández ◽  
E. J. Sambriski ◽  
...  
Keyword(s):  
Order Parameter ◽  
Nematic Phase ◽  
Orientational Order ◽  
Topological Defects ◽  
Md Simulations ◽  
Structural Behavior ◽  
Nematic Order ◽  
Lower Temperature ◽  
Geometry Characteristic ◽  
Strong Confinement

A bidimensional (2D) thermotropic liquid crystal (LC) is investigated with Molecular Dynamics (MD) simulations. The Gay-Berne mesogen with parameterization GB(3, 5, 2, 1) is used to model a calamitic system. Spatial orientation of the LC samples is probed with the nematic order parameter: a sharp isotropic-smectic (I-Sm) transition is observed at lower pressures. At higher pressures, the I-Sm transition involves an intermediate nematic phase. Topology of the orthobaric phase diagram for the 2D case differs from the 3D case in two important respects: 1) the nematic region appears at lower temperatures and slightly lower densities, and 2) the critical point occurs at lower temperature and slightly higher density. The 2D calamitic model is used to probe the structural behavior of LC samples under strong confinement when either planar or homeotropic anchoring prevails. Samples subjected to circular, square, and triangular boundaries are gradually cooled to study how orientational order emerges. Depending on anchoring mode and confining geometry, characteristic topological defects emerge. Textures in these systems are similar to those observed in experiments and simulations of lyotropic LCs.

scholarly journals Inference of molecular orientation/ordering change nearby topological defects by the neural network function from the microscopic color information

2021 ◽  
Author(s):  
Haruka Sakanoue ◽  
Yuki Hayashi ◽  
Kenji Katayama
Keyword(s):  
Neural Network ◽  
Order Parameter ◽  
Orientation Angle ◽  
Topological Defects ◽  
Molecular Alignment ◽  
Polarization Microscopy ◽  
Color Information ◽  
Time Resolved ◽  
Network Function ◽  
The Neural Network

Abstract Topological defects in liquid crystals (LCs) dominate molecular alignment/motion in many cases. Here, the neural network (NN) function has been introduced to predict the LC orientation condition (orientation angle and order parameter) at local positions around topological defects from the phase/polarization microscopic color images. The NN function was trained in advance by using the color information of an LC in a planar alignment cell for different orientation angles and temperatures. The photo-induced changes of LC molecules around topological defects observed by the time-resolved measurement was converted into the image sequences of the orientation angle and the order parameter change. We found that each pair of brushes with different colors around topological defects showed different orientation angle and ordering changes. The photo-induced change was triggered by the photoisomerization reaction of molecules, and one pair of brushes increased in its order parameter just after light irradiation, causing gradual rotation in the brush. The molecules in the other pair of brushes were disordered and rotated by the effect of the initially affected region. This combination approach of the time-resolved phase/polarization microscopy and the NN function can provide detailed information on the molecular alignment dynamics around the topological defects.

Liquid Crystals

2015 ◽  
Author(s):  
Oleg D. Lavrentovich
Keyword(s):  
Molecular Weight ◽  
Thermal Expansion ◽  
Liquid Crystals ◽  
Order Parameter ◽  
Soft Matter ◽  
Topological Defects ◽  
Low Molecular Weight ◽  
Surface Anchoring ◽  
Director Dynamics ◽  
Anisotropic Viscosity

This article discusses modern directions of research in liquid crystals (LCs). LCs represent one of the best studied classes of soft matter, along with colloids, polymer solutions and melts, gels, and foams. Phenomena observed in LCs and approaches developed for their description become of heuristic value in other branches of science. This article considers the basic properties of low-molecular weight thermotropic LCs, with an additional emphasis on the developments of the last decade, such as LC colloids. It begins with an overview of thermotropic and lyotropic systems, followed by a review of the concept of order parameter, elasticity, surface anchoring, and topological defects. It also evaluates hybrid systems combining LCs with polymers or colloids, along with new ways of creating mesomorphic systems and the dynamics of LCs, including anisotropic viscosity, director dynamics and the Frederiks transition, and flow induced by thermal expansion. Finally, it describes various applications of LCs.

A novel approach to topological defects in a vector order parameter system

2009 ◽  
Vol 18 (7) ◽  
pp. 2901-2904 ◽  
Author(s):  
Ren Ji-Rong ◽  
Rong Shu-Jun ◽  
Zhu Tao
Keyword(s):  
Order Parameter ◽  
Topological Defects ◽  
Parameter System ◽  
Novel Approach

scholarly journals Phase transition in space: how far does a symmetry bend before it breaks?

2008 ◽  
Vol 366 (1877) ◽  
pp. 2953-2972 ◽  
Author(s):  
Wojciech H Zurek ◽  
Uwe Dorner
Keyword(s):  
Phase Transitions ◽  
Symmetry Breaking ◽  
Order Parameter ◽  
Energy Gap ◽  
Quantum Phase Transitions ◽  
Topological Defects ◽  
Critical Value ◽  
Quantum Ising Model ◽  
The Right ◽  
Symmetry Breaking Dynamics

We extend the theory of symmetry-breaking dynamics in non-equilibrium second-order phase transitions known as the Kibble–Zurek mechanism (KZM) to transitions where the change of phase occurs not in time but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the ‘scar’ over which the order parameter adjusts as it ‘bends’ interpolating between the phases with different symmetries follows from a KZM-like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale—the size of the scar—is directly reflected in the energy spectrum of the system: in particular, it determines the size of the energy gap.

scholarly journals Inference of molecular orientation/ordering change nearby topological defects by the neural network function from the microscopic color information

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Haruka Sakanoue ◽  
Yuki Hayashi ◽  
Kenji Katayama
Keyword(s):  
Neural Network ◽  
Order Parameter ◽  
Orientation Angle ◽  
Topological Defects ◽  
Molecular Alignment ◽  
Polarization Microscopy ◽  
Color Information ◽  
Time Resolved ◽  
Network Function ◽  
The Neural Network

AbstractTopological defects in liquid crystals (LCs) dominate molecular alignment/motion in many cases. Here, the neural network (NN) function has been introduced to predict the LC orientation condition (orientation angle and order parameter) at local positions around topological defects from the phase/polarization microscopic color images. The NN function was trained in advance by using the color information of an LC in a planar alignment cell for different orientation angles and temperatures. The photo-induced changes of LC molecules around topological defects observed by the time-resolved measurement was converted into the image sequences of the orientation angle and the order parameter change. We found that each pair of brushes with different colors around topological defects showed different orientation angle and ordering changes. The photo-induced change was triggered by the photoisomerization reaction of molecules, and one pair of brushes increased in its order parameter just after light irradiation, causing gradual rotation in the brush. The molecules in the other pair of brushes were disordered and rotated by the effect of the initially affected region. This combination approach of the time-resolved phase/polarization microscopy and the NN function can provide detailed information on the molecular alignment dynamics around the topological defects.

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