scholarly journals Nematic Liquid Crystal Locking Menisci

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Milan Svetec ◽  
Mitja Slavinec
Keyword(s):  
Differential Equation ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Coordinate System ◽  
Point Defects ◽  
Cylindrical Tube ◽  
Curvilinear Coordinate System ◽  
Director Field ◽  
Nematic Director ◽  
Curvilinear Coordinate

We study meniscus driven locking of point defects of nematic liquid crystals confined within a cylindrical tube with free ends. Curvilinear coordinate system is introduced in order to focus on the phenomena of both (convex and concave) types of menisci. Frank's description in terms of the nematic director field is used. The resulting Euler-Lagrange differential equation is solved numerically. We determine conditions for the defects to be trapped by the meniscus.

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

scholarly journals The partial banana mapping: a robust linear method for impact probability estimation

2019 ◽  
Vol 492 (3) ◽  
pp. 4546-4552
Author(s):  
Dmitrii E Vavilov
Keyword(s):  
Coordinate System ◽  
Confidence Region ◽  
Linear Method ◽  
Probability Estimation ◽  
Curvilinear Coordinate System ◽  
The Earth ◽  
Curvilinear Coordinate ◽  
Near Earth Asteroids ◽  
The Impact ◽  
Confidence Ellipsoid

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

Liquid crystal/glass interface effects on the orientation of lyotropic liquid crystals in magnetic fields

1978 ◽  
Vol 56 (16) ◽  
pp. 2178-2183 ◽  
Author(s):  
Fred Y. Fujiwara ◽  
Leonard W. Reeves
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Cylindrical Tube ◽  
Lyotropic Liquid Crystals ◽  
Crystal Glass ◽  
Type I ◽  
Type Ii ◽  
Glass Interface ◽  
Interface Effects

Lyotropic mesophases of both positive (type I) and negative (type II) diamagnetic anisotropy have been prepared. The deuterium magnetic resonance signal from D2O in the sample bas been studied during the process of orientation in a magnetic field. A type II mesophase oriented by a magnetic field in a cylindrical tube perpendicular to the lines of force does not achieve a uniform distribution of directors in a plane perpendicular to the field. The re orientation of a type I mesophase after an initial displacement of the director at an angle to the field has been studied. Previous equations derived for thermotropic liquid crystals are applicable but the velocity of re-orientation was found to be an inverse function of the radius, for nmr tubes of less than 4 mm in diameter, indicating that liquid crystal/glass interface effects are important.

scholarly journals Stable and Metastable Patterns in Chromonic Nematic Liquid Crystal Droplets Forced with Static and Dynamic Magnetic Fields

Crystals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 138 ◽  
Author(s):  
Jordi Ignés-Mullol ◽  
Marc Mora ◽  
Berta Martínez-Prat ◽  
Ignasi Vélez-Cerón ◽  
R. Santiago Herrera ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Boundary Conditions ◽  
Isotropic Phase ◽  
Director Field ◽  
Line Defects ◽  
The One ◽  
Bulk Structures ◽  
Microscopy Images

Spherical confinement of nematic liquid crystals leads to the formation of equilibrium director field configurations that include point and line defects. Driving these materials with flows or dynamic fields often results in the formation of alternative metastable states. In this article, we study the effect of magnetic field alignment, both under static and dynamic conditions, of nematic gems (nematic droplets in coexistence with the isotropic phase) and emulsified nematic droplets of a lyotropic chromonic liquid crystal. We use a custom polarizing optical microscopy assembly that incorporates a permanent magnet whose strength and orientation can be dynamically changed. By comparing simulated optical patterns with microscopy images, we measure an equilibrium twisted bipolar pattern within nematic gems that is only marginally different from the one reported for emulsified droplets. Both systems evolve to concentric configurations upon application of a static magnetic field, but behave very differently when the field is rotated. While the concentric texture within the emulsified droplets is preserved and only displays asynchronous oscillations for high rotating speeds, the nematic gems transform into a metastable untwisted bipolar configuration that is memorized by the system when the field is removed. Our results demonstrate the importance of boundary conditions in determining the dynamic behavior of confined liquid crystals even for configurations that share similar equilibrium bulk structures.

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