Singular limits in polymer-stabilized liquid crystals

2003 ◽  
Vol 133 (1) ◽  
pp. 11-34 ◽  
Author(s):  
P. Bauman ◽  
D. Phillips ◽  
Q. Shen
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
External Field ◽  
Fibre Composite ◽  
Nonlinear Partial Differential Equation ◽  
Critical Values ◽  
Perforated Domain ◽  
Small Scale ◽  
Equilibrium Configurations ◽  
Polymer Stabilized

We investigate equilibrium configurations for a polymer-stabilized liquid-crystal material subject to an applied magnetic field. The configurations are determined by energy minimization, where the energies of the system include those of bulk, surface and external field. The Euler–Lagrange equation is a nonlinear partial differential equation with nonlinear boundary conditions defined on a perforated domain modelling the cross-section of the liquid-crystal–polymer-fibre composite. We analyse the critical values for the external magnetic field representing Fredericks transitions and describe the equilibrium configurations under any magnitude of the external field. We also discuss the limit of the critical values and configurations as the number of polymer fibres approaches infinity. In the case where, away from the boundary of the composite, the fibres are part of a periodic array, we prove that non-constant configurations develop order-one oscillations on the scale of the array's period. Furthermore, we determine the small-scale structure of the configurations as the period tends to zero.

Uniqueness of director configuration states for liquid crystals in the case of weak anchoring

2019 ◽  
Vol 84 (4) ◽  
pp. 748-762
Author(s):  
Carlo Greco
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
External Field ◽  
Thin Layer ◽  
Elastic Constants ◽  
Cholesteric Liquid Crystal ◽  
Stable Configuration ◽  
Director Field ◽  
Critical Thresholds ◽  
Bounding Surfaces

Abstract In a thin layer of liquid crystal the configuration of the director field depends on the interaction between the elastic properties of the material, the thickness $d$ of the layer, the boundary conditions and the external fields that may have been applied. Suitable combinations of these factors can give rise to distorted configurations (Freedericksz transitions). In this paper we assume the Oseen-Frank model for the energy and that the director field depends only on the direction orthogonal to the layer; we assume also weak anchoring conditions at the two bounding surfaces, and we mainly study the problem of uniqueness of such distorted configurations. More precisely, we first consider the nematic case in the presence of a magnetic field $\mathbf H$, and we prove the uniqueness of the stable configuration provided the magnitude of $\mathbf H$ is between two critical thresholds, simplifying some results already known in the literature, and calculating explicitly the critical thresholds. Then we study the case of a cholesteric liquid crystal without external field. In this case the director field tends to form a right-angle helicoid around a twist axis orthogonal to the layer, and we have distorted configurations (namely oblique helicoid) for suitable value of $d$. Also in this case, with suitable restrictions on the elastic constants in the Oseen-Frank energy, we find two critical thresholds for $d$, and we prove the existence of only one stable director configuration if $d$ is between them.

scholarly journals Patterned waveguide liquid crystal displays

RSC Advances ◽  
2020 ◽  
Vol 10 (68) ◽  
pp. 41693-41702
Author(s):  
Yunho Shin ◽  
Jinghua Jiang ◽  
Guangkui Qin ◽  
Qian Wang ◽  
Ziyuan Zhou ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Switching Time ◽  
Contrast Ratio ◽  
Liquid Crystal Displays ◽  
High Contrast ◽  
High Brightness ◽  
Photo Polymerization ◽  
Ultrafast Switching ◽  
Light Waveguide ◽  
Polymer Stabilized

A polymer stabilized LC based light waveguide display is reported. Performance is improved by patterned photo-polymerization or electrode. It has high brightness, ultrafast switching time, high contrast ratio, and high transmittance for transparent and augmented displays.

Dynamic guiding of bacteria in lyotropic chromonic liquid crystal using magnetic field

2020 ◽  
Vol 712 (1) ◽  
pp. 10-23
Author(s):  
Marc-Antoine Boulé ◽  
Simon Rainville ◽  
Tigran Galstian
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal

scholarly journals The Evolution of the Solar Magnetic Field

2012 ◽  
Vol 10 (H16) ◽  
pp. 86-89 ◽  
Author(s):  
J. Todd Hoeksema
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Solar Magnetic Field ◽  
Coronal Holes ◽  
Active Regions ◽  
Statistical Characteristics ◽  
Field Pattern ◽  
Small Scale ◽  
Polar Caps ◽  
Magnetic Elements

AbstractThe almost stately evolution of the global heliospheric magnetic field pattern during most of the solar cycle belies the intense dynamic interplay of photospheric and coronal flux concentrations on scales both large and small. The statistical characteristics of emerging bipoles and active regions lead to development of systematic magnetic patterns. Diffusion and flows impel features to interact constructively and destructively, and on longer time scales they may help drive the creation of new flux. Peculiar properties of the components in each solar cycle determine the specific details and provide additional clues about their sources. The interactions of complex developing features with the existing global magnetic environment drive impulsive events on all scales. Predominantly new-polarity surges originating in active regions at low latitudes can reach the poles in a year or two. Coronal holes and polar caps composed of short-lived, small-scale magnetic elements can persist for months and years. Advanced models coupled with comprehensive measurements of the visible solar surface, as well as the interior, corona, and heliosphere promise to revolutionize our understanding of the hierarchy we call the solar magnetic field.

Dynamics of a disc in a nematic liquid crystal

Soft Matter ◽  
2016 ◽  
Vol 12 (4) ◽  
pp. 1279-1294 ◽  
Author(s):  
Alena Antipova ◽  
Colin Denniston
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
Numerical Simulations ◽  
Nematic Liquid Crystal ◽  
Weak Magnetic Field ◽  
Angular Speed ◽  
The Magnetic Field

We explain the motion of a micron-sized ferromagnetic disc immersed in a nematic liquid crystal under the action of a weak magnetic field using numerical simulations. We show that the disc's behaviour can be controlled by the angular speed of the magnetic field and its magnitude.

scholarly journals On the origin of variable structures in the winds of hot luminous stars

2013 ◽  
Vol 440 (1) ◽  
pp. 2-9 ◽  
Author(s):  
Yannick J. L. Michaux ◽  
Anthony F. J. Moffat ◽  
André-Nicolas Chené ◽  
Nicole St-Louis
Keyword(s):  
Magnetic Field ◽  
Empirical Evidence ◽  
Temporal Variability ◽  
Large Scale ◽  
Small Scale ◽  
Ionization Zone ◽  
Corotating Interaction Regions ◽  
Wind Variability ◽  
Global Magnetic Field ◽  
Interaction Regions

Abstract Examination of the temporal variability properties of several strong optical recombination lines in a large sample of Galactic Wolf–Rayet (WR) stars reveals possible trends, especially in the more homogeneous WC than the diverse WN subtypes, of increasing wind variability with cooler subtypes. This could imply that a serious contender for the driver of the variations is stochastic, magnetic subsurface convection associated with the 170 kK partial-ionization zone of iron, which should occupy a deeper and larger zone of greater mass in cooler WR subtypes. This empirical evidence suggests that the heretofore proposed ubiquitous driver of wind variability, radiative instabilities, may not be the only mechanism playing a role in the stochastic multiple small-scaled structures seen in the winds of hot luminous stars. In addition to small-scale stochastic behaviour, subsurface convection guided by a global magnetic field with localized emerging loops may also be at the origin of the large-scale corotating interaction regions as seen frequently in O stars and occasionally in the winds of their descendant WR stars.

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