scholarly journals Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation

2016 ◽  
Vol 26 (14) ◽  
pp. 2769-2808 ◽  
Author(s):  
Georgy Kitavtsev ◽  
J. M. Robbins ◽  
Valeriy Slastikov ◽  
Arghir Zarnescu
Keyword(s):  
Liquid Crystal ◽  
Boundary Conditions ◽  
Elastic Constants ◽  
Critical Points ◽  
Two Dimensions ◽  
Crystal Defects ◽  
Radial Profiles ◽  
Liquid Crystal System ◽  
The Stability ◽  
The One

We consider the two-dimensional (2D) Landau–de Gennes energy with several elastic constants, subject to general [Formula: see text]-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case [Formula: see text]. In this case we identify three types of radial profiles: with two, three of full five components and numerically investigate their minimality and stability depending on suitable parametres. We also numerically study the stability properties of the critical points of the Landau–de Gennes energy and capture the intricate dependence of various qualitative features of these solutions on the elastic constants and the physical regimes of the liquid crystal system.

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.

Automatic First Arrival Picking Workflow by Global Path Tracing

Geophysics ◽  
2021 ◽  
pp. 1-46
Author(s):  
Dongliang Zhang ◽  
Tong W. Fei ◽  
Song Han ◽  
Constantine Tsingas ◽  
Yi Luo ◽  
...  
Keyword(s):  
Field Data ◽  
Amplitude Ratio ◽  
Optimal Path ◽  
Two Dimensions ◽  
Higher Dimension ◽  
Path Tracing ◽  
Higher Dimensional ◽  
First Arrival ◽  
The Stability ◽  
The One

It can be challenging to pick high quality first arrivals on noisy seismic datasets. The stability and smoothness criteria of the picked first arrival are not satisfied for datasets with shingles and interferences from unexpected and backscattered events. To improve first arrival picking, we propose an automatic first arrival picking workflow using global path tracing to find a global solution for first arrival picking with the condition of smoothness of the traced path. The proposed methodology is composed of data preconditioning, global path tracing, and final addition of traced and piloted travel times to compute the total picked travel time. We propose several ways to precondition the dataset, including the use of amplitude and amplitude ratio with and without a pilot. 2D global path tracing is comprised of two steps, namely, accumulation of energy on the potential path and backtracking of the optimal path with a strain factor for smoothness. For higher dimensional datasets, two strategies were adopted. One was to split the higher-dimension data into sub-domains of two dimensions to which 2D global path tracing was applied. The alternative method was to smooth the preconditioned dataset in directions except for the one used to trace the path before applying 2D global path tracing. Next, we discussed the importance of choosing proper parameters in both data preconditioning and constraining global path tracing. We demonstrated the robustness and stability of the proposed automatic first arrival picking via global path tracing using synthetic and field data examples.

scholarly journals Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

2014 ◽  
Vol 742 ◽  
pp. 636-663 ◽  
Author(s):  
P. Ripesi ◽  
L. Biferale ◽  
M. Sbragaglia ◽  
A. Wirth
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Two Dimensions ◽  
Turbulent Regime ◽  
Thermal Insulating ◽  
Pattern Length ◽  
The Stability ◽  
The Impact ◽  
Rayleigh Numbers

AbstractWe investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh–Bénard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, at both low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of ‘bulk’ convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to $\mathit{Ra} \sim 10^{10}$.

scholarly journals Statistical Theory of Elastic Constants of Cholesteric Liquid Crystals

2002 ◽  
Vol 57 (3-4) ◽  
pp. 105-118 ◽  
Author(s):  
Andrzej Kapanowski
Keyword(s):  
Statistical Theory ◽  
Liquid Crystals ◽  
Elastic Constants ◽  
Binary Systems ◽  
Cholesteric Liquid Crystals ◽  
Cholesteric Phase ◽  
Small Density ◽  
Nematic Phases ◽  
The Stability ◽  
The One

A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded as a distorted form of the uniaxial (biaxial) nematic phase. The chirality of the interactions and the implementation of the inversion to the rotation matrix elements are discussed in detail. General microscopic expressions for the elastic constants are derived. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. It is shown that the elastic constants determine the twist of the phase. The stability condition for the cholesteric and nematic phases is presented. The theory is used to study unary and binary systems. The temperature and concentration dependence of the order parameters, the elastic constants and the twist of the phase are obtained. The possibility of phase separation is not investigated.

Difference Schemes with Nonlocal Boundary Conditions

2001 ◽  
Vol 1 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Alexei V. Goolin ◽  
Nikolai I. Ionkin ◽  
Valentina A. Morozova
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Equation ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Conduction Equation ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient

AbstractThe paper deals with the stability, with respect to initial data, of difference schemes that approximate the heat-conduction equation with constant coefficients and nonlocal boundary conditions. Some difference schemes are considered for the one-dimensional heat-conduction equation, the energy norm is constructed, and the necessary and sufficient stability conditions in this norm are established for explicit and weighted difference schemes.

scholarly journals ON THE LANDAU-GINZBURG DESCRIPTION OF N=2 MINIMAL MODELS

1994 ◽  
Vol 09 (27) ◽  
pp. 4783-4800 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Boundary Conditions ◽  
Path Integral ◽  
Critical Points ◽  
Two Dimensions ◽  
Superconformal Algebra ◽  
Minimal Models ◽  
Low Levels ◽  
Twisted Boundary Conditions

The conjecture that N=2 minimal models in two dimensions are critical points of a superrenormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary conditions. This leads to simple expressions for certain characters of the N=2 models which can be verified at least at low levels. An N=2 superconformal algebra can in fact be found directly in the noncritical Landau-Ginzburg system, giving further support for the conjecture.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

Structure, Stability and Water Adsorption on Ultra-Thin TiO2 Supported on TiN

2019 ◽  
Author(s):  
Jose Julio Gutierrez Moreno ◽  
Marco Fronzi ◽  
Pierre Lovera ◽  
alan O'Riordan ◽  
Mike J Ford ◽  
...  
Keyword(s):  
Density Functional ◽  
Water Adsorption ◽  
Chemical Potential ◽  
Energy Gap ◽  
Molecular Water ◽  
Structure Stability ◽  
Ambient Conditions ◽  
Rutile Structure ◽  
The Stability ◽  
The One

<p></p><p>Interfacial metal-oxide systems with ultrathin oxide layers are of high interest for their use in catalysis. In this study, we present a density functional theory (DFT) investigation of the structure of ultrathin rutile layers (one and two TiO<sub>2</sub> layers) supported on TiN and the stability of water on these interfacial structures. The rutile layers are stabilized on the TiN surface through the formation of interfacial Ti–O bonds. Charge transfer from the TiN substrate leads to the formation of reduced Ti<sup>3+</sup> cations in TiO<sub>2.</sub> The structure of the one-layer oxide slab is strongly distorted at the interface, while the thicker TiO<sub>2</sub> layer preserves the rutile structure. The energy cost for the formation of a single O vacancy in the one-layer oxide slab is only 0.5 eV with respect to the ideal interface. For the two-layer oxide slab, the introduction of several vacancies in an already non-stoichiometric system becomes progressively more favourable, which indicates the stability of the highly non-stoichiometric interfaces. Isolated water molecules dissociate when adsorbed at the TiO<sub>2</sub> layers. At higher coverages the preference is for molecular water adsorption. Our ab initio thermodynamics calculations show the fully water covered stoichiometric models as the most stable structure at typical ambient conditions. Interfacial models with multiple vacancies are most stable at low (reducing) oxygen chemical potential values. A water monolayer adsorbs dissociatively on the highly distorted 2-layer TiO<sub>1.75</sub>-TiN interface, where the Ti<sup>3+</sup> states lying above the top of the valence band contribute to a significant reduction of the energy gap compared to the stoichiometric TiO<sub>2</sub>-TiN model. Our results provide a guide for the design of novel interfacial systems containing ultrathin TiO<sub>2</sub> with potential application as photocatalytic water splitting devices.</p><p></p>

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

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