scholarly journals The Well Order Reconstruction Solution for three-dimensional wells, in the Landau–de Gennes theory

2020 ◽  
Vol 119 ◽  
pp. 103342 ◽  
Author(s):  
Giacomo Canevari ◽  
Joseph Harris ◽  
Apala Majumdar ◽  
Yiwei Wang
Keyword(s):  
Three Dimensional ◽  
Order Reconstruction ◽  
Gennes Theory

scholarly journals Radial symmetry on three-dimensional shells in the Landau–de Gennes theory

2016 ◽  
Vol 314 ◽  
pp. 18-34 ◽  
Author(s):  
Giacomo Canevari ◽  
Mythily Ramaswamy ◽  
Apala Majumdar
Keyword(s):  
Three Dimensional ◽  
Radial Symmetry ◽  
Gennes Theory

Theory and Simulation of Texture Transformations in Chiral Systems: Applications to Biological Fibrous Composites

2001 ◽  
Vol 709 ◽  
Author(s):  
Gino De Luca ◽  
Alejandro D. Rey
Keyword(s):  
Three Dimensional ◽  
Front Propagation ◽  
Fibrous Composites ◽  
Propagation Process ◽  
Chiral Nematic ◽  
New Information ◽  
Biological Structures ◽  
Planar Film ◽  
Chiral Systems ◽  
Gennes Theory

ABSTRACTNumerous studies [1-3] have shown that chiral biological structures share common properties with liquids crystals, in particular a tendency to assemble in three-dimensional lattices very similar to that of chiral nematics. Biological fibrous composites are usually found in planar (film) and cylindrical (fibber) twist geometries. In this work, the formation process of the planar twist architecture is numerically investigated using a mesoscopic model based on the Landau-de Gennes theory of chiral nematic liquid crystals. The simulations and visualizations of the computed textures provide new information on some of the principles that govern the formation of chiral biological structures. It is found that a defect-free planar twist architecture arises from a chiral front propagation process with a fully relaxed wake.

scholarly journals Order reconstruction patterns in nematic liquid crystal wells

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140276 ◽  
Author(s):  
Samo Kralj ◽  
Apala Majumdar
Keyword(s):  
Liquid Crystal ◽  
Cross Section ◽  
Nematic Liquid Crystal ◽  
Correlation Length ◽  
Critical Threshold ◽  
Two Dimensional ◽  
Liquid Crystal Material ◽  
Order Reconstruction ◽  
Anchoring Strength ◽  
Gennes Theory

We numerically study structural transitions inside shallow sub-micrometre scale wells with square cross section, filled with nematic liquid crystal material. We model the wells within the Landau–de Gennes theory. We obtain two qualitatively different states: (i) the diagonal state with defects for relatively large wells with lateral dimension greater than a critical threshold and (ii) a new, two-dimensional star-like biaxial order reconstruction pattern called the well order-reconstruction structure (WORS), for wells smaller than the critical threshold. The WORS is defined by an uniaxial cross connecting the four vertices of the square cross section. We numerically compute the critical threshold in terms of the bare biaxial correlation length and study its dependence on the temperature and on the anchoring strength on the lateral well surfaces.

scholarly journals Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory

2010 ◽  
Vol 21 (2) ◽  
pp. 181-203 ◽  
Author(s):  
APALA MAJUMDAR
Keyword(s):  
Three Dimensional ◽  
Energy Functional ◽  
Order Parameters ◽  
Tensor Order ◽  
Temperature Regimes ◽  
Explicit Bounds ◽  
Scalar Order ◽  
Definition Of ◽  
Gennes Theory ◽  
The Continuum

We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.

Coupling phenomenon of anti-connected hybrid alignment nematics in thin cell: From submicron to nanoscale

2019 ◽  
Vol 33 (04) ◽  
pp. 1950002 ◽  
Author(s):  
Sibo Chen ◽  
Xiaoting Liu ◽  
Huimin Yu ◽  
Xuan Zhou ◽  
Zhidong Zhang
Keyword(s):  
Numerical Simulation ◽  
Coherence Length ◽  
Structure Transition ◽  
Maximum Value ◽  
Order Reconstruction ◽  
Novel Approach ◽  
New Type ◽  
Degenerate States ◽  
Simulation Results ◽  
Gennes Theory

Within Landau–de Gennes theory, we modeled a system consisting of two anti-connected hybrid alignment nematics (HAN). Our numerical simulation results indicated the occurrence of four states denoted as I, II, III and IV. The states undergo a structure transition as a function of the cell gap d. For d [Formula: see text] d0, where d0 is the maximum value for the structure transition to occur, state I and II are bistable, whereas state III and IV are metastable and quadruply degenerate. We found that d0 = 15[Formula: see text], where [Formula: see text] is the biaxial characteristic coherence length. When d[Formula: see text] [Formula: see text] d [Formula: see text] d0, where d[Formula: see text] = 7[Formula: see text] and d[Formula: see text] is the critical cell gap for order reconstruction (OR), continuous inversion walls appear both in state III and IV. We first found that the structure transition from inversion walls to defect walls occurs with decreasing d from the submicron to nanoscale. During this process, quadruply degenerate states in state III and IV transformed into doubly degenerate states. Meanwhile, states I and II remained bistable. When d = d[Formula: see text], all states reached a new type of OR pattern with two biaxial walls cross-linked with each other by a novel approach; i.e., from defect walls to OR.

scholarly journals On the Disclination Lines of Nematic Liquid Crystals

2016 ◽  
Vol 19 (2) ◽  
pp. 354-379 ◽  
Author(s):  
Yucheng Hu ◽  
Yang Qu ◽  
Pingwen Zhang
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Practical Importance ◽  
Three Dimensional ◽  
Defect Structures ◽  
Static Structure ◽  
Spherical Droplet ◽  
Topological Constraint ◽  
Defects In Liquid Crystals ◽  
Gennes Theory

AbstractDefects in liquid crystals are of great practical importance and theoretical interest. Despite tremendous efforts, predicting the location and transition of defects under various topological constraint and external field remains to be a challenge. We investigate defect patterns of nematic liquid crystals confined in three-dimensional spherical droplet and two-dimensional disk under different boundary conditions, within the Landau-de Gennes model. We implement a spectral method that numerically solves the Landau-de Gennes model with high accuracy, which allows us to study the detailed static structure of defects. We observe five types of defect structures. Among them the 1/2-disclination lines are the most stable structure at low temperature. Inspired by numerical results, we obtain the profile of disclination lines analytically. Moreover, the connection and difference between defect patterns under the Landau-de Gennes model and the Oseen-Frank model are discussed. Finally, three conjectures are made to summarize some important characteristics of defects in the Landau-de Gennes theory. This work is a continuing effort to deepen our understanding on defect patterns in nematic liquid crystals.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

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