Chiral spiral cyclic twins

2022 ◽  
Vol 78 (1) ◽  
Author(s):  
Wolfgang Hornfeck
Keyword(s):  
Long Range ◽  
Orientational Order ◽  
Two Dimensional ◽  
Point Sets ◽  
Degenerate Cases

A formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.

scholarly journals Long-range orientational order in two-dimensional microfluidic dipoles

2014 ◽  
Vol 10 (2) ◽  
pp. 140-144 ◽  
Author(s):  
Itamar Shani ◽  
Tsevi Beatus ◽  
Roy H. Bar-Ziv ◽  
Tsvi Tlusty
Keyword(s):  
Long Range ◽  
Orientational Order ◽  
Two Dimensional

Dimensionality of hexatic melting in liquid crystals by in situ electron diffraction

1992 ◽  
Vol 50 (1) ◽  
pp. 270-271
Author(s):  
S.W. Hui ◽  
M. Cheng ◽  
J.T. Ho ◽  
R. Pindak
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electron Diffraction ◽  
Long Range ◽  
Organic Liquid ◽  
Orientational Order ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Free Standing

The theory of melting in two dimensions indicates that it is very different from the melting in three dimensions. An intermediate hexatic phase, with long range orientational but short range translational order, is proposed to exist between two dimensional solid and fluid phases. Because the long range order is limited experimentally by the domain or “grain” size, which is expected to be of sub-millimeter size, selected area electron diffraction is the method of choice for observing orientational order. Free-standing smectic liquid crystal films prove to be a most attractive system in which to verify this theory. However, multilayered liquid crystal samples are not strictly two dimensional systems because of interlayer interaction, their melting characteristics are expected to deviate from that of two dimensional systems. Furthermore, the outer layers may behave differently from the inner ones due to interfacial tension. We have applied low dose electron diffraction to study the effect of dimensionality, or number of layers, on the melting of multilayer organic liquid crystals.

Long-range orientational order in two-dimensional liquid crystals

1983 ◽  
Vol 27 (2) ◽  
pp. 1221-1224 ◽  
Author(s):  
J. Tobochnik ◽  
G. V. Chester
Keyword(s):  
Liquid Crystals ◽  
Long Range ◽  
Orientational Order ◽  
Two Dimensional

Long-range orientational order of random near-lattice hard sphere and hard disk processes

2020 ◽  
Vol 57 (2) ◽  
pp. 559-577
Author(s):  
Alexisz Tamás Gaál
Keyword(s):  
Long Range ◽  
Hard Spheres ◽  
Random Perturbation ◽  
Orientational Order ◽  
Three Dimensional ◽  
Hard Disk ◽  
Local Geometry ◽  
Two Dimensional ◽  
Point Configurations ◽  
Carry Over

AbstractWe show that a point process of hard spheres exhibits long-range orientational order. This process is designed to be a random perturbation of a three-dimensional lattice that satisfies a specific rigidity property; examples include the FCC and HCP lattices. We also define two-dimensional near-lattice processes by local geometry-dependent hard disk conditions. Earlier results about the existence of long-range orientational order carry over, and we obtain the existence of infinite-volume measures on two-dimensional point configurations that turn out to follow the orientation of a fixed triangular lattice arbitrarily closely.

scholarly journals Recovery of long-range order in two-dimensional charge density waves at high temperatures

2021 ◽  
Vol 27 (S1) ◽  
pp. 952-954
Author(s):  
Suk Hyun Sung ◽  
Yin Min Goh ◽  
Noah Schnitzer ◽  
Ismail El Baggari ◽  
Kai Sun ◽  
...  
Keyword(s):  
Charge Density ◽  
Long Range ◽  
High Temperatures ◽  
Charge Density Waves ◽  
Range Order ◽  
Long Range Order ◽  
Two Dimensional ◽  
Density Waves
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