Pure discrete spectrum and regular model sets in <i>d</i>-dimensional unimodular substitution tilings

Akiyama, Shigeki; Lee, Jeong Yup

doi:10.1107/s2053273320009717

Cited by 3 publications

(1 citation statement)

References 30 publications

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“…showed that the nematic phase becomes ferroelectric when a rod‐shaped molecule has a large dipole moment that exceeds a certain critical magnitude along its long axis. [ 32,33 ] This theoretical prediction is supported by the fact that nematic liquid crystals of aromatic polyesters and helical polypeptides with a large dipole moment along their long axis form ferroelectric nematic (N F ) phases via dipole–dipole interaction. [ 34–36 ] Furthermore, more recent studies have indicated that low‐molecular‐weight liquid crystals with a dioxane group at the molecular end (referred to as DIO hereafter) exhibit a ferroelectric N F phase and that their relative dielectric constant exceeds 10 000.…”

Section: Introductionmentioning

confidence: 99%

Lowering of Electrostatic Actuator Driving Voltage and Increasing Generated Force Using Spontaneous Polarization of Ferroelectric Nematic Liquid Crystals

Nishimura

Masuyama

Shimizu

et al. 2022

Advanced Physics Research

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Although electrostatic actuators have a simple structure and are lightweight, their range of application is limited because a high applied voltage of more than several kilovolts is required for practical use. Since the force acting between the electrodes of an electrostatic actuator is determined by the electric charge accumulated at the electrode/dielectric interface, the focus is on spontaneous polarization of ferroelectrics to increase the charge. As the ferroelectric material, a nematic liquid crystal material with a spontaneous polarization of 5 μC cm −2 is used. It is demonstrated that a force of 1.3 N is generated at an applied electric field of 0.5 MV m −1 . This force is 1200 times higher than that for standard paraelectric materials with a dielectric constant of ten. Further, the generated force responds linearly to the applied voltage, whereas it is proportional to the square of the applied voltage for paraelectric materials. The actuator function of this ferroelectric is examined using a double-helical coil electrode fabricated using a 3D printer. It can be successfully operated at a voltage of several tens of volts. Under an electric field of 0.25 MV m −1 , a remarkable contraction of 6.3 mm occurs, corresponding to 19% of the original length.

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Section: Introductionmentioning

confidence: 99%

Lowering of Electrostatic Actuator Driving Voltage and Increasing Generated Force Using Spontaneous Polarization of Ferroelectric Nematic Liquid Crystals

Nishimura

Masuyama

Shimizu

et al. 2022

Advanced Physics Research

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Equivalence between pure point diffractive sets and cut-and-project sets on substitution tilings

Lee

2023

J. Phys.: Conf. Ser.

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Quasicrystals are characterized by the property of pure point diffractive spectrum mathematically. We look at substitution tilings and characterize the pure point diffractive spectrum by regular model sets defined from a cut-and-project scheme. The cut-and-project scheme is built with a physical space ℝ d and an internal space which is a product of a Euclidean space and a profinite group. The assumptions we make here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with same multiplicity. We give a precise argument for the proof on a specific example.

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Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings

Lee¹

2022

Acta Cryst Sect A

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Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600–610] is that unimodularity is no longer assumed in this paper.

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Pure discrete spectrum and regular model sets in d-dimensional unimodular substitution tilings

Cited by 3 publications

References 30 publications

Lowering of Electrostatic Actuator Driving Voltage and Increasing Generated Force Using Spontaneous Polarization of Ferroelectric Nematic Liquid Crystals

Lowering of Electrostatic Actuator Driving Voltage and Increasing Generated Force Using Spontaneous Polarization of Ferroelectric Nematic Liquid Crystals

Equivalence between pure point diffractive sets and cut-and-project sets on substitution tilings

Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings

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