Fiber torsion sensor demodulated by a high-birefringence fiber Bragg grating

A new high-birefringence (Hi-Bi) fiber torsion sensor demodulated by a Hi-Bi fiber Bragg grating (FBG) is proposed in this study. The twisted Hi-Bi fiber sensor characteristics are analyzed using the Jones matrix. The intensity ratio from two reflected Bragg wavelengths is associated with the twist angle of the measured Hi-Bi fiber. It is found that the twist angle resolution is estimated at around 0.3° under ±0.1 dB readout from an optical spectrum analyzer if the polarization state of the light source is stable. The advantages of this new torsion sensor are: (1) insensitivity to intensity variations from the light source, (2) insensitivity to the torsion gauge length, and (3) absolute measurement in the twist angle. However, the polarization state of light in the proposed method needs to be controlled, and any birefringence change in the twisted Hi-Bi fiber needs to be prevented.     

Letter: Axial Torsion-Dirac Spin Effect in Rotating Frame with Relativistic Factor

In the framework of spacetime with torsion and without curvature, the Dirac particle spin precession in the rotational system is studied. We write out the equivalent tetrad of the rotating frame, in the polar coordinate system, through considering the relativistic factor, and the resultant equivalent metric is a flat Minkowski one. The obtained rotation-spin coupling formula can be applied to the high speed rotating case, which is consistent with the expectation.     

Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

Teleparallel versions of Friedmann and Lewis–Papapetrou spacetimes

This paper is devoted to investigating the teleparallel versions of the Friedmann models as well as the Lewis–Papapetrou solution. We obtain the tetrad and the torsion fields for both spacetimes. It is shown that the axial-vector vanishes for the Friedmann models. We discuss the different possibilities for the axial-vector, depending on the arbitrary functions ω and ψ in the Lewis–Papapetrou metric. The vector related to spin has also been evaluated.     

Theoretical study on the structure and property relationship of the cationic conjugated polyelectrolytes

A theoretical study using density functional theory was performed to understand the structure/property relationship of the cationic conjugated polyelectrolytes, poly[9,9-bis-(6′-N,N,N-trimethylammonium) hexyl] fluorene-alt-4,7-(2,1,3-benzothiadiazole)] (PFBT-X, where X = Br). The torsion angle between the fluorene and benzothiadiazole units in the PFBT monomer was found to substantially affect the structural and electronic properties of the cationic PFBT monomer. The changes of geometrical parameter, HOMO and LUMO energy levels, and band gap, as well as the absorption maximum are discussed in terms of the torsion in the PFBT monomer structure. For comparison, its neutral analogue, the monomer of poly(9,9-di-n-octylfluorene-alt-benzothiadiazole) (F8BT) was also studied. The length of conjugation backbone was also examined.     

An ab initio potential energy surface for the υ4 vibrational mode of hydrogen peroxide

In this paper, the levels and the torsional microstates of hydrogen peroxide are determined from fully optimized ab initio calculations using a nuclear model in one dimension. Calculations have been performed at the MP2 level with the 6-311 G(2df,2pd), 6-31 1+G(2df,2pd), cc-pVTZ and AUG-cc-pVTZ basis sets including polarization orbitals and diffuse functions. The most stable conformation, calculated with the MP2/AUG-cc-pVTZ approach, is a trans–gauche conformer lying at 67.5° from the trans structure. By using the same level of calculations, the heights of the trans and cis barriers have been determined to be 386.5 and 2643.8 cm⁻¹ in a good agreement with the experimental data. The variational torsional levels split into four components by the tunnelling effect of the barriers. The splitting of the fundamental level caused by the trans barrier has been found to be 11.8683 cm⁻¹, whereas the splitting caused by the cis barrier is insignificant under n=2. Current ab initio energies confirm the experimental assignments and verify the separability of the torsion from the rest of the vibrations. However, the experimental relation of dependence on the torsion of the rotational constants cannot be reproduced in one-dimension and depends on several additional vibrational effects.     

Two questions on semi-clean group rings

It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2.     

New measurements and analysis of the far-infrared spectrum of CH2DOH in the lowest torsional vibrational state (e0)

In this work the far infrared (FIR) absorption spectrum has been measured for the asymmetrically mono deuterated Methanol (CH₂DOH) species in the wavenumber range of 15–1200 cm⁻¹ better accuracy and signal/noise ratio than known before. Assignments have been made for b-type transitions in the lowest lying torsional vibrational state trans-(e₀) for a wide range of rotational angular momentum. The assignments have been rigorously confirmed by the residual loop defect methods. The ^rR–branch wavenumbers are analyzed by the usual state dependent expansion parameters and the Q-Branch origins. These origins have been used to calculate the torsional and torsional-rotation interaction contributions. These findings are in good agreement with predicted from the Hamiltonian model described in recent publications. A large number of assignments have also been made in the millimeter wave spectrum recorded earlier and thereby evaluated the asymmetry splitting parameters for 4 different axial rotational angular momentum quantum numbers. The analysis and interpretation of the spectra are reported. New assignments for about 260 transitions are included the text and a catalog of about 1500 transitions belonging to the e₀ species is prepared (Appendix 1) and is made available through the open server in “Research Gate” and will be freely available to others.     

Torsion balances with fibres of zero length

Torsion balances have good immunity to tilt and low rotational stiffness. However precise control of the position of the suspended torsion ‘bob’ is difficult in the presence of ground vibrations and tilt and this is a limiting factor in applications where Casimir forces or putative non-Newtonian short-range forces are being measured. We describe how the desirable characteristics of torsion balances can be reproduced in a rigid body that is suspended using applied forces rather than a torsion fibre. The suspension system can then provide a more precise control of the degrees of freedom of the suspended body. We apply these ideas to a superconducting levitated torsion balance, developed by the authors, and a generic electrostatic suspension. We present results of preliminary experiments that provide support for our analyses.