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1. Vorticity of Twisted Spinor Fields

   A. Afanasev, C.E. Carlson (August 2022, ArXivorg)

   Spinor fields with a vortex structure in free space that allow them to have arbitrary integer orbital angular momentum along the direction of motion have been studied for some time. Relatively new is the observation in a certain context that the vortex center of this field structure is, unlike a classical whirlpool, not singular. We point out that there are several ways to calculate the local velocity of the spinor field and that all but one show a singular vorticity at the vortex line. That one, using the Dirac bilinear current with no derivatives, is the only one so far (to our knowledge) studied in the literature in this context and we further show how to understand an apparent conflict in the existing results. 

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2. Twisted Hermitian Codes

   https://doi.org/10.3390/math9010040  

   Allen, Austin; Blackwell, Keller; Fiol, Olivia; Kshirsagar, Rutuja; Matsick, Bethany; Matthews, Gretchen L.; Nelson, Zoe (January 2021, Mathematics)

   null (Ed.)

   We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-dimensional Schur squares, and we identify a subfamily of twisted Hermitian codes that achieves a Schur square dimension close to that of a random linear code. Twisted Hermitian codes allow one to work over smaller alphabets than those based on Reed–Solomon codes of similar lengths. 

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3. Twisted tetrathiafulvalene crystals

   https://doi.org/10.1039/D2ME00010E  

   Yang, Yongfan; Zong, Kai; Whittaker, St. John; An, Zhihua; Tan, Melissa; Zhou, Hengyu; Shtukenberg, Alexander G.; Kahr, Bart; Lee, Stephanie S. (January 2022, Molecular Systems Design & Engineering)

   Optically-active optoelectronic materials are of great interest for many applications, including chiral sensing and circularly polarized light emission. Traditionally, such applications have been enabled by synthetic strategies to design chiral organic semiconductors and conductors. Here, centrosymmetric tetrathiafulvalene (TTF) crystals are rendered chiral on the mesoscale by crystal twisting. During crystallization from the melt, helicoidal TTF fibers were observed to grow radially outwards from a nucleation centre as spherulites, twisting in concert about the growth direction. Because molecular crystals exhibit orientation-dependent refractive indices, periodic concentric bands associated with continually rotating crystal orientations were observed within the spherulites when imaged between crossed polarizers. Under certain conditions, concomitant crystal twisting and bending was observed, resulting in anomolous crystal optical behavior. X-ray diffraction measurements collected on different spherulite bands indicated no difference in the molecular packing between straight and twisted TTF crystals, as expected for microscopic twisting pitches between 20–200 μm. Mueller matrix imaging, however, revealed preferential absorption and refraction of left- or right-circularly polarized light in twisted crystals depending on the twist sense, either clockwise or counterclockwise, about the growth direction. Furthermore, hole mobilities of 2.0 ± 0.9 × 10 −6 cm 2 V −1 s −1 and 1.9 ± 0.8 × 10 −5 cm 2 V −1 s −1 were measured for straight and twisted TTF crystals deposited on organic field-effect transistor platforms, respectively, demonstrating that crystal twisting does not negatively impact charge transport in these systems. 

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4. Twisted Schubert polynomials

   https://doi.org/10.1007/s00029-022-00802-1  

   Liu, Ricky Ini (November 2022, Selecta Mathematica)
5. Acyclic Twisted Amides

   https://doi.org/10.1021/acs.chemrev.1c00225  

   Meng, Guangrong; Zhang, Jin; Szostak, Michal (October 2021, Chemical Reviews)