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Curved channels with constant cross sections are constructed which support a trapped surface wave. Since corresponding eigenvalues are embedded in the continuous spectrum of the water wave problem and therefore possess the natural instability, the construction procedure requires "fine-tuning" of several parameters in the (small) curvature of the channel as well as geometrical restrictions on the cross section. In particular, the mirror symmetry of the cross section with respect to the vertical axis disrupts the procedure, but examples of suitable non-symmetric cross sections are provided. [ABSTRACT FROM AUTHOR]

Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson–Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons' relationship as to how to develop the DNA molecule on the principle of Watson–Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system. [ABSTRACT FROM AUTHOR]

Abstract—Nucleocytoplasmic exchange in the cell occurs through the nuclear pore complexes (NPCs). NPCs are large multiprotein complexes with octagonal symmetry about their axis and imperfect mirror symmetry about a plane parallel with the nuclear envelop (NE). NPC fuses the inner and outer nuclear membranes and opens up a channel between nucleus and cytoplasm. NPC is built of nucleoporins. Each nucleoporin occurs in at least eight copies per NPC. Inside the NPC a permeability barrier forms by which NPCs can provide fast and selectable transport of molecules from one side of the nuclear membrane to the other. NPC architecture is based on hierarchical principle of organization. Nucleoporins are integrated into complexes that oligomerizes into bigger octomeric high-order structures. These structures are the main components of NPCs. In the first part of this work, the main attention is paid to NPC structure and nucleoporin properties. The second part is dedicated to mechanisms of NPC assembly and disassembly at different stages of the cell cycle. [ABSTRACT FROM AUTHOR]

Generating out-of-plane spins in sputtered materials holds immense potential for achieving field-free spin–orbit torque switching in practical applications and mass production. In this work, we present the detection of out-of-plane spins from single-layer ferromagnetic Co layers, which are visualized through helicity-dependent photomapping techniques. Our experiments have shown that out-of-plane spins are dependent on the magnetization direction, current density, and Co thickness. Our findings indicate that amorphous sputtered Co can be a promising candidate as an out-of-plane spin source material for industrial massive production. [ABSTRACT FROM AUTHOR]

Let |$\textsf {X}$| and |$\textsf {X}^{!}$| be a pair of symplectic varieties dual with respect to 3D mirror symmetry. The |$K$| -theoretic limit of the elliptic duality interface is an equivariant |$K$| -theory class |$\mathfrak {m} \in K(\textsf {X}\times \textsf {X}^{!})$|⁠. We show that this class provides correspondences $$ \begin{align*} & \Phi_{\mathfrak{m}}: K(\textsf{X}) \leftrightarrows K(\textsf{X}^{!}) \end{align*}$$ mapping the |$K$| -theoretic stable envelopes to the |$K$| -theoretic stable envelopes. This construction allows us to relate various representation theoretic objects of |$K(\textsf {X})$|⁠ , such as action of quantum groups, quantum dynamical Weyl groups, |$R$| -matrices, etc. to those for |$K(\textsf {X}^{!})$|⁠. In particular, we relate the wall |$R$| -matrices of |$\textsf {X}$| to the |$R$| -matrices of the dual variety |$\textsf {X}^{!}$|⁠. As an example, we apply our results to |$\textsf {X}=\textrm {Hilb}^{n}({{\mathbb {C}}}^2)$| —the Hilbert scheme of |$n$| points in the complex plane. In this case, we arrive at the conjectures of Gorsky and Negut from [ 10 ]. [ABSTRACT FROM AUTHOR]

Two-dimensional Janus materials have unique structural characteristics due to their lack of out-of-plane mirror symmetry, resulting in many excellent physical and chemical properties. Using first-principle calculations, we performed a detailed investigation of the possible stable structures and properties of two-dimensional Janus NbSH. We found that both Janus 1T and 2H structures are semiconductors, unlike their metallic counterparts MoSH. Furthermore, we predicted a new stable NbSH monolayer using a particle swarm optimization method combined with first-principle calculations. Interestingly, the out-of-plane mirror symmetry is preserved in this newly found 2D structure. Furthermore, the newly found NbSH is metallic and exhibits intrinsic superconducting behavior. The superconducting critical temperature is about 6.1 K under normal conditions, which is found to be very sensitive to stress. Even under a small compressive strain of 1.08%, the superconducting critical temperature increases to 9.3 K. In addition, the superconductivity was found to mainly originate from Nb atomic vibrations. Our results show the diversity of structures and properties of the two-dimensional Janus transition metal sulfhydrate materials and provide some guidelines for further investigations. [ABSTRACT FROM AUTHOR]

We define a new Gromov–Witten theory relative to simple normal crossing divisors as a limit of Gromov–Witten theory of multi-root stacks. Several structural properties are proved including relative quantum cohomology, Givental formalism, Virasoro constraints (genus zero) and a partial cohomological field theory. Furthermore, we use the degree zero part of the relative quantum cohomology to provide an alternative mirror construction of Gross and Siebert (Intrinsic mirror symmetry, arXiv:1909.07649) and to prove the Frobenius structure conjecture of Gross et al. (Publ Math Inst Hautes Études Sci 122:65–168, 2015) in our setting. [ABSTRACT FROM AUTHOR]

The inference of fluid motion below the core–mantle boundary from geomagnetic observations presents a highly non-unique inverse problem. We propose a new method that provides a unique local estimate of the velocity field, assuming quasi-geostrophic flow in the core interior (which implies equatorial mirror symmetry) and negligible magnetic diffusion. These assumptions remove the theoretical underdetermination, enabling us to invert for the flow at each point of a spherical grid representing the core surface. The unreliable reconstruction of small-scale flows, which arises because only large-scale observations are available, is mitigated by smoothing the locally estimated velocity field using a Gaussian process regression. Application of this method to synthetic data provided by a state-of-the-art geodynamo simulation suggests that using this approach, the large-scale flow pattern of the core surface flow can be well reconstructed, while the flow amplitude tends to be underestimated. We compare these results with a core flow inversion using a Bayesian framework that incorporates statistics from numerical geodynamo models as prior information. We find that whether the latter method provides a more accurate recovery of the reference flow than the local estimation depends heavily on how realistic/relevant the chosen prior information is. Application to real geomagnetic data shows that both methods are able to reproduce the main features found in previous core flow studies. [ABSTRACT FROM AUTHOR]

The two discrete generators of the full Lorentz group O (1 , 3) in 4 D spacetime are typically chosen to be parity inversion symmetry P and time reversal symmetry T, which are responsible for the four topologically separate components of O (1 , 3) . Under general considerations of quantum field theory (QFT) with internal degrees of freedom, mirror symmetry is a natural extension of P, while C P symmetry resembles T in spacetime. In particular, mirror symmetry is critical as it doubles the full Dirac fermion representation in QFT and essentially introduces a new sector of mirror particles. Its close connection to T-duality and Calabi–Yau mirror symmetry in string theory is clarified. Extension beyond the Standard Model can then be constructed using both left- and right-handed heterotic strings guided by mirror symmetry. Many important implications such as supersymmetry, chiral anomalies, topological transitions, Higgs, neutrinos, and dark energy are discussed. [ABSTRACT FROM AUTHOR]

We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind-coherent sheaves on the moduli space of rank one de Rham local systems with a flat section. Our result establishes a conjecture coming out of the 3d mirror symmetry program, which obtains new compatibilities for the geometric Langlands program from rich dualities of QFTs that are themselves obtained from string theory conjectures. [ABSTRACT FROM AUTHOR]

We discuss the transformation of nonlocal two-qubit gates and symmetries possessed by Weyl chamber of two-qubit gates under mirror operation. We define the mirror operation as reflections about a specific set of planes of Weyl chamber in c-space which is spanned by Cartan coordinates. For the lines at the intersection of two specific reflecting planes, both the mirror operation and inverse operation cause the same transformation of Cartan coordinates. The point representing B-gate being the only common point to all reflecting planes, Cartan coordinates and all nonlocal characteristics of B-gate are invariant under mirror operation. In g-space which is spanned by local invariants, the mirror operation can be defined as parity transformation. With the point representing B-gate at the center of Weyl chamber, the mirror symmetry of Weyl chamber is apparent in g-space. In addition, we show that the gate typicality is a linear function of a local invariant and discuss its transformation under mirror operation. We also discuss the ability of a special perfect entangler (SPE) and its mirror gate to construct other nonlocal two-qubit gates and show that an SPE and its mirror together with local y-rotations can generate SWAP operation. Further, we propose universal two-qubit quantum circuits involving two applications of SPEs and local y-rotations. Finally, we propose a scheme to implement SPEs in ion-trap quantum computers which allows the usage of proposed universal two-qubit quantum circuits in quantum computation. We show that B -gate can generate all two-qubit gates in four applications with suitable single-qubit gates. In terms of implementation time, B -gate and one of the proposed universal two-qubit quantum circuits are advantageous over CNOT gate being used as entangling basis gate in ion-trap quantum computer. [ABSTRACT FROM AUTHOR]

Lorentz‐violating type‐II Dirac nodal line semimetals (DNLSs), hosting curves of band degeneracy formed by two dispersion branches with the same sign of slope, represent a novel state of matter. While being studied extensively in theory, convincing experimental evidence of type‐II DNLSs remain elusive. Recently, vanadium‐based kagome materials have emerged as a fertile ground to study the interplay between lattice symmetry and band topology. This work studies the low‐energy band structure of double‐kagome‐layered CsV8Sb12 and identifies it as a scarce type‐II DNLS protected by mirror symmetry. This work observes multiple DNLs consisting of type‐II Dirac cones close to or almost at the Fermi level via angle‐resolved photoemission spectroscopy (ARPES), which provides an electronic explanation for the nonsaturating magnetoresistance effect as observed. First‐principles theory analyses show that spin‐orbit coupling only opens a small gap, resulting in effectively gapless ARPES spectra, yet generating large spin Berry curvature. These type‐II DNLs, together with the interaction between a low‐energy van Hove singularity and quasi‐one‐dimensional band as observed in the same material, suggest CsV8Sb12 as an ideal platform for exploring novel transport properties. [ABSTRACT FROM AUTHOR]

Twins are common defects in β-Ga2O3 crystals that affect the development of large single crystal substrates. To investigate the generation and development of twins, we grew a (100) oriented β-Ga2O3 crystal using edge-defined film-fed growth (EFG). We characterized the (010) sample containing twins by polarized light stress meter, chemical etching, laser scanning confocal microscopy (LSCM) and transmission electron microscopy (TEM). The polarized light stress meter clearly distinguishes areas containing twins from those without. After H3PO4 etching at 150 °C for 1 h, LSCM observations revealed etch pits with mirror symmetry across the (100) twin boundary, with an angle of approximately 77° between the array of etch pits and the boundary. The twins originate at the boundary (102¯) along the [2¯01¯] direction, which is nearly perpendicular to the (100) plane, and then grow in steps on the side near the interior of the crystal. The twin boundary on the side near the edge of the crystal first undergoes stepwise extension and then gradually bends and grows, eventually forming a (100) twin boundary on both sides. TEM observations reveal a different arrangement of atomic density on either side of the twin boundary possessing the [2¯01¯] orientation component. Furthermore, both (102¯) and (100) are slip planes for the β-Ga2O3 crystal, indicating that the generation of twins is closely related to the slip plane. [ABSTRACT FROM AUTHOR]

Novel paradigms of strong ergodicity breaking have recently attracted significant attention in condensed matter physics. Understanding the exact conditions required for their emergence or breakdown not only sheds more light on thermalization and its absence in closed quantum many-body systems, but it also has potential benefits for applications in quantum information technology. A case of particular interest is many-body localization whose conditions are not yet fully settled. Here, we prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a non-degenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized–MBL). We provide evidence of delocalization at all energy densities and show that delocalization persists when the symmetry is broken. We use our results to construct two localized systems which, when coupled, delocalize each other. Our work demonstrates the dramatic effect symmetries can have on disordered systems, proves that the existence of exact resonances is not a sufficient condition for delocalization, and opens the door to generalization to higher spatial dimensions and different conservation laws. Many-body localization is an important example of non-ergodic behaviour, however the conditions for its existence and stability are not fully established. Kloss et al establish theoretically and numerically the absence of many-body localization in a broad class of spin models respecting certain symmetries. [ABSTRACT FROM AUTHOR]

We study the generation of homochirality in a general chemical model (based on the homogeneous, fully connected Smoluchowski aggregation-fragmentation model) that obeys thermodynamics and can be easily mapped onto known origin of life models (e.g. autocatalytic sets, hypercycles, etc.), with essential aspects of origin of life modeling taken into consideration. Using a combination of theoretical modeling and numerical simulations, we look for minimal conditions for which our general chemical model exhibits spontaneous mirror symmetry breaking. We show that our model spontaneously breaks mirror symmetry in various catalytic configurations that only involve a small number of catalyzed reactions and nothing else. Of particular importance is that mirror symmetry breaking occurs in our model without the need for single-step autocatalytis or mutual inhibition, which may be of relevance for prebiotic chemistry. [ABSTRACT FROM AUTHOR]

The target mono‐BF2 complex is weakly emissive in fluid solution because radiationless decay of the excited‐singlet state is promoted through an intramolecular N⋅⋅⋅H−N hydrogen bond. The lack of mirror symmetry for this compound is attributed to vibronic effects, as reported previously for the bis‐BF2 complex (BOPHY). Red‐shifted fluorescence is observed from single crystals, the emission quantum yield approaching 30 % with a fluorescence lifetime of 2 ns. The large Stokes shift of 5,700 cm−1 helps minimize self‐absorption. Crystallography indicates that the internal fold and twist angles are increased substantially in the crystal, but the hydrogen bond is weakened relative to solution. The crystal structure is compiled from pairs of head‐to‐tail molecules having a shift of ca. 4.1 Å and closest approach of ca. 3.5 Å. These molecular pairs are arranged in columns, which, in turn, assemble into sheets. The proximity favors excitonic coupling between individual molecules, with the coupling strength obtained by analysis of the absorption spectrum reaching ca. 1,000 cm−1. Both the ideal dipole approximation and the extended dipole methodology seriously overestimate the coupling strength, but the atomic transition charge density procedure leads to good agreement with experiment. Emission is attributed to the closely coupled molecular pair functioning in an excimer‐like manner with the exciton trapped in a local minimum. Increasing temperature causes a slight blue shift and loss of fluorescence. [ABSTRACT FROM AUTHOR]

Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for 3d N = 4 linear quivers and for their 4d N = 1 uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the 3d theories, where mirror symmetry is realized as S-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of S-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is SL(2, ℤ) in 3d and PSL(2, ℤ) in 4d. This also produces dualities for 3d N = 3 theories with Chern-Simons couplings, some of which have enhanced N = 4 supersymmetry, and their new 4d N = 1 counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany-Witten move in field theory. [ABSTRACT FROM AUTHOR]

Electromagnetic phenomena, such as magnetization switching, are guided by parity and time-reversal symmetries. Magnetic field and magnetization are time-odd axial vectors. Therefore, the magnetic field can switch magnetization reversibly. In contrast, the electric field is a time-even polar vector that cannot directly switch magnetization. For magnetic recording, an electrical coil-generated local magnetic field is used to switch the magnetic bit. However, in order to integrate the magnetic functionality, e.g., nonvolatile magnetic memory with high speed and low energy consumption, into the chip, it is essential to implement the magnetization switching by an electrical current, where the current induces other axial vectors through spin-transfer torque or spin–orbit torque (SOT). As an energy-efficient tool of magnetization switching, current-induced SOT has been intensively studied for the past decade, which holds great promise in the next generation of magnetic memories and magnetic logic devices [A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019); X. Han et al., Appl. Phys. Lett. 118, 120502 (2021); C. Song et al., Prog. Mater. Sci. 118, 100761 (2021); Q. Shao et al., IEEE Trans. Magn. 57, 21076639 (2021); J. Ryu et al., Adv. Mater. 32, 1907148 (2020); Y. Cao et al., iScience 23, 101614 (2020)]. In this review, we will first give the basic principle of the symmetry considerations for current-induced magnetization switching. Then, different methods to break the mirror symmetry for deterministic SOT switching will be discussed, together with examples that contain recent progress. In the end, we will give a discussion on the challenges and perspectives of the symmetry designs for SOT, which aim to inspire future fundamental studies and device applications. [ABSTRACT FROM AUTHOR]

Optical metasurfaces have great potential to overcome the functional limitations of conventional optical devices. In addition to polarization- or wavelength-multiplexed metasurfaces, angle-multiplexed metasurfaces can provide new degrees of freedom, enabling previously unrealized complex functionality in diverse applications such as LiDAR, augmented reality glasses, and imaging. However, there have been fundamental trade-offs in transmission efficiency and angular sensitivity for practically important paraxial rays. In this paper, we overcome this limitation by breaking mirror symmetries of single-layer metasurface structures. Based on an effective medium theory, we intuitively explain which material parameters affect the sensitivity and efficiency and prove that high sensitivity and high efficiency can be achieved simultaneously by breaking the mirror symmetry. Based on this, we propose optimized metasurfaces for two applications: an angle-multiplexed beam-steering device with up to 93% relative efficiency and an angle-multiplexed metalens array that can break the fundamental resolution–density trade-off of microlens arrays with high efficiency. The proposed angle-selective designs could pave the way for the development of new classes of compact optical devices with novel functions. [ABSTRACT FROM AUTHOR]

Ferroelectricity in ultrathin two-dimensional (2D) materials has attracted broad interest due to potential applications in nonvolatile memory, nanoelectronics and optoelectronics. However, ferroelectricity is barely explored in materials with native centro or mirror symmetry, especially in the 2D limit. Here, we report the first experimental realization of room-temperature ferroelectricity in van der Waals layered GaSe down to monolayer with mirror symmetric structures, which exhibits strong intercorrelated out-of-plane and in-plane electric polarization. The origin of ferroelectricity in GaSe comes from intralayer sliding of the Se atomic sublayers, which breaks the local structural mirror symmetry and forms dipole moment alignment. Ferroelectric switching is demonstrated in nano devices fabricated with GaSe nanoflakes, which exhibit exotic nonvolatile memory behavior with a high channel current on/off ratio. Our work reveals that intralayer sliding is a new approach to generate ferroelectricity within mirror symmetric monolayer, and offers great opportunity for novel nonvolatile memory devices and optoelectronics applications. Here, the authors observe room-temperature ferroelectricity in van der Waals layered GaSe down to monolayer with mirror symmetric structures and attribute it to the intralayer sliding of the Se atomic sublayers. [ABSTRACT FROM AUTHOR]

We study the mirror symmetry on the singular locus of the Hitchin system at two levels. First, by covering it by (supports of) (BBB)‐branes, corresponding to Higgs bundles reducing their structure group to the Levi subgroup of some parabolic subgroup P, whose conjectural dual (BAA)‐branes we describe. Heuristically speaking, the latter are given by Higgs bundles reducing their structure group to the unipotent radical of P. Second, when P is a Borel subgroup, we are able to construct a family of hyperholomorphic bundles on the (BBB)‐brane and study the variation of the dual under this choice. We give evidence of both families of branes being dual under mirror symmetry via an integral functor induced by Fourier–Mukai in the moduli stack of Higgs bundles. [ABSTRACT FROM AUTHOR]

Biomolecules are frequently chiral compounds, existing in enantiomeric forms. Amino acids represent a meaningful example of chiral biological molecules. Both L- and D-amino acids play key roles in the biochemical structure and metabolic processes of living organisms, from bacteria to mammals. In this review, we explore the enantiospecific interaction between proteins and chiral amino acids, introducing theoretical models and describing the molecular basis of the ability of some of the most important enzymes involved in the metabolism of amino acids (i.e., amino acid oxidases, dehydrogenases, and aminotransferases) to discriminate the opposite enantiomers. Our analysis showcases the power of natural evolution in shaping biological processes. Accordingly, the importance of amino acids spurred nature to evolve strictly enantioselective enzymes both through divergent evolution, starting from a common ancestral protein, or through convergent evolution, starting from different scaffolds: intriguingly, the active sites of these enzymes are frequently related by a mirror symmetry. [ABSTRACT FROM AUTHOR]

We compute genus zero correlators of hybrid phases of Calabi-Yau gauged linear sigma models (GLSMs), i.e. of phases that are Landau-Ginzburg orbifolds fibered over some base. These correlators are generalisations of Gromov-Witten and FJRW invariants. Using previous results on the structure of the of the sphere- and hemisphere partition functions of GLSMs when evaluated in different phases, we extract the I-function and the J-function from a GLSM calculation. The J-function is the generating function of the correlators. We use the field theoretic description of hybrid models to identify the states that are inserted in these correlators. We compute the invariants for examples of one- and two-parameter hybrid models. Our results match with results from mirror symmetry and FJRW theory. [ABSTRACT FROM AUTHOR]

Gyrocheilos is a small genus of Gesneriaceae endemic to hight altitude mountains in Southwest China and Guangdong Province, with only five species. This genus is characterized by laterally bending style, which curves 90° at the top of the style and the stigma right at the mouth of floral tube. This unusual floral trait may have special evolutionary and adaptive mechanisms. In this paper, three Gyrocheilos species, i.e. G. chorisepalus, G. retrotrichus, G. microtrichus were examined to figure out the developmental patterns of floral lateral bending. Breeding systems, floral syndrome and pollination processes were also studied in G. retrotrichus at Dawuling Mountain, Guangdong Province, to explore its pollination adaptations. The results were as follows: (1) G. microtrichus had only left-bending style, while right-bending style were observed in several flowers (2% -3% of the total flowers) of G. chorisepalus and G. retrotrichus, although the individuals and populations were dominated by left-bending style. (2) Pollination observation found that style lateral bending occurred at the early stage of floral bud in G. retrotrichus, with two fertile stamens were anther-united and hidden at the middle of the floral throat, and there was no left and right mirror symmetry relationship with the lateral style. (3) The pollen-ovule ratio (P/O) was (456.98 ± 15.55), belonging to facultative outcross breeding system. G. retrotrichus had a certain pollen limitation and self-pollination, but the germination rate of outcross seeds was higher, and there might be inbreeding decline. (4) There were few floral visitors and the frequency was low of G. retrotrichus. The main floral visitors were Halictidae, Bombus and Syrphidae. Bombus were large, and they landed on the bent style and the lower lip of the petals when visiting flowers. The side and lower part of the chest could effectively contact the stigma. (5) The detected reflected lights of flowers were composed of purple and blue-purple lights and the lower lips and outer floral tube with the highest reflection intensity, more likely to attract bees to land on the corolla's lower lip. Molecular phylogeny indicated that the closest genus of Gyrocheilos was Didymorcarpus, which was characterized by style downward bending and mirror-image flowers, suggesting the style lateral bending in Gyrocheilos probably evolved from either of these conditions. In conclusion, the lateral bending style might provide landing platform for pollinators and the stigma above the lower lips increase contact probability the floral visitors, which is an adaptation to the very low insect visitation due to fragmented and foggy habitats in high altitude areas. [ABSTRACT FROM AUTHOR]

Rectangular billiards have two mirror symmetries with respect to perpendicular axes and a twofold (fourfold) rotational symmetry for differing (equal) side lengths. The eigenstates of rectangular neutrino billiards (NBs), which consist of a spin-1/2 particle confined through boundary conditions to a planar domain, can be classified according to their transformation properties under rotation by π ( π / 2 ) but not under reflection at mirror-symmetry axes. We analyze the properties of these symmetry-projected eigenstates and of the corresponding symmetry-reduced NBs which are obtained by cutting them along their diagonal, yielding right-triangle NBs. Independently of the ratio of their side lengths, the spectral properties of the symmetry-projected eigenstates of the rectangular NBs follow semi-Poisson statistics, whereas those of the complete eigenvalue sequence exhibit Poissonian statistics. Thus, in distinction to their nonrelativistic counterpart, they behave like typical quantum systems with an integrable classical limit whose eigenstates are non-degenerate and have alternating symmetry properties with increasing state number. In addition, we found out that for right triangles which exhibit semi-Poisson statistics in the nonrelativistic limit, the spectral properties of the corresponding ultrarelativistic NB follow quarter-Poisson statistics. Furthermore, we analyzed wave-function properties and discovered for the right-triangle NBs the same scarred wave functions as for the nonrelativistic ones. [ABSTRACT FROM AUTHOR]

Topological crystalline insulators (TCIs) can host anomalous surface states which inherits the characteristics of crystalline symmetry that protects the bulk topology. Especially, the diversity of magnetic crystalline symmetries indicates the potential for novel magnetic TCIs with distinct surface characteristics. Here, we propose a topological magnetic Dirac insulator (TMDI), whose two-dimensional surface hosts fourfold-degenerate Dirac fermions protected by either the p c ′ 4 m m or p 4 ′ g ′ m magnetic wallpaper group. The bulk topology of TMDIs is protected by diagonal mirror symmetries, which give chiral dispersion of surface Dirac fermions and mirror-protected hinge modes. We propose candidate materials for TMDIs including Nd4Te8Cl4O20 and DyB4 based on first-principles calculations, and construct a general scheme for searching TMDIs using the space group of paramagnetic parent states. Our theoretical discovery of TMDIs will facilitate future research on magnetic TCIs and illustrate a distinct way to achieve anomalous surface states in magnetic crystals. [ABSTRACT FROM AUTHOR]

This survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs (X , D) with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X , D) , including the log Gromov–Witten invariants of the pair, the Gromov–Witten invariants of an associated higher dimensional Calabi–Yau variety, the open Gromov–Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed BPS-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants. [ABSTRACT FROM AUTHOR]

Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi–Yau manifolds, which is now called the BCOV torsion. Based on it, a metric-independent invariant, called BCOV invariant, was constructed by Fang–Lu–Yoshikawa and Eriksson–Freixas i Montplet–Mourougane. The BCOV invariant is conjecturally related to the Gromov–Witten theory via mirror symmetry. Based upon previous work of the second author, we prove the conjecture that birational Calabi–Yau manifolds have the same BCOV invariant. We also extend the construction of the BCOV invariant to Calabi–Yau varieties with Kawamata log terminal singularities, and prove its birational invariance for Calabi–Yau varieties with canonical singularities. We provide an interpretation of our construction using the theory of motivic integration. [ABSTRACT FROM AUTHOR]

This paper reviews the puzzles in modern neutron lifetime measurements and related unitarity issues in the CKM matrix. It is not a comprehensive and unbiased compilation of all historic data and studies, but rather a focus on compelling evidence leading to new physics. In particular, the largely overlooked nuances of different techniques applied in material and magnetic trap experiments are clarified. Further detailed analysis shows that the "beam" approach of neutron lifetime measurements is likely to give the "true" β -decay lifetime, while discrepancies in "bottle" measurements indicate new physics at play. The most feasible solution to these puzzles is a newly proposed ordinary-mirror neutron ( n − n ′ ) oscillation model under the framework of mirror matter theory. This phenomenological model is reviewed and introduced, and its explanations of the neutron lifetime anomaly and possible non-unitarity of the CKM matrix are presented. Most importantly, various new experimental proposals, especially lifetime measurements with small/narrow magnetic traps or under super-strong magnetic fields, are discussed in order to test the surprisingly large anomalous signals that are uniquely predicted by this new n − n ′ oscillation model. [ABSTRACT FROM AUTHOR]

This paper studies a notion of enumerative invariants for stable A-branes and discusses its relation to invariants defined by spectral and exponential networks. A natural definition of stable A-branes and their counts is provided by the string theoretic origin of the topological A-model. This is the Witten index of the supersymmetric quantum mechanics of a single D3 brane supported on a special Lagrangian in a Calabi–Yau threefold. Geometrically, this is closely related to the Euler characteristic of the A-brane moduli space. Using the natural torus action on this moduli space, we reduce the computation of its Euler characteristic to a count of fixed points via equivariant localization. Studying the A-branes that correspond to fixed points, we make contact with definitions of spectral and exponential networks. We find agreement between the counts defined via the Witten index, and the BPS invariants defined by networks. By extension, our definition also matches with Donaldson–Thomas invariants of B-branes related by homological mirror symmetry. [ABSTRACT FROM AUTHOR]

A model of symmetry breaking is described for a system that may spontaneously choose between a left-handed and a right-handed weak current. For a hierarchic structure of the fermion mass spectrum, this mirror-symmetric system permits reproducing all qualitative properties of the weak-mixing matrices for both quarks (CKM matrix) and leptons (PMNS matrix) without numerically adjusting model parameters. The hierarchy of the CKM matrix elements is directly related to the hierarchic mass spectrum of quark generations. Qualitative properties of the PMNS matrix arise in the case where the spectrum has an inverse character ( is the smallest mass) and where the Standard Model neutrino is a Dirac particle. A relative smallness of the neutrino-mixing angle is due here to the smallness of and the smallness of the charged-lepton mass ratio . [ABSTRACT FROM AUTHOR]

In this short note we describe the isomorphism of generalized complex structure between T -dual manifolds introduced by Cavalcanti-Gualtieri, in the case of elliptic curves. We also compare this isomorphism with the mirror map for elliptic curves described by Polishchuk and Zaslow. [ABSTRACT FROM AUTHOR]

In toroidal pipes, the secondary flow in cross section is a mirror symmetric pair of counter-rotating axially oriented Dean vortices. This mirror symmetry is broken in helical pipes. We investigate in detail the mirror symmetry breaking in these secondary flows in going from toroidal to helical geometries. We quantify the degree of mirror symmetry breaking in helical flows by calculating both an (i) order-parameter − 1 ≤ χ ≤ 1 that measures the net integrated chirality of vortices in section and (ii) the entropy production due to both viscous shear forces and convection for Dean vortices as the Dean number and pitch of the helix are varied. We prove that the entropy production due to convective processes is always greater than that due to viscous shear, for stationary incompressible flows in the absence of body forces. For the same pipe radius and pipe curvature, fluid density, viscosity, and entrance flows, the vortex entropy production in the stationary state is minimized for helical conduits (for a given Dean number) with respect to that of toroidal pipes (zero pitch). The dissipation in the fluid flow due to Dean vortices decreases in going from a toroidal to a helical geometry, while the chiral order parameter tends to χ = ± 1 for finite values of the pitch as the Dean number is decreased. [ABSTRACT FROM AUTHOR]

Unlike electrons, phonons do not have the charge and spin degrees of freedom. Consequently, it is a big challenge for the control of phonon currents and the design of quantum phonon devices due to the lack of versatile degrees of freedom. In this work, we show that phonon bands of mirror-symmetric materials can be labeled by parities, which can act as a pseudospin of phonons. As a proof-of-concept, we show that perfect pseudospin filtering can be realized using mirror-symmetric graphene-nanoribbon heterojunctions. In addition, we show that the filtering takes place within a remarkably short length scale of just 3 nanometers. Our work reveals an intriguing new facet of phonon behavior and also underscores the immense potential of utilizing phonons as information carriers.

Based on the mathematical model of a nonlinear finance system, a novel finance chaotic system that generates mirror symmetric multiscroll chaotic attractors is proposed in this paper. The chaotic dynamical behaviors such as symmetry, chaoticity, bifurcation and boundedness are discussed in detail for the finance system with state variables; interest rate, investment demand and price index. The complex composite symmetrical attractors of finance system with different magnitudes are obtained. Moreover, with the help of multilevel-logic pulse signal, the generation of two pairs of different magnitudes symmetrical attractors are explored. The novel grid composite multiscroll chaotic attractors is one of the most interesting result is found in the finance system. By adjusting the parameters of multilevel-logic pulse signals, the finance system is controlled and a novel grid composite multiscroll chaotic attractor is explored in this article. [ABSTRACT FROM AUTHOR]

We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On the algebro-geometric side, we introduce a new method based on symplectic flexibility and mirror symmetry to bound the Rouquier dimension of derived categories of coherent sheaves on certain complex algebraic varieties and stacks. These bounds are sharp in dimension at most $3$. As an application, we resolve a well-known conjecture of Orlov for new classes of examples (e.g. toric $3$ -folds, certain log Calabi–Yau surfaces). We also discuss applications to non-commutative motives on partially wrapped Fukaya categories. On the symplectic side, we study various quantitative questions including the following. (1) Given a Weinstein manifold, what is the minimal number of intersection points between the skeleton and its image under a generic compactly supported Hamiltonian diffeomorphism? (2) What is the minimal number of critical points of a Lefschetz fibration on a Liouville manifold with Weinstein fibers? We give lower bounds for these quantities which are to the best of the authors' knowledge the first to go beyond the basic flexible/rigid dichotomy. [ABSTRACT FROM AUTHOR]

The framework of the tight-binding model and Green's function formalism have been derived to investigate the electronic properties of few-layer T-graphene nanoribbons (TGNRs) with different edges including zigzag, bearded, and armchair TGNR (zTGNR, bTGNR, and aTGNR) and the results are compared with those of monolayers. It was observed that single-layer zTGNRs and bTGNRs with metallic properties retain this characteristic as the number of layers increases. In addition, by virtue of their mirror symmetry, aTGNR monolayers exhibit metallic and semiconducting properties by even and odd widths, respectively. When layers are added, symmetric aTGNRs display metallic behavior, while asymmetric aTGNRs display metallic and semiconducting characteristics, depending on the layer stacking. It is also found that the band structure of symmetric aTGNRs and metallic few-layer asymmetric aTGNRs contain Dirac points which increase with increasing their width and layers. [ABSTRACT FROM AUTHOR]

In this paper, the temperature dependence of defect modes of several one-dimensional superconducting-dielectrics photonic crystals was studied implementing the matrix transformation method. The thermo-optical effect and the thermal expansion effect were considered for a closer look (to obtain more accurate results). The studied photonic crystals contained SiO2 (L), Bi4Ge3O12 (H), MoSe2 (M) dielectrics, and the YBa2Cu3O7 (S) superconductor. Our results indicated that among the considered photonic crystals, the (HLM)NS(MLH)NL structure had the most temperature sensitivity, which could be applied as a low-temperature sensor and a tunable filter. The thickness of the layers was assumed in the nano-meter range. In order to validate our method, we compared our simulation result with an available experimental data in the literature. [ABSTRACT FROM AUTHOR]

Background: Plant shape and structure are important factors in peanut breeding research. Constructing a three-dimension (3D) model can provide an effective digital tool for comprehensive and quantitative analysis of peanut plant structure. Fast and accurate are always the goals of the plant 3D model reconstruction research. Results: We proposed a 3D reconstruction method based on dual RGB-D cameras for the peanut plant 3D model quickly and accurately. The two Kinect v2 were mirror symmetry placed on both sides of the peanut plant, and the point cloud data obtained were filtered twice to remove noise interference. After rotation and translation based on the corresponding geometric relationship, the point cloud acquired by the two Kinect v2 was converted to the same coordinate system and spliced into the 3D structure of the peanut plant. The experiment was conducted at various growth stages based on twenty potted peanuts. The plant traits' height, width, length, and volume were calculated through the reconstructed 3D models, and manual measurement was also carried out during the experiment processing. The accuracy of the 3D model was evaluated through a synthetic coefficient, which was generated by calculating the average accuracy of the four traits. The test result showed that the average accuracy of the reconstructed peanut plant 3D model by this method is 93.42%. A comparative experiment with the iterative closest point (ICP) algorithm, a widely used 3D modeling algorithm, was additionally implemented to test the rapidity of this method. The test result shows that the proposed method is 2.54 times faster with approximated accuracy compared to the ICP method. Conclusions: The reconstruction method for the 3D model of the peanut plant described in this paper is capable of rapidly and accurately establishing a 3D model of the peanut plant while also meeting the modeling requirements for other species' breeding processes. This study offers a potential tool to further explore the 3D model for improving traits and agronomic qualities of plants. [ABSTRACT FROM AUTHOR]

Applying tensile strain on an intrinsic lattice always results in the reduction in thermal conductivity due to the red-shift of phonon frequency and enhanced phonon anharmonicity. However, in this work, we explored an unexpected strain-enhanced thermal conductivity of a planar biphenylene network (BPN) in the frame of a Boltzmann transport equation combined with the machine learning interatomic potential. Under 5% biaxial tensile strain, the room temperature thermal conductivity of BPN reaches to about 4–5 times of that in an intrinsic sample. This phenomenon can be understood by considering a mirror symmetry induced phonon selection rule. This work highlights the significant effect of the selection rule on thermal transport and enriches the understanding of the thermal conductivity regulation in strained two-dimensional materials. [ABSTRACT FROM AUTHOR]

We introduce algebraic structures on the polyvector fields of an algebraic torus that serve to compute multiplicities in tropical and log Gromov–Witten theory while also connecting to the mirror symmetry dual deformation theory of complex structures. Most notably these structures include a tropical quantum field theory and an |$L_{\infty }$| -structure. The latter is an instance of Getzler's gravity algebra, and the |$l_2$| -bracket is a restriction of the Schouten–Nijenhuis bracket. We explain the relationship to string topology in the Appendix (thanks to Janko Latschev). [ABSTRACT FROM AUTHOR]

Calabi-Yau threefolds with infinitely many flops to isomorphic manifolds have an extended Kähler cone made up from an infinite number of individual Kähler cones. These cones are related by reflection symmetries across flop walls. We study the implications of this cone structure for mirror symmetry, by considering the instanton part of the prepotential in Calabi-Yau threefolds. We show that such isomorphic flops across facets of the Kähler cone boundary give rise to symmetry groups isomorphic to Coxeter groups. In the dual Mori cone, non-flopping curve classes that are identified under these groups have the same Gopakumar-Vafa invariants. This leads to instanton prepotentials invariant under Coxeter groups, which we make manifest by introducing appropriate invariant functions. For some cases, these functions can be expressed in terms of theta functions whose appearance can be linked to an elliptic fibration structure of the Calabi-Yau manifold. [ABSTRACT FROM AUTHOR]

Let X be a smooth projective variety with a simple normal crossing divisor D : = D 1 + D 2 + ⋯ + D n , where D i ⊂ X are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks X D , r → by constructing an I-function lying in a slice of Givental's Lagrangian cone for Gromov–Witten theory of multi-root stacks. We provide three applications: (1) We show that some genus zero invariants of X D , r → stabilize for sufficiently large r → . (2) We state a generalized local-log-orbifold principle conjecture and prove a version of it. (3) We show that regularized quantum periods of Fano varieties coincide with classical periods of the mirror Landau–Ginzburg potentials using orbifold invariants of X D , r → . [ABSTRACT FROM AUTHOR]

In this paper, we propose a geometrical proof of the generalized mirror transformation of genus 0 Gromov–Witten invariants of degree k hypersurface in C P N − 1 . [ABSTRACT FROM AUTHOR]