Search

This paper is devoted to systematically extend $f$-mirror symmetry between families of hypersurfaces in complete toric varieties, as introduced in \cite{R-fTV}, to families of complete intersections subvarieties. Namely, $f$-mirror symmetry is induced by framed duality of framed toric varieties extending Batyrev-Borisov polar duality between Fano toric varieties. Framed duality has been defined and essentially well described for families of hypersurfaces in toric varieties in the previous \cite{R-fTV}. Here it is developed for families of complete intersections, allowing us to strengthening some previous results on hypersurfaces. In particular, the class of projective complete intersections and their mirror partners are studied in detail. Moreover, a (generalized) Landau-Ginzburg/Complete-Intersection correspondence is discussed, extending to the complete intersection setup the LG/CY correspondence firstly studied Chiodo-Ruan and Krawitz., Comment: v4: Abstract and Introduction modified and some other minor modifications, according with the Referee's report. Final version to be published in the Journal of Geometry and Physics; 57 pages

Symmetry perception in dot patterns is tolerant to temporal delays of up to 60 ms within and between element pairs. However, it is not known how factors effecting symmetry discrimination in static patterns might affect temporal integration in dynamic patterns. One such feature is luminance polarity. Using dynamic stimuli with increasing temporal delay (SOA) between the onset of the first and second element in a symmetric pair, we investigated how four different luminance-polarity conditions affected the temporal integration of symmetric patterns. All four luminance polarity conditions showed similar upper temporal limits of approximately 60 ms. However psychophysical performance over all delay durations showed significantly higher symmetry thresholds for unmatched-polarity patterns at short delays, but also significantly less sensitivity to increasing temporal delay relative to matched-polarity patterns. These varying temporal windows are consistent with the involvement of a fast, sensitive first-order mechanism for matched-polarity patterns, and a slower, more robust second-order mechanism for unmatched-polarity patterns. Temporal integration windows for unmatched-polarity patterns were not consistent with performance expected from attentional mechanisms alone, and instead supports the involvement of second-order mechanisms that combines information from ON and OFF channels.

A 2D supercell photonic crystal consisting of dielectric cylindrical rods in air medium was used to study the effect of symmetry of the defects on the resonance modes. A single defect was introduced at every possible position in the crystal and the transmission properties were studied. When a defect is introduced on an axis which passes through the centre of the crystal and is perpendicular to the direction of propagation of EM wave, the mirror symmetry along an axis passing through the centre of the supercell ( S oy axis) is preserved. When a defect is introduced on an axis that passes through the centre of the crystal and is parallel to the direction of propagation of EM wave, the mirror symmetry along the axis S ox passing through the centre of the supercell is preserved but the mirror symmetry along S oy is broken. However, when the defect is placed at the centre of the crystal, the mirror symmetries is preserved along both the axes defined in the supercell. It is seen that TM mode needs to see mirror symmetry in the direction of propagation within the supercell, (mirror symmetry of defects with respect to S oy axis) in order to produce a strong resonance peak. However the presence of mirror symmetry along S ox seems to have little to no effect on the resonance peak. The single defects placed on the E ∥ and E ⊥ axes passing through the centre of the crystal and their respective supercell defect modes have been discussed in this paper.

Generally speaking, a spiral is a 2D curve which winds about a fixed point. Now, we present a new, alternative, and easy way to describe and generate spirals by means of the use of the Slope Chain Code (SCC) [E. Bribiesca, A measure of tortuosity based on chain coding, Pattern Recognition 46 (2013) 716-724]. Thus, each spiral is represented by only one chain. The chain elements produce a finite alphabet which allows us to use grammatical techniques for spiral classification. Spirals are composed of constant straight-line segments and their chain elements are obtained by calculating the slope changes between contiguous straight-line segments (angle of contingence) scaled to a continuous range from − 1 ( − 180 ∘ ) to 1 (180 ∘ ). The SCC notation is invariant under translation, rotation, optionally under scaling, and it does not use a grid. Other interesting properties can be derived from this notation, such as: the mirror symmetry and inverse spirals, the accumulated slope, the slope change mean, and tortuosity for spirals. We introduce new concepts of projective polygonal paths and osculating polygons. We present a new spiral called the SCC polygonal spiral and its chain which is described by the numerical sequence 2 n for n ≥ 3, to the best of our knowledge this is the first time that this spiral and its chain are presented. The importance of this spiral and its chain is that this chain is covering all the slope changes of all the regular polygons composed of n edges (n-gons). Also, we describe the chain which generates the spiral of Archimedes. Finally, we present some results of different kind of spirals from the real world, including spiral patterns in shells.

In this manuscript we investigate one-way wave propagation in spatio-temporal phononic wave-guides in which the modulation of material properties is provided piecewise in space and time. Non-reciprocal dispersion diagram is computed using a generalized plane wave expansion method, whose formulation, provided in the paper, is able to describe how a generic discrete or continuous unit cell is able to break the mirror symmetry in the momentum space, as already shown in other works by means of more expensive and less accurate computational tools. The proposed method is then used to verify a physical interpretation we provided for bandgap formation by means of wave superposition in spatio-temporal modulated waveguides.

It was shown by Kuznetsov that complete intersections of n generic quadrics in P 2 n − 1 are related by Homological Projective Duality to certain non-commutative (Clifford) varieties which are in some sense birational to double covers of P n − 1 ramified over symmetric determinantal hypersurfaces. Mirror symmetry predicts that the Hodge numbers of the complete intersections of quadrics must coincide with the appropriately defined Hodge numbers of these double covers. We observe that these numbers must be different from the well-known Batyrev's stringy Hodge numbers, else the equality fails already at the level of Euler characteristics. We define a natural modification of stringy Hodge numbers for the particular class of Clifford varieties, and prove the corresponding equality of Euler characteristics in arbitrary dimension.

We carry out the SYZ program for the local Calabi–Yau manifolds of type A ˜ by developing an equivariant SYZ theory for the toric Calabi–Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov–Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood–Iqbal–Vafa (Hollowood et al., 2008).

Starting from the Kahler moduli space of the rigid orbifold Z = E 3 ∕ Z 3 one would expect for the cohomology of the generalized mirror to be a Hodge structure of Calabi–Yau type ( 1 , 9 , 9 , 1 ) . We show that such a structure arises in a natural way from rational Hodge structures on Λ 3 Q [ ω ] 6 , where ω is a primitive third root of unity. We do not try to identify an underlying mirror geometry, but we show how special geometry arises in our abstract construction. We also show how such Hodge structure can be recovered as a polarized substructure of a bigger Hodge structure given by the third cohomology group of a six-dimensional abelian variety of Weil-type. Moreover, we recover a result of Zheng Zhang on the associates variation of Hodge structure.

In this work, we theoretically investigate the evolution of the soliton pairs in strongly nonlocal nonlinear media, which is modeled by the nonlocal nonlinear Schrodinger equation. Taking two pairs of solitons as an example, which initial incident directions have a mirror symmetry, a set of mathematical expressions are derived to describe the soliton pairs’ propagation, the soliton spacing, the area of the optical field. The results demonstrate that the motion state of the soliton pairs is mirror-symmetry. Numerical simulations are carried out to illustrate the quintessential propagation properties.

This paper describes an angular acceleration sensor that uses liquid ring channels and piezoresistive cantilevers. The detection of fluidic rotation has attracted attention as a sensing principle for angular acceleration due to the simple structure and potentially low power consumption of devices that use said principle. Although the existing angular acceleration sensors that use this sensing principle have the potential for high sensitivity to angular acceleration about the target axis, crosstalk is an issue—specifically, crosstalk with angular accelerations about other axes and with linear acceleration. Here, we propose an angular acceleration sensor that uses a MEMS piezoresistive cantilever as the sensing element and two mirror-symmetric ring channels. This mirror symmetry cancels out the signals due to accelerations about the other axes, while the signal for the angular acceleration about the target axis is doubled. The experimental results show that the sensitivity to other axial angular accelerations and linear acceleration is sufficiently small. The obtained sensitivity for the angular acceleration is as high as 3.1 × 10−4 (rad/s2)-1, similar to theoretical predictions. This value for the sensitivity is maintained over a range of frequencies from 0.1 Hz to 100 Hz. Therefore, the proposed sensor is suitable for practical angular acceleration detection applications.

Symmetry is an important feature in natural and man-made objects; particularly, mirror symmetry is a relevant task in fields such as computer vision and pattern recognition. In the current work, we propose a new method to characterize mirror-symmetry in open and closed curves represented by means of the Slope Chain Code. This representation is invariant under scale, rotation, and translation, highly desirable properties for object recognition applications. The proposed method detects symmetries through simple inversion, concatenation and reflection operations on the chains, thus allowing the classification of symmetrical and asymmetrical contours. It also introduces a measure to quantify the degree of symmetry in quasi-mirror-symmetrical objects. Furthermore, it allows the identification of multiple symmetry axes and their location. Results show high performances in symmetrical/asymmetrical classification (0.9 recall, 0.9 accuracy, 0.97 precision) and axes’ detection (0.8 recall, 0.84 accuracy, 0.99 precision). Compared to other methods, the proposed algorithm provides properties such as: global, local, and multiple axes’ detection, as well as the capability to classify symmetrical objects, which makes it adequate for several practical applications, like the three exemplified in the paper.

We consider a definition of the Fukaya category of a singular hypersurface proposed by Auroux, given by localizing the Fukaya category of a nearby fiber at Seidel's natural transformation, and show that this possesses several desirable properties. Firstly, we prove an A-side analog of Orlov's derived Kn\"orrer periodicity theorem by showing that Auroux' category is derived equivalent to the Fukaya-Seidel category of a higher-dimensional Landau-Ginzburg model. Secondly, we describe how this definition should imply homological mirror symmetry at various large complex structure limits, in the context of forthcoming work of Abouzaid-Auroux and Abouzaid-Gross-Siebert., Comment: v2: 34 pages, 11 figures; clarified statements of theorems; updated to reflect referee's suggestions, to appear in Adv. Math

In this work, high resolution transmission electron microscopy and numerical simulation at the atomic scale were coupled, for the first time to our knowledge, to study the atomic structure of two Σ5 symmetric tilt grain boundaries in uranium dioxide (UO2) bicrystals. We show that whereas the Σ5 (021)/[100] is fully symmetric, with the grain boundary plane forming a mirror symmetry plane, a rigid body translation exists between the crystals in the Σ5 (031)/[100]. We particularly believe that the excellent agreement between experimentally observed and simulated structures highlights the relevance of the coupled approach. Such result emphasize that the use of CRG and Yakub empirical potentials including a Morse contribution can be relied upon to model the behavior of UO2.

We study quantum-state transfer in XX spin-1/2 chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modeled by long-range correlated sequences with self-similar profile obeying a power-law spectrum. We show that the channel is able to perform almost perfect quantum-state transmissions even in the presence of significant amounts of disorder provided the degree of those correlations is strong enough, with the cost of having long transfer times and unavoidable timing errors. Still, we show that the lack of mirror symmetry in the channel does not affect much the likelihood of having high-quality outcomes. Our results suggest that coexistence between localized and delocalized states can diminish effects of static perturbations in solid-state devices for quantum communication.

In this paper we investigate the idea of a tropical critical point of the superpotential for the full flag variety of type A. Recall that associated to an irreducible representation of G = S L n ( C ) are various polytopes whose integral points parameterize a basis for the representation, e.g. the Gelfand–Zetlin polytope. Such polytopes can be constructed via the theory of geometric crystals by tropicalising a certain function, and in fact, the function involved coincides with the superpotential from the Landau–Ginzburg model for G / B coming from mirror symmetry. In mirror symmetry a special role is played by the critical points of the superpotential, and motivated by this, we give a definition of the tropical critical points and use it to find a canonical point in each polytope. We then characterise the highest weights for which this tropical critical point is integral and therefore corresponds to a basis vector of the corresponding representation. Finally we give an interpretation of the tropical critical point by constructing a special vector in the representation using Borel–Weil theory and conjecturing a correspondence between this vector and the tropical critical point.

We prove a version of equivariant split generation of Fukaya category when a symplectic manifold admits a free action of a finite group $G$. Combining this with some generalizations of Seidel's algebraic frameworks from Seidel's book, we obtain new cases of homological mirror symmetry for some symplectic tori with non-split symplectic forms, which we call \textit{special isogenous tori}. This extends the work of Abouzaid-Smith. We also show that derived Fukaya categories are complete invariants of special isogenous tori., 42 pages

The incorporation of Wilson lines leads to an extension of the modular symmetries of string compactification beyond SL ( 2 , Z ) . In the simplest case with one Wilson line Z, Kahler modulus T and complex structure modulus U, we are led to the Siegel modular group Sp ( 4 , Z ) . It includes SL ( 2 , Z ) T × SL ( 2 , Z ) U as well as Z 2 mirror symmetry, which interchanges T and U. Possible applications to flavor physics of the Standard Model require the study of orbifolds of Sp ( 4 , Z ) to obtain chiral fermions. We identify the 13 possible orbifolds and determine their modular flavor symmetries as subgroups of Sp ( 4 , Z ) . Some cases correspond to symmetric orbifolds that extend previously discussed cases of SL ( 2 , Z ) . Others are based on asymmetric orbifold twists (including mirror symmetry) that do no longer allow for a simple intuitive geometrical interpretation and require further study. Sometimes they can be mapped back to symmetric orbifolds with quantized Wilson lines. The symmetries of Sp ( 4 , Z ) reveal exciting new aspects of modular symmetries with promising applications to flavor model building.

Circular dichroism of chiral structure can be used in biological sensing and analytical chemistry, which has been extensively explored. However, previous studies on chiral structures are mainly focused on geometric symmetry breaking, further investigation about the effect of the near-field perturbation on the chirality remains unrevealed. In this paper, circular dichroism of the honeycomb-shaped elliptical hole structure is investigated. By discussing the impact of the period of the structure on chirality, it is found that the near-field perturbation can trigger strong circular dichroism without breaking the rotational symmetry and mirror symmetry. Furthermore, the distributions of electric field and Poynting vector are studied to confirm the effect of the near-field perturbation. We believe that our work not only facilitates the understanding between the circularly polarized light and matter, but also provides a new approach for designing chiral structures.

Janus structures have attracted wide attention because they break the mirror symmetry of two-dimensional (2D) material monolayer structures and make the materials very easy to obtain piezoelectric properties. However, there are few reports about 2D Janus piezoelectric materials with polyatomic thickness. In this paper, we study the piezoelectric properties of Janus Bi2X2Y (X = S, Se, Te; Y = S, Se, Te; X ≠ Y) monolayers with polyatomic thickness. They all contain large in-plane piezoelectric coefficient d11, of which the d11 of 2D Bi2Te2S monolayer up to 34.96 pm/V. It is an order of magnitude larger than the previously reported d11 of MoS2. We believe that Janus Bi2Te2S monolayers have potential in the application of micro-nano piezoelectric devices and flexible electronic devices, and broaden the choice of 2D piezoelectric materials in polyatomic thickness.

Problems with diffusing probability distribution in the presence of sink traps, where the moving entity can be a particle, an entity, or a relevant coordinate in a reaction can represent a variety of physical processes. So far, the theoretical solutions gave time-domain understanding only if the problem had a translational invariance in potential or a mirror symmetry about the trap or the both. In this paper, we present a time-domain solution for diffusion in the presence of a harmonic potential well ( V ( x ) = 1 2 kx 2 ) with a finite absorbing sink S ( x , t ) . Considering the Smoluchowski equation as the governing equation for the process, a special exit condition given by, S ( x , t ) = k 0 e kt δ ( x - x c e - kt ) can be solved analytically using variable transformations from a simple model. Interesting insights into the diffusion dynamics emerge from the interplay between the initial position of the distribution, diffusivity, position of the sink, etc. The derived survival probability profile gives an understanding of chemical dynamics in condensed phases.

SnTe is a prototypical topological crystalline insulator, in which the gapless surface state is protected by a crystal symmetry. The hallmark of the topological properties in SnTe is the Dirac cones projected to the surfaces with mirror symmetry, stemming from the band inversion near the L points of its bulk Brillouin zone, which can be measured by angle-resolved photoemission. We have obtained the (111) surface of SnTe film by molecular beam epitaxy on BaF2(111) substrate. Photon-energy-dependence of in situ angle-resolved photoemission, covering multiple Brillouin zones in the direction perpendicular tothe (111) surface, demonstrate the projected Dirac cones at the Gamma_bar and M_bar points of the surface Brillouinzone. In addition, we observe a Dirac-cone-like band structure at the Gamma point of the bulk Brillouin zone,whose Dirac energy is largely different from those at the Gamma_bar and M_bar points., 8 pages, 4 figures

The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation—a mathematical transformation that takes the time variable t to negative imaginary time— it —was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a “translation manual” between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in developments in pure mathematics as well as theoretical physics is another feature that this case study has in common with dualities in string theory.

Gasparim, Grama and San Martin (2016) showed that height functions give adjoint orbits of semisimple Lie algebras the structure of symplectic Lefschetz fibrations (superpotential of the LG model in the language of mirror symmetry). We describe how to extend the superpotential to compactifications. Our results explore the geometry of the adjoint orbit from 2 points of view: algebraic geometry and Lie theory.

In our earlier work (Steinbach et al., 2016 [1] ) we investigated a homogeneous system of magnetically capped colloidal particles that self-assembled via two structural patterns of different symmetry. The particles could form a compact, equilateral triangle with a three-fold rotational symmetry and zero dipole moment and a staggered chain with mirror symmetry with a net magnetisation perpendicular to the chain. The system exhibited a bistability already in clusters of three particles. Based on observations of a real magnetic particles system, analytical calculations and molecular dynamics simulations, it has been shown that the bistability is a result of an anisotropic magnetisation distribution with rotational symmetry inside the particles. The present study is a logical extension of the above research and forms a preparatory stage for the study of a self-assembly of such magnetic particles under the influence of an external magnetic field. Since the magnetic field is only an additive contribution to the total ground state energy, we can study the interparticle interaction energies of candidate ground state structures based on the field-free terms.

In some degraded situations of heat-exchangers, tubes may be loosely supported while subjected to intense cross-flow generating both turbulence and fluid-elastic forces, and so have vibro-impacting responses. This paper aims at providing a better understanding of the dynamics of such systems in which the conjunction of stops with gaps, broadband random excitation, and fluid-elastic coupling forces, either stabilizing or destabilizing, produces some rather amazing effects linked to a general capacity for the system to be auto-adjusted by the impacts. It is especially shown, (i) how a non-linear gap-system “escapes from instability” by reinforcing the sequence of impacts, (ii) the almost perfect time-history mirror symmetry between the works of turbulence and fluid-elastic forces in the energy balance; (iii) the dissipative aspect of turbulence in some cases. Moreover the paper deals with the relative weight of turbulence and fluid-elastic forces in the tube response that notably depends on the gap size. For this, turbulence is considered as a perturbation of limit cycles obtained when the fluid-elastic forces are the only acting fluid-forces. The study is based on configurations mainly 1-DOF, like the one that has been experimentally tested, but extrapolations for real tube bundle are evoked in conclusion.

Let $W\in \mathbb{C}[x_1,\cdots,x_N]$ be an invertible polynomial with an isolated singularity at origin, and let $G\subset {{\sf SL}}_N\cap (\mathbb{C}^*)^N$ be a finite diagonal and special linear symmetry group of $W$. In this paper, we use the category ${{\sf MF}}_G(W)$ of $G$-equivariant matrix factorizations and its associated VSHS to construct a $G$-equivariant version of Saito's theory of primitive forms. We prove there exists a canonical categorical primitive form of ${{\sf MF}}_G(W)$ characterized by $G_W^{{\sf max}}$-equivariance. Conjecturally, this $G$-equivariant Saito theory is equivalent to the genus zero part of the FJRW theory under LG/LG mirror symmetry. In the marginal deformation direction, we verify this for the FJRW theory of $\big(\frac{1}{5}(x_1^5+\cdots+x_5^5),\mathbb{Z}/5\mathbb{Z}\big)$ with its mirror dual B-model Landau-Ginzburg orbifold $\big(\frac{1}{5}(x_1^5+\cdots+x_5^5), (\mathbb{Z}/5\mathbb{Z})^4\big)$. In the case of the Quintic family $\mathcal{W}=\frac{1}{5}(x_1^5+\cdots+x_5^5)-\psi x_1x_2x_3x_4x_5$, we also prove a comparison result of B-model VSHS's conjectured by Ganatra-Perutz-Sheridan., Comment: 30 pages, comments welcome! Minor modification in V2

We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$ that includes the modular symmetries $\mathrm{SL}(2,\mathbb{Z})_T$ and $\mathrm{SL}(2,\mathbb{Z})_U$ (of the "geometric" moduli $T$ and $U$) as well as mirror symmetry. In addition, string theory provides a candidate for a CP-like symmetry that enhances the Siegel modular group to $\mathrm{GSp}(4,\mathbb{Z})$., Comment: 18 pages, 1 figure, 1 table; v2: some statements in the conclusions clarified, matches version published in PLB

We study the Hodge numbers f p , q of Landau–Ginzburg models as defined by Katzarkov, Kontsevich, and Pantev. First we show that these numbers can be computed using ordinary mixed Hodge theory, then we give a concrete recipe for computing these numbers for the Landau–Ginzburg mirrors of Fano threefolds. We finish by proving that for a crepant resolution of a Gorenstein toric Fano threefold X there is a natural LG mirror ( Y , w ) so that h p , q ( X ) = f 3 − q , p ( Y , w ) .

The Invariant Imbedding (IIM) T-matrix method is recognized as one of the most promising scattering models since it can perform the scattering simulation of the nonspherical particles in a semi-analytical way. However, because the T-matrix should be updated in each iterative process, its computational efficiency is an important issue in the actual scattering simulation. To alleviate this problem, the symmetrical properties for the nonspherical particles with symmetrical geometries are systematically investigated in this paper. Firstly, the symmetry of the U-matrix (an important matrix in the IIM T-matrix model) is derived for the particles with mirror symmetry with respect to the coordinate planes. In this case, the U-matrix is firstly decomposed into the sine and cosine components, and then its symmetrical properties are obtained by combining the spatial symmetry of the permittivity and the symmetry of the angular functions. In the second part, the symmetry of the U-matrix is derived for the particles with N-folds symmetrical geometry, and based on the symmetrical properties, the method to simplify the T-matrix iteration is further proposed. In this case, it can be found that by using the symmetry of the U-matrix, both the U-matrix and T-matrix can be rearranged into the block diagonal ones, and the calculation of the T-matrix can be decomposed into the iteration of several block sub-matrices, which can cut down the computational amount and memory consumption notably. Also, it can be seen that the derivation process also provides another point of view to understand the symmetry of T-matrix for the particles with N-folds symmetrical geometry.

We study the bigraded vector space structure of Landau–Ginzburg orbifolds with the permutation symmetries of variables. We calculate the formula of the Poincare polynomial for a certain loop polynomial orbifoldized by a semidirect product of a diagonal symmetry group and cyclic permutation group and check that the generalization of Berglund–Hubsch transpose gives mirror symmetric pairs for these cases.

Janus transition-metal dichalcogenides MoSSe has been attracted much attention due to its excellent electronic properties induced by mirror symmetry breaking. In this work, based on machine learning and density functional theory, the photoelectric conversion coefficient (PCE) along with the variation of Se concentration in MoS2(1-x)Se2x (0

As part of a strategy for creating 3D models of engineering objects from a sketched input, we attempt to identify mirror symmetry planes early in the process. Our input is a 2D line-drawing derived from a single view sketch of a polyhedral shape, and suitable cues are used to identify mirror symmetry planes algorithmically. Previous attempts to simplify the search space use incomplete criteria. In this paper, we further simplify the search space by scoring valid symmetry planes by their likelihood, i.e., we do not assert “this is a symmetry plane” but “this is more/less likely to be a symmetry plane”.

We prove that generic complete intersections associated to multiple mirror nef-partitions are all birational. This result solves a conjecture by Batyrev and Nill under some mild assumptions., Comment: published version, to appear at Adv. Math

This paper further investigates a novel method for generating complex grid multi-wing chaotic attractors by double-mirror symmetry conversion both in z direction and in y direction. First, multi-wing chaotic attractors are obtained from a three-dimensional quadratic chaotic system by designing an even-symmetry multi-segment quadratic function to extend the number of saddle-focus equilibrium points with index 2 in y direction. Second, the principle of mirror symmetry conversion for generating grid multi-wing is given. Third, based on the principle, by the double-mirror symmetry conversion with respect to z-axis and y-axis, respectively, intended grid n × m-wing chaotic systems can be obtained. Finally, improved module-based circuits are designed for generating grid multi-wing chaotic attractors, which has demonstrated the feasibility of the proposed approaches.

We report on the existence of unidirectional phononic band gaps that may span over extended regions of the Brillouin zone and can find application in trapping elastic (acoustic) waves in properly designed multilayered 3D structures. Phononic isolators operate as a result of asymmetrical wave transmission through a slab of a crystallographic phononic structure with broken mirror symmetry. Due to the use of lossless materials in the crystal, the absorption rate is dramatically enhanced when the proposed isolator is placed next to a vibrational harvesting cell.

This research paper introduces mirror symmetry multi-wing attractors from a novel four-dimensional hyperchaotic system. A mirror symmetry conversion-based approach is developed and verified. To confirm the existence of hyperchaotic system, Lyapunov exponent spectrums are investigated. Furthermore, the improved module-based circuit designs of mirror symmetry multi-wing hyperchaotic attractors are further implemented. The proposed novel mirror symmetry multi-wing hyperchaotic attractors are very useful for deliberate generation of chaos in applications.

Macroscopic quantum effects in living systems have been studied widely in pursuit of fundamental explanations for biological energy transport and sensing. While it is known that type II endonucleases, the largest class of restriction enzymes, induce DNA double-strand breaks by attacking phosphodiester bonds, the mechanism by which simultaneous cutting is coordinated between the catalytic centers remains unclear. We propose a quantum mechanical model for collective electronic behavior in the DNA helix, where dipole-dipole oscillations are quantized through boundary conditions imposed by the enzyme. Zero-point modes of coherent oscillations would provide the energy required for double-strand breakage. Such quanta may be preserved in the presence of thermal noise by the enzyme’s displacement of water surrounding the DNA recognition sequence. The enzyme thus serves as a decoherence shield. Palindromic mirror symmetry of the enzyme-DNA complex should conserve parity, because symmetric bond-breaking ceases when the symmetry of the complex is violated or when physiological parameters are perturbed from optima. Persistent correlations in DNA across longer spatial separations—a possible signature of quantum entanglement—may be explained by such a mechanism.

We introduce a relative version of the spherical objects of Seidel and Thomas. Define an object E in the derived category D(Z x X) to be spherical over Z if the corresponding functor from D(Z) to D(X) gives rise to autoequivalences of D(Z) and D(X) in a certain natural way. Most known examples come from subschemes of X fibred over Z. This categorifies to the notion of an object of D(Z x X) orthogonal over Z. We prove that such an object is spherical over Z if and only if it has certain cohomological properties similar to those in the original definition of a spherical object. We then interpret this geometrically in the case when our objects are actual flat fibrations in X over Z., 29 pages; v2: A missing assumption reinstated in Prop. 3.7, some notation cleaned up. The final version to appear in Adv. in Math

In this paper, we investigate a duality between Hermitian and almost Kahler structures on the tangent manifold T M induced by pairs of conjugate connections on its base, affine Riemannian manifold M . In the context of information geometry, the classical theory of statistical manifold (which we call S -geometry) prescribes a parametrized family of probability distributions with a Fisher-Rao metric g and, using the Amari-Chensov tensor, a family of dualistic, torsion-free connections ∇ ( α ) , known as α-connections on M . Here we prescribe an alternative geometric framework (which we call P -geometry or partially flat geometry) by treating such parametrization as affine coordinates with respect to a flat connection ∇, and considering its g-conjugate connection ∇ ⁎ which is curvature-free but generally carries torsion. Under P -geometry, the triplet ( g , ∇ , ∇ ⁎ ) on M leads to a pair of complex and almost Kahler structures on T M , in “mirror correspondence” to each other. Such complex-to-symplectic correspondence is reminiscent of mirror symmetry in string theory. We discuss the statistical meaning of mirror correspondence in terms of reference duality and representation duality in (various generalizations of) contrast/divergence functions characterizing proximity of probability distributions within a parametric statistical model.

Motivated by observations in physics, mirror symmetry is the concept that certain manifolds come in pairs $X$ and $Y$ such that the complex geometry on $X$ mirrors the symplectic geometry on $Y$. It allows one to deduce symplectic information about $Y$ from known complex properties of $X$. Strominger-Yau-Zaslow arXiv:hep-th/9606040 described how such pairs arise geometrically as torus fibrations with the same base and related fibers, known as SYZ mirror symmetry. Kontsevich arXiv:alg-geom/9411018 conjectured that a complex invariant on $X$ (the bounded derived category of coherent sheaves) should be equivalent to a symplectic invariant of $Y$ (the Fukaya category, see references in article abstract). This is known as homological mirror symmetry. In this project, we first use the construction of "generalized SYZ mirrors" for hypersurfaces in toric varieties following Abouzaid-Auroux-Katzarkov arXiv:1205.0053v4, in order to obtain $X$ and $Y$ as manifolds. The complex manifold is the genus 2 curve $\Sigma_2$ (so of general type $c_1, Comment: Accepted manuscript to Advances in Mathematics. 103 pages, 25 figures

Short-term prediction technology has a vital role in improving the efficacy and safety of several offshore operations. Motivated by nonlinear learning ability of support vector regression model (SVR model) and non-stationary data processing ability of empirical mode decomposition (EMD), this study offers a hybrid EMD-SVR model for short-term prediction of ship motion using mirror symmetry and SVR algorithm to eliminate EMD boundary effect. This model is abbreviated as the MSEMD-SVR model in this study. Even though EMD is efficient in dealing with non-stationary data, its boundary effect decreases the prediction accuracy. Raw data are initially processed by improved EMD and then predicted by SVR in the MSEMD-SVR model. This study confirms the negative EMD boundary effect on the prediction accuracy of classical EMD-SVR model and validity of the mirror symmetry method using the rolling and pitching of ship motion data collected during sailing for experiments. Based on the results of contrast experiments, the MSEMD-SVR model is more feasible and reliable for short-term prediction of ship motion than the EMD-SVR model, which does not deal with EMD boundary effect or only applies the mirror symmetry method to deal with.

The electronic and topological properties of Sn 1 - x In x Te have been investigated based on first principles calculations. Sn 1 - x In x Te presents inverted bands at the L point, but the number of inverted bands depends on the In x composition. Nevertheless the computed mirror Chern number is always n M = - 2 for all In concentrations studied here. Pairs of topologically protected states on the (001) surface of Sn 1 - x In x Te with ± i mirror eigenvalues have been identified. The character of these topological states is affected by In dopant as compared to the parent topological crystalline insulator SnTe. As the In content x increases, the Dirac crossing point moves further away from the L point, and the Fermi velocity of the topological states increases significantly. Also we verify that a hole to electron carrier-like transition takes place at x = 0.25 due to depopulation of the In-5s orbital. As Sn 1 - x In x Te is a superconductor, there is a co-existence of topological states protected by mirror symmetry on the surface with superconductivity in the bulk.

We investigated the structure, symmetry, and distribution of stacking faults and growth twins in 18R and 14H long-period stacking ordered (LPSO) structures in a near-equilibrium Mg97Zn1Y2 (at.%) alloy by transmission electron microscopy. The stacking faults and growth twins here result from the insertion of the n-Mg components in the LPSO structure, and some of them possess inversion centers or mirror symmetry. The stacking faults and growth twins in 18R LPSO depend on whether the sum of inserted Mg layers of all n-Mg components in defects is even number or odd number, respectively, while only stacking faults appear in 14H LPSO. The gliding of Shockley partial dislocation pairs induces the transformation of stacking faults and motion of twin boundary. Statistically, the periodical arrangement of stacking faults in 18R or 14H LPSO structures results in the formation of superstructures, such as 62L, 86L, 152L, and 235L.

We consider the Grassmannian X = G r n − k ( C n ) and describe a ‘mirror dual’ Landau-Ginzburg model ( X ˇ ∘ , W q : X ˇ ∘ → C ) , where X ˇ ∘ is the complement of a particular anti-canonical divisor in a Langlands dual Grassmannian X ˇ , and we express W succinctly in terms of Plucker coordinates. First of all, we show this Landau-Ginzburg model to be isomorphic to one proposed for homogeneous spaces in a previous work by the second author. Secondly we show it to be a partial compactification of the Landau-Ginzburg model defined in the 1990's by Eguchi, Hori, and Xiong. Finally we construct inside the Gauss-Manin system associated to W q a free submodule which recovers the trivial vector bundle with small Dubrovin connection defined out of Gromov-Witten invariants of X. We also prove a T-equivariant version of this isomorphism of connections. Our results imply in the case of Grassmannians an integral formula for a solution to the quantum cohomology D-module of a homogeneous space, which was conjectured by the second author. They also imply a series expansion of the top term in Givental's J-function, which was conjectured in a 1998 paper by Batyrev, Ciocan-Fontanine, Kim and van Straten.

We investigate non-reciprocal wave propagation in spatiotemporal phononic plates. Specifically, the first aim of this manuscript is to propose a general formulation of the Plane Wave Expansion Method (PWEM) that, in contrast with previous works, is applicable to any class of 2D spatiotemporal unit cells whose properties can be expanded in traveling plane waves. The second aim is to exploit this analysis tool in order to study a class of phononic materials capable of violating mirror symmetry in reciprocal space, therefore breaking reciprocity principle along different propagation directions in physical space. This is obtained by considering the plate elastic properties to be discretely modulated in space and continuously in time. Theoretical dispersion profiles are validated and compared with numerical simulations.

Topological nodal line semimetals with protected 1-D Fermi lines have continuously attracted great interest. In this study, based on first-principles calculations, we demonstrate that type-I and type-II nodal lines can coexist in the dynamically stable monolayer TiBF. Both types of nodal lines are protected by mirror symmetry in the absence of spin-orbital coupling. Besides, we find that the closed nodal lines can be effectively tuned by applying biaxial tensile strain. Interestingly, with a moderate compressive biaxial strain, a novel metal-semimetal-semiconductor phase transition can be induced, during which a 2-D double Weyl fermion emerges. The 2-D double Weyl fermion features a single Fermi point, where the conduction and the valence bands contact quadratically. We construct an effective Hamiltonian to characterize the 2-D double Weyl fermion. Additionally, we show that TiBX (X = Cl, Br, I) monolayers possess similar properties. Our findings show that the monolayer TiBF is a fascinating platform to investigate unique topological phases and that it demonstrates a great potential for nanoscale device applications.

Let X be a toric Fano manifold and denote by C r i t ( f X ) ⊂ ( C ∗ ) n the solution scheme of the corresponding Landau–Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L : C r i t ( f X ) → P i c ( X ) such that E L ( X ) : = L ( C r i t ( f X ) ) ⊂ P i c ( X ) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M : π 1 ( L ( X ) ∖ R X , f X ) → A u t ( C r i t ( f X ) ) where L ( X ) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of f X , the Landau–Ginzburg potential of X , and R X ⊂ L ( X ) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of C r i t ( f X ) admit non-trivial relations to quiver representations of the exceptional collection E L ( X ) . We refer to this property as the M -aligned property of the maps L : C r i t ( f X ) → P i c ( X ) . We discuss possible applications of the existence of such M -aligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.