Elliptic Fibrations Research Articles

Quantitative analysis of failure performance uncertainty based on multiscale mechanical analysis of PEMFCs’ C/C composite bipolar plates

In order to quantify the failure performance of PEMFCs’ C/C composite bipolar plates (BPs) under considering the uncertainty in multiscale sizes and loads, the failure probability function (FPF) of BPs at cold start is estimated. A three-stage multiscale simulation method is proposed for mechanical behavior analysis of multi-component heterogeneous composites. And the efficient estimation of FPF for C/C composite BPs is achieved via the proposed multiscale simulation method and decoupling sparse integration method, in which the unified density weight is constructed to decouple the double-loop framework of analyzing FPF, thereby reducing the computational complexity. Results indicate that the dangerous positions of BPs are around the gas flow channels and bolt holes. And the dangerous components are the carbon matrix and the interface between the matrix and fiber. The radius of elliptical fibers affects the distribution of failure factors on microscopic components, thereby affecting the variation of failure probability with fiber sizes significantly. The distribution parameter of composite layer thickness in BPs has a significant effect on structural safety, and the FPF result can be used to effectively guide the design of structure. Therefore, the proposed method is of great significance for guiding the rapid parameter design of composite BPs.

Application of Computer-Aided Design Software to the Simulation and Analysis of Composite Material Properties in Housing Engineering Structures

Reinforced polymer composites are widely used in engineering applications due to their excellent mechanical properties, and this paper combines experiments and numerical simulations to fully examine the properties of the composites. The article takes the reinforced concrete structure of civil engineering as the basis for experimental testing on the basic properties of carbon fiber composites in its application. Subsequently, the intrinsic model of reinforced concrete and carbon fiber composites was constructed, and each finite element unit of the member was selected to simulate and finite element analysis the performance of the composites through ABAQUS computer-aided design software. The results show that increasing the diameter of carbon fibers will reduce the number of carbon fibers at the same time, which will reduce the toughness of the composite material, random and chaotic distribution of carbon fibers for the improvement of the compressive properties of concrete can achieve a relatively balanced effect, and the high elastic modulus carbon fibers for the improvement of uniaxial and cyclic compressive properties of concrete play a dominant role. In addition, the oriented elliptical fibers in the long-axis direction have a significant increase in the modulus of elasticity and strength of the material, and this phenomenon will become more and more obvious with the increase of the length-to-diameter ratio. The reasonable structural design may help to improve the performance of composites and enhance their adaptability for engineering applications.

A Novel High Birefringence Single Elliptic Photonic Quasicrystal Fiber

This A novel single elliptical photonic quasi-crystal fiber (PQF) structure based on ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) is proposed. There is a single elliptical air hole at the fiber core and a ten-fold Person-type quasi-crystal structure distributed in the outer layer. The birefringence and confinement loss (CL) of the PQF are numerically proposed in short-wavelength infrared region (SWIR) based on finite element method. The high birefringence is achieved thanks to a single ellipse near the fiber core breaking the symmetry of the structure. Fluoride materials ZBLAN have lower CL in SWIR than traditional quartz glass. The birefringence of this novel PQF can be maintained above 10-2, which will have great potential in optical devices.

The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces

Brandhorst and Shimada described a large class of Enriques surfaces, called (\tau,\bar{\tau}) -generic, for which they gave generators for the automorphism groups and calculated the elliptic fibrations and the smooth rational curves up to automorphisms. In the present paper, we give lower bounds for the non-degeneracy invariant of such Enriques surfaces, we show that in most cases the invariant has generic value 10 , and we present the first known example of complex Enriques surface with infinite automorphism group and non-degeneracy invariant not equal to 10 .

Generation of the radial higher-order orbital angular momentum mode in helically twisted elliptic fiber.

The generation mechanism and regulation method of the radial higher-order orbital angular momentum (OAM) mode based on helically twisted elliptic fiber (HTEF) are investigated. This work aims to reveal the quantitative relation between the twisted rate (α) and the target radial higher-order OAM mode. From theoretical simulations, it is concluded that α is the key to regulating the radial higher-order OAM mode. In the experiment, OAM2n modes with radial higher-order n of 2, 3, 4, and 5 are successfully generated at 1550 nm by regulating α of the HTEF. Finally, the transmission spectrum and purity measurements are performed for the OAM24 mode, and it can be concluded that the fabricated experimental samples have more than 90% conversion efficiency and close to 94% purity under the appropriate α and twisted length.

Non-minimal elliptic threefolds at infinite distance. Part I. Log Calabi-Yau resolutions

We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open string moduli space. The limits are described as degenerations of elliptic threefolds whose central elements exhibit non-minimal elliptic fibers, in the Kodaira sense, over curves on the base. We show how these non-crepant singularities can be removed by a systematic sequence of blow-ups of the base, leading to a union of log Calabi-Yau spaces glued together along their boundaries. We identify criteria for the blow-ups to give rise to open chains or more complicated trees of components and analyse the blow-up geometry. While our results are general and applicable to all non-minimal degenerations of Calabi-Yau threefolds in codimension one, we exemplify them in particular for elliptic threefolds over Hirzebruch surface base spaces. We also explain how to extract the gauge algebra for F-theory probing such reducible asymptotic geometries. This analysis is the basis for a detailed F-theory interpretation of the associated infinite-distance limits that will be provided in a companion paper [1].

Fatigue and residual strain monitoring for thermoplastic composite using embedded FBG inscribed in highly‑birefringent side-hole elliptical core optical fiber

Monitoring of thermoplastic carbon reinforced composites is critical for the safe operation and optimization of composite structures. Strain measurement during their manufacturing and operation is often achieved with embedded Fiber Bragg Gratings (FBG). However, conventional FBGs can only measure axial strain. To measure multiaxial strain in thermoplastic composites, FBGs inscribed in highly-birefringent side-hole elliptical core optical fiber (SH2 FBG) are proposed. SH2 FBG were used to monitor composite produced by automated tape laying process, first − to measure residual in-plane and out-of-plane strain during the manufacturing stage, second − in plane transverse strain during cyclic loading. It was demonstrated that the sensors can be used to measure multiaxial residual strain, observe changes in material stiffness, and calculate the area of the mechanical hysteresis loop. As a result − it was shown that embedding SH2 FBG can be an effective and robust method for monitoring the carbon fiber reinforced thermoplastic composite.

Emergence in string theory and Fermi gases

The Emergence Proposal suggests that some Swampland criteria, in particular on large field distances, are a consequence of the emergent nature of dynamics for fields in the infrared. In the context of type II string theory compactified on Calabi-Yau manifolds, it proposes that the cubic tree-level piece of the genus-zero prepotential is emergent from integrating out massive non-perturbative states. For a certain special non-compact Calabi-Yau, the blown-up conifold, it is known that the full all-genus prepotential can be matched onto the Grand Canonical potential of a two-dimensional Fermi gas. We propose here that this should be understood in the context of emergence: the prepotential is induced by integrating out the Fermi gas degrees of freedom. To make contact with the Swampland we need dynamical gravity, so compact Calabi-Yau manifolds. We show that for specifically the cubic term, an integrating out calculation also works for compact cases. In particular, the exact cubic term coefficient can be recovered from integrating out a Fermi gas for any compact Calabi-Yau that is an elliptic fibration over a reflexive toric base. We also propose a general map, for any one-parameter Calabi-Yau, between the Grand Canonical potential of the ultraviolet non-perturbative system and the period. In particular, this map leads to an emergent cubic term in the genus-zero prepotential for any such one-parameter model.

Design and dual-parameter sensing analysis of a weakly-coupled polarization-maintaining few-mode fiber based on the intramodal SBS

We propose and numerically analyze a weakly-coupled polarization-maintaining few-mode fiber sensor based on stimulated Brillouin scattering (SBS) for simultaneous multiple-parameter measurement. First, a weakly-coupled double bow-tie steering wheel-type ring elliptical core few-mode fiber (DBT-SWTREC-FMF) supporting 16 eigenmodes across the whole C band is designed to improve the performance of simultaneous multiple-parameter sensing by optimizing the structural parameters of the fiber. Then, the designed fiber’s intramodal Brillouin characteristics, such as Brillouin gain spectrum (BGS) and Brillouin frequency shift (BFS), are analyzed. Finally, based on intramodal SBS, the temperature and strain sensing performance in the designed fiber are studied and discussed. Numerical investigation shows the minimum errors for synchronized temperature and strain measurement can reach 0.18 °C and 4.01 με, respectively. This work is significant for studying intramodal SBS in the FMFs. Furthermore, the proposed weakly-coupled DBT-SWTREC-FMF sensor also provides a potential guide for further improving the performance of simultaneous multiple-parameter sensing.

Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories

We study how the global structure of rank-one 4d \mathcal{N}=2𝒩=2 supersymmetric field theories is encoded into global aspects of the Seiberg-Witten elliptic fibration. Starting with the prototypical example of the \mathfrak{su}(2)𝔰𝔲(2) gauge theory, we distinguish between relative and absolute Seiberg-Witten curves. For instance, we discuss in detail the three distinct absolute curves for the SU(2)SU(2) and SO(3)_±SO(3)± 4d \mathcal{N}=2𝒩=2 gauge theories. We propose that the 11-form symmetry of an absolute theory is isomorphic to a torsion subgroup of the Mordell-Weil group of sections of the absolute curve, while the full defect group of the theory is encoded in the torsion sections of a so-called relative curve. We explicitly show that the relative and absolute curves are related by isogenies (that is, homomorphisms of elliptic curves) generated by torsion sections - hence, gauging a one-form symmetry corresponds to composing isogenies between Seiberg-Witten curves. We apply this approach to Kaluza-Klein (KK) 4d \mathcal{N}=2𝒩=2 theories that arise from toroidal compactifications of 5d and 6d SCFTs to four dimensions, uncovering an intricate pattern of 4d global structures obtained by gauging discrete 00-form and/or 11-form symmetries. Incidentally, we propose a 6d BPS quiver for the 6d M-string theory on \mathbb{R}^4× T^2ℝ4×T2.

On the intermediate Jacobian of M5-branes

We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal ℤ2 singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.

High-Sensitivity Twist Sensor Based on Sagnac Interference With a Helical Elliptical Core Fiber

High-Sensitivity Twist Sensor Based on Sagnac Interference With a Helical Elliptical Core Fiber

Derived Equivalence for Elliptic K3 Surfaces and Jacobians

Abstract We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived Torelli Theorem that describes Fourier-Mukai partners. In Picard rank two, derived elliptic structures are fully determined by the Lagrangian subgroups of the discriminant group. As a consequence, we prove that for a large class of Picard rank 2 elliptic K3 surfaces all Fourier-Mukai partners are Jacobians, and we partially extend this result to non-closed fields. We also show that there exist elliptic K3 surfaces with Fourier-Mukai partners, which are not Jacobians of the original K3 surface. This gives a negative answer to a question raised by Hassett and Tschinkel.

Hwang-Oguiso invariants and frozen singularities in special geometry

In Special Geometry there are two inequivalent notions of “Kodaira type” for a singular fiber: one associated with its local monodromy and one with its Hwang-Oguiso characteristic cycle. When the two Kodaira types are not equal the geometry is subtler and its deformation space gets smaller (“partially frozen” singularities). The paper analyzes the physical interpretation of the Hwang-Oguiso invariant in the context of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 QFT and describes the surprising phenomena which appear when it does not coincide with the monodromy type. The Hwang-Oguiso multiple fibers are in one-to-one correspondence with the partially frozen singularities in M-theory compactified on a local elliptic K3: a chain of string dualities relates the two geometric set-ups. Paying attention to a few subtleties, this correspondence explains in purely geometric terms how the “same” Kodaira elliptic fiber may have different deformations spaces. The geometric computation of the number of deformations agrees with the physical expectations. At the end we briefly outline the implications of the Hwang-Oguiso invariants for the classification program of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs.

Compactified Jacobians of extended ADE curves and Lagrangian fibrations

We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalize Kodaira’s classification of singular elliptic fibers and thus call them extended ADE curves. On such a curve [Formula: see text], we describe a compactified Jacobian and show that its components reflect the intersection graph of [Formula: see text]. This extends known results when [Formula: see text] is reduced, but new difficulties arise when [Formula: see text] is non-reduced. As an application, we get an explicit description of general singular fibers of certain Lagrangian fibrations of Beauville–Mukai type.

Dispersion of optical vortices in twisted elliptical-core optical fibers with torsional stresses

In this paper, the dispersion of optical vortices (OVs) with a topological charge l >= 1 in twisted elliptical fibers (TEF) with torsional stresses (TS) is studied. Analytical expressions for polarization, topological, and hybrid dispersion are derived from the spectra of vortex modes in step- and gradient-index TEFs with TS. It is shown that in strongly twisted fibers with a gradient refractive index profile, new types of dispersion appear in comparison with the case of a step-index profile. The dependence of the dispersion of OVs on the material and geometrical parameters of the fiber is studied numerically. It is established that in step-index TEFs with TS, there is a spectral region near which all types of dispersion for OVs with l >= 1 take a near zero value. It is also demonstrated that for TEFs with a gradient profile, this regime is realized for strongly twisted strongly elliptical fibers.

Back to heterotic strings on ALE spaces. Part II. Geometry of T-dual little strings

This work is the second of a series of papers devoted to revisiting the properties of Heterotic string compactifications on ALE spaces. In this project we study the geometric counterpart in F-theory of the T-dualities between Heterotic ALE instantonic Little String Theories (LSTs) extending and generalising previous results on the subject by Aspinwall and Morrison. Since the T-dualities arise from a circle reduction one can exploit the duality between F-theory and M-theory to explore a larger moduli space, where T-dualities are realised as inequivalent elliptic fibrations of the same geometry. As expected from the Heterotic/F-theory duality the elliptic F-theory Calabi-Yau we consider admit a nested elliptic K3 fibration structure. This is central for our construction: the K3 fibrations determine the flavor groups and their global forms, and are the key to identify various T-dualities. We remark that this method works also more generally for LSTs arising from non-geometric Heterotic backgrounds. We study a first example in detail: a particularly exotic class of LSTs which are built from extremal K3 surfaces that admit flavor groups with maximal rank 18. We find all models are related by a so-called T-hexality (i.e. a 6-fold family of T-dualities) which we predict from the inequivalent elliptic fibrations of the extremal K3.

Anomaly cancellation in string theory

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups [Formula: see text] and [Formula: see text]. The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin-[Formula: see text] fields transform under the adjoint representation in these models, compactification of the heterotic string over [Formula: see text] or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over [Formula: see text], provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin-[Formula: see text] fields now would transform under the fundamental representation of [Formula: see text] and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the [Formula: see text] model vanishes at [Formula: see text]. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions.

A novel description of the supporting system of the orbicularis oculi muscle in the infraorbital area: Tear trough muscle fiber.

The aim of this study was to elucidate the anatomical structures of supporting system of the infraorbital area. Forty-four hemifaces from eleven Korean and eleven Thai cadavers were used to dissect the infraorbital area. Based on the dissection and previous histologic results, they were analyzed. The orbicularis oculi muscle (OOc) had two portions (palpebral and orbital portion) and four subparts (pretarsal, preseptal, prezygomatic, and premaxillary part). The elliptical muscle fiber of OOc was supported by circumferential connective tissue including skin ligament, orbicularis retaining ligament, zygomatic ligament, and zygomatic cutaneous ligament. The vertical muscle fiber, the tear trough muscle fiber, and medial muscular band directly attached to the skin. Full of subcutaneous tissue in the tear trough groove, strong attachment to the bone by tear trough ligament and to the skin by tear trough muscle fiber would multiply result in the tear trough on the face.

New families of scale separated vacua

Massive type IIA flux compactifications of the form AdS4 × X6, where X6 admits a Calabi-Yau metric and O6-planes wrapping three-cycles, display families of vacua with parametric scale separation between the compactification scale and the AdS4 radius, generated by an overall rescaling of internal four-form fluxes. For toroidal orbifolds one can perform two T-dualities and map this background to an orientifold of massless type IIA compactified on an SU(3)-structure manifold with fluxes. Via a 4d EFT analysis, we generalise this last construction and embed it into new branches of supersymmetric and non-supersymmetric vacua with similar features. We apply our results to propose new infinite families of vacua based on elliptic fibrations with metric fluxes. Parametric scale separation is achieved by an asymmetric flux rescaling which, however, in general is not a simple symmetry of the 4d equations of motion. At this level of approximation the vacua are stable but, unlike in the Calabi-Yau case, they display a non-universal mass spectrum of light fields.