Deformations Of Complex Structure Research Articles

Finite element analysis-A biomechanical tool in orthodontics

In orthodontic research, the finite element method (FEM) has been widely used as an engineering resource for calculating the stress and deformation of complex structures. Applying the FEM can predict the graphic representation of these tissue responses through the observation of areas of stress created by applied orthodontic mechanics. This method has the advantage of being non-invasive, accurate, and providing quantitative and detailed data on the physiological reactions possible to occur in tissues. The purpose of this article is to review and discuss the steps involved in applying the concept of finite elements and how they can be used in orthodontics. The stress distribution at the interface between the alveolar bone and the periodontal ligament, as well as the shifting trend in different tooth movement types while employing different kinds of orthodontic devices, may both be assessed using FEM. For this reason, expertise with certain software is required. Despite the drawbacks of other experimental techniques, FEM is a crucial technique for addressing inquiries regarding tooth movement.

Calculation and Validation of Planet Gear Sliding Bearings for a Three-Stage Wind Turbine Gearbox

In recent years, the trend towards larger wind turbines and higher power densities has led to increasing demands on planet gear bearings. The use of sliding bearings instead of rolling bearings in planetary bearings makes it possible to increase the power density with lower component costs and higher reliability. Therefore, the use of planet gear sliding bearings in wind turbine gearboxes has become more common. However, the flexible structure and complex load conditions from the helical tooth meshes lead to highly complex elastic structure deformation that modifies the lubricant film thickness and pressure distribution and, thus, has to be considered in the calculation of the bearing’s load-carrying capacity. This paper introduces a highly time-efficient calculation procedure that is validated with pressure measurement data from a three-stage planetary gearbox for a multi-megawatt wind energy plant. The investigations focus on three main objectives: (i) analyses of experimental and predicted results for different load cases, (ii) validation of the results of planet gear sliding bearing code, and (iii) discussion on mandatory modeling depths for the different planet stages. Results indicate the necessity of further research in this field of applications, particularly for the third-stage bearings.

Double field theory, twistors, and integrability in 4-manifolds

The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be understood in terms of generalized geometry and, more recently, para-Hermitian geometry. In this work we apply techniques associated to this doubled geometry to four-dimensional manifolds, and we show that they are particularly well-suited to the analysis of integrability in special spacetimes, especially in connection with Penrose's twistor theory and its applications to general relativity. This shows a close relationship between some of the geometrical structures in the para-Hermitian approach to double field theory and those in algebraically special solutions to the Einstein equations. Particular results include the classification of four-dimensional, possibly complex-valued, (para-)Hermitian structures in different signatures, the Lie and Courant algebroid structures of special spacetimes, and the analysis of deformations of (para-)complex structures. We also discuss a notion of “weighted algebroids” in relation to a natural gauge freedom in the framework. Finally, we analyze the connection with two- and three-dimensional (real and complex) twistor spaces, and how the former can be understood in terms of the latter, in particular in terms of twistor families.

U-Pb-Hf isotope compositions of detrital zircons from Tongtian River sediments of northern-central Tibetan Plateau: Implications for the closure of the Jinshajiang Ocean

The closure time of the Jinshajiang Ocean (a branch ocean of the Paleo-Tethys) has been widely debated due to the complex structure and strong deformation of the northern-central Tibetan Plateau. In this paper, the U-Pb-Hf isotope compositions of detrital zircons from Tongtian River sand sediments from the northern-central Tibetan Plateau were analyzed via laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). The UPb ages of the detrital zircons from Tongtian River sand sediments were distributed in six major groups: 2685–2346 Ma, 2035–1676 Ma, 1220–580 Ma, 544–407 Ma, 297–157 Ma, and 46–20 Ma. The εHf(t) values (range from −30 to +19) of the detrital zircons varied within a wide range from negative to positive, indicating that the zircons were sourced from diverse host magmas. The 46–20 Ma zircons and their Hf isotope compositions reveal that the far-field effect of the Cenozoic India-Eurasia plate collision triggered reworking of the Neoproterozoic basement of the North Qiangtang terrane. The U-Pb-Hf isotope compositions of these detrital zircons indicate that the Tongtian River sand sediments are composed of a mixture of materials from the Bayan Har-Songpan Ganzi terrane and the North Qiangtang terrane, with a contribution ratio of 3:7. The UPb ages and Hf isotope compositions of the zircons from the Tongtian River sediments and regional igneous rocks suggest that the εHf(t) values of the Permian zircons are predominantly positive while those of the Triassic, especially the Late Triassic, are negative. This marked shift most likely indicates that the closure of the Jinshajiang Ocean occurred by at least the Late Triassic.

A new superimposed model of the Tongnanba anticline in northeastern Sichuan and its exploration implications

Understanding the structural style, kinematic process, and timing of superimposed structures worldwide is often difficult due to complex structure deformation process. Fortunately, the newly acquired high-quality seismic reflection data and geological observations covering the Tongnanba anticline provide an excellent chance to characterize such structures. Here, we used geological and seismic data from the Tongnanba region to evaluate the structural style and deformation sequence of Tongnanba anticline. In this regard, we propose a new model of the northeastern Sichuan Basin, which are different from the model that deep structures formed earlier than shallow structures demonstrated by previous studies, and we also discussed the implications of this new model for the deep oil and gas exploration. Compressed by Micangshan and Dabashan thrust belts and controlled by three detachment layers, the Tongnanba anticline shows a complex multi-stage, multi-directional, and multi-level superimposed structure. There were three deformation layers vertically, leading to the multi-level detachment thrust structure style. Specifically, the upper and middle deformation layers were mainly controlled by South Dabashan thrust belt in the early stage, forming long-distance detachment thrust structure extended in the NW-SE direction. A series of pop-up structures propagated toward the upper and middle detachment layers. On the other hand, the lower deformation layer was primarily controlled by the Micangshan thrust belt in the late stage, forming complex basement faults extended in the NE-SW direction, which was consistent with Trishear fault-propagation fold. Along the basement detachment developed multiple branch slopes spread from northeast to southwest. The middle and upper deformation layers was transformed by the basement faults, thus forming the complex superimposed structure of north-south zonation and east-west segmentation at present. It was such complex superimposed structure that control the process of hydrocarbon accumulation and adjustment in each deformation layer, and the deep-ultra-deep ancient oil and gas reservoirs may be worth of exploring.

Scalar curvature and deformations of complex structures

Abstract We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kähler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an infinite-dimensional Kähler reduction, which is a hyperkähler reduction for a particular choice of the spectral function. The main tool for studying the system is a flat connection on the space of first-order deformations of the complex structure, that allows to obtain a formal complexification of the moment map equations. Using this connection, we describe a variational characterization of the equations, a Futaki invariant for the system, and a generalization of K-stability that is conjectured to characterize the existence of solutions.

Two 6D origins of 4D SCFTs: Class S and 6D (1, 0) on a torus

We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $(\mathfrak{e}_n,\mathfrak{e}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4d SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4d theories from different origins via mirror symmetry.

Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds

The purpose of this paper is to study the properties of holomorphic Poisson manifolds (M,π) under the assumption of ∂∂¯–lemma or ∂π∂¯–lemma. Under these assumptions, we show that the Koszul–Brylinski homology can be recovered by the Dolbeault cohomology, and prove that the DGLA (AM•,•,∂¯,[−,−]∂π) is formal. Furthermore, we discuss the Maurer–Cartan elements of (AM•,•[[t]],∂¯,[−,−]∂π) which induce the deformations of complex structure of M.

The tadpole conjecture in asymptotic limits

The tadpole conjecture suggests that the complete stabilization of complex structure deformations in Type IIB and F-theory flux compactifications is severely obstructed by the tadpole bound on the fluxes. More precisely, it states that the stabilization of a large number of moduli requires a flux background with a tadpole that scales linearly in the number of stabilized fields. Restricting to the asymptotic regions of the complex structure moduli space, we give the first conceptual argument that explains this linear scaling setting and clarifies why it sets in only for a large number of stabilized moduli. Our approach relies on the use of asymptotic Hodge theory. In particular, we use the fact that in each asymptotic regime an orthogonal sl(2)-block structure emerges that allows us to group fluxes into sl(2)-representations and decouple complex structure directions. We show that the number of stabilized moduli scales with the number of sl(2)-representations supported by fluxes, and that each representation fixes a single modulus. Furthermore, we find that for Calabi-Yau four-folds all but one representation can be identified with representations occurring on two-folds. This allows us to discuss moduli stabilization explicitly and establish the relevant scaling constraints for the tadpole.

A microstructural rafting state-based constitutive model for single crystal Ni-based superalloys at elevated temperature

Single crystal (SC) Ni-based superalloys undergo microstructural degradations such as rafting and coarsening due to the extremely harsh service environment, which consequently introduce the challenge in inelastic behaviours prediction when considering the time-varying microstructural state. Within this content, a thermodynamically microstructural state-based constitutive model for SC Ni-based superalloys is proposed at elevated temperature. A rafting state variable satisfying the positive dissipation is determined and then is introduced into the crystal plasticity framework to depict the inelastic deformation of SC Ni-based superalloys with different rafting microstructures. The interconnection between rafting and constitutive law is achieved by altering the internal state variables (ISVs) through a series of micromechanical mechanisms rather than through continuum damage mechanics. Specially, a novel microstructure-based back stress model is proposed considering the morphology and size variation of the γ'/γ structure on the basis of dislocation wall theory. The capability of the model is validated by the stress-strain responses and the microstructural rafting behaviours by coupling the thermodynamic rafting model. Finally, an application case of a centre-hole component made by a SC Ni-based superalloy is provided to highlight the capability of the model for the analysis of inelastic deformation combined with inhomogeneous microstructural rafting for engineering components. The proposed framework not only gives inherent understanding on the interaction between microstructural rafting and constitutive law by means of microphysical mechanisms, but also provides a powerful tool for analysing rafting and inelastic deformation of complex structures.

Derived brackets in bosonic string sigma-model

We study the worldsheet theory of bosonic string from the point of view of the BV formalism. We explicitly describe the derived Poisson structure which arises when we expand the Master Action near a Lagrangian submanifold. The resulting higher Poisson brackets are all degenerate and essentially constant along their symplectic leaves. Deformations of the worldsheet complex structures define a family of Lagrangian submanifolds, parametrized by Beltrami differential. The worldsheet action depends nonlinearly on the Beltrami differential, but the structure of nonlinearity is governed by the BV Master Equation. This helps to clarify the mechanism of holomorphic factorization of string amplitudes.

Sections of Lagrangian fibrations on holomorphically symplectic manifolds and degenerate twistorial deformations

Let (M,I,Ω) be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration π:M↦X, and η a closed form of Hodge type (1,1)+(2,0) on X. We prove that Ω′:=Ω+π⁎η is again a holomorphically symplectic form, for another complex structure I′, which is uniquely determined by Ω′. The corresponding deformation of complex structures is called “degenerate twistorial deformation”. The map π is holomorphic with respect to this new complex structure, and X and the fibers of π retain the same complex structure as before. Let s be a smooth section of π. We prove that there exists a degenerate twistorial deformation (M,I′,Ω′) such that s is a holomorphic section.

A universe field theory for JT gravity

We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean Jackiw-Teitelboim (JT) gravity. We show how the gravitational path integral, defined as a sum over topologies, can be reproduced from the perturbative expansion of a Kodaira-Spencer (KS) field theory for the complex structure deformations of the spectral curve. We use that the Schwinger-Dyson equations for the KS theory can be mapped to the topological recursion relations. We refer to this dual description of JT gravity as a ‘universe field theory’. By introducing non-compact D-branes in the target space geometry, we can probe non-perturbative aspects of JT gravity. The relevant operators are obtained through a modification of the JT path integral with Neumann boundary conditions. The KS/JT identification suggests that the ensemble average for JT gravity can be understood in terms of a more standard open/closed duality in topological string theory.

Non-invariant deformations of left-invariant complex structures on compact Lie groups

Abstract We give small deformations of a left-invariant complex structure on each simply connected semisimple compact Lie group of even dimension which are not biholomorphic to any left-invariant (right-invariant) complex structure by using the Kuranishi space. On such deformed complex manifolds, we prove the Borel–Weil–Bott type theorem, and we compute the cohomology of holomorphic tangent bundles.

Deformations of surface defect moduli spaces

Given a 4d mathcal{N} = 2 superconformal theory with an mathcal{N} = (2, 2) superconformal surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE.

Deformations of Dolbeault cohomology classes for Lie algebra with complex structures

In this paper, we study deformations of complex structures on Lie algebras and its associated deformations of Dolbeault cohomology classes. A complete deformation of complex structures is constructed in a way similar to the Kuranishi family. The extension isomorphism is shown to be valid in this case. As an application, we prove that given a family of left-invariant deformations $$\{M_t\}_{t\in B}$$ of a compact complex manifold $$M=(\Gamma \setminus G, J)$$ where G is a Lie group, $$\Gamma$$ a sublattice and J a left-invariant complex structure, the set of all $$t\in B$$ such that the Dolbeault cohomology on $$M_t$$ may be computed by left-invariant tensor fields is an analytic open subset of B.

Generalized deformation of complex structures on nilmanifolds

On a 2-step nilmanifold with abelian complex structure, there exists an invariant (1,0)-form ρ such that dρ is type-(1,1). It acts on the kernel of ρ by contraction. When this contraction map is non-degenerate, for any given infinitesimal generalized complex deformation Γ1 we construct a solution (Γ,∂→) for the extended Maurer-Cartan equation. It amounts to identifying the obstruction ∂→ for Γ1 to be integrable, and constructing the deformation Γ when the obstruction vanishes. As a consequence of our explicit solutions for (Γ,∂→), we prove that on any real six-dimensional 2-step nilmanifold with abelian complex structure, when the contraction map is non-degenerate, every infinitesimal generalized complex deformation sufficiently close to zero is integrable. We also show that in all dimensions, if the contraction map is skew-Hermitian, then every infinitesimal generalized complex deformation sufficiently close to zero is integrable. Moreover the differential graded algebra controlling the generalized deformation of the underlying abelian complex structure is quasi-isomorphic to the one after deformation.

Application of 3D Laser Scanning Technology in Monitoring Deformation of Port Trail

Qinhuangdao Port, as the main hub port for coal transportation from north to south, has become an important coal, oil and other energy export port in China. The port facilities are in continuous operation all the year round, especially in the peak period of coal transportation in the south. The maintenance and monitoring of the equipment are faced with such problems as heavy work tasks, poor working environment, many construction disturbances, and the influence of monitoring on port production. This paper mainly introduces the application of ground 3D laser scanner in building deformation measurement based on the deformation measurement project of positioning car cable track in the unloading department of coal terminal of Qinhuangdao Port. Through actual results illustrate using the ground three-dimensional laser scanner for high-risk, complex structure deformation monitoring operation is of field operation is simple, short construction period, small impact on the continuity of production equipment, complete data and reliable advantages of accuracy, which is the ground three-dimensional laser scanner in Qinhuangdao port for the first time application, for the future of 3 d laser scanning technology in the port risk measuring project and digital 3 d modeling and so on has certain reference value.

Deformation-obstruction theory for diagrams of algebras and applications to geometry

Let X be an algebraic variety over an algebraically closed field of characteristic 0 and let \operatorname{Coh} (X) denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the deformation theory of \operatorname{Coh}(X) as an Abelian category can be seen to be controlled by the Gerstenhaber–Schack complex associated to the restriction of the structure sheaf \mathcal O_X \vert_{\mathfrak U} to a cover of affine open sets. We construct an explicit L _\infty algebra structure on the Gerstenhaber–Schack complex controlling the higher deformation theory of \mathcal O_X \vert_{\mathfrak U} or \operatorname{Coh}(X) in case X can be covered by two acyclic open sets, giving an explicit deformation-obstruction calculus for such deformations. For smooth X , such deformations recover the deformation of complex structures and deformation quantizations of X as degenerate cases, as we show by means of concrete examples.

A simple Galerkin meshless method, the Fragile Points method using point stiffness matrices, for 2D linear elastic problems in complex domains with crack and rupture propagation

SummaryThe Fragile Points method (FPM) is an elementarily simple Galerkin meshless method, employing Point‐based discontinuous trial and test functions only, without using element‐based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM for simulating the deformations of complex structures, and for simulating complex crack propagations and rupture developments, are also thoroughly discussed. Numerical examples of deformation and stress analyses of benchmark problems, as well as of realistic structures with complex geometries, demonstrate the accuracy, efficiency, and robustness of the proposed FPM. Simulations of crack initiation and propagations are also given in this study, demonstrating the advantages of the present FPM in modeling complex rupture and fracture phenomena. The crack and rupture propagation modeling in FPM is achieved without remeshing or augmenting the trial functions as in standard, extended, or generalized finite element method. The simulation of impact, penetration, and other extreme problems by FPM will be discussed in our future articles.