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ON CONFORMALLY FLAT CENTROAFFINE HYPERSURFACES 认领 引用
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作者 Cheng XING Cece LI 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1109-1138,共30页
This paper is concerned with an open problem regarding classifying n-dimensional locally strongly convex centroaffine hypersurfaces with conformally flat centroaffine metrics for n≥3.First of all,we give a classifica... This paper is concerned with an open problem regarding classifying n-dimensional locally strongly convex centroaffine hypersurfaces with conformally flat centroaffine metrics for n≥3.First of all,we give a classification of such hypersurfaces by assuming that the Tchebychev operator(i.e.,centroaffine shape operator)is Codazzi;this includes those hypersurfaces with vanishing or parallel Tchebychev operators as subclasses.Second,these hypersurfaces are classified under the geometric condition that the Ricci tensor is semi-parallel,as a natural extension of the Einstein condition.New examples are constructed in this paper,and all examples in the classifications above are calculated in detail in order to better illustrate our results. 展开更多
关键词 centroaffine hypersurface conformally flat Tchebychev operator semi-parallel Ricci tensor warped product
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The Submanifolds with Parallel Mean Curvature Vector in a Locally Symmetric and Conformally Flat Riemannian Manifold 认领 引用 被引量：8
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作者 孙华飞 《Chinese Quarterly Journal of Mathematics》 1992年第1期32-36,共5页
In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold Nn+p(p>1). If the... In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold Nn+p(p>1). If then M^n lies in a totally geodesic submanifold Nn+1. 展开更多
关键词 Locally symmetric conformally flat parallel mean curvature vector
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On Submanifolds in Locally Symmetric and Conformally Flat Riemannian Manifolds 认领 引用
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作者 SUN Hua-fei TANG Li CHEN Chun 《Journal of Beijing Institute of Technology》 EI CAS 2005年第2期208-211,共4页
Let N n+p be an(n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p.Instead of(n+p)-dimensional unit sphere,we general... Let N n+p be an(n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p.Instead of(n+p)-dimensional unit sphere,we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold. 展开更多
关键词 locally symmetric conformally flat minimal submanifold
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RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD 认领 引用 被引量：8
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作者 陈广华 徐森林 《Acta Mathematica Scientia》 SCIE 1996年第1期89-97,共9页
The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method... The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method is completely different. Meanwhile,we get better conclusion than that of [3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan[4]. 展开更多
关键词 Locally symetric,conformally flat minimal submanifold,scalar curvature sectional curvature.
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The Conformally Symmetric K-Contact Manifolds 认领 引用
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作者 郭震 《Chinese Quarterly Journal of Mathematics》 1992年第1期5-10,共6页
In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvatu... In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds. 展开更多
关键词 Conformally symmetric Contact Structure Killing vector field
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CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM 认领 引用 被引量：1
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作者 徐辉阳 李策策 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2413-2429,共17页
In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we... In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined. 展开更多
关键词 affine hypersurface semi-parallel cubic form Levi-Civita connection conformally flat warped product
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A HARNACK TYPE INEQUALITY FOR SOME CONFORMALLY INVARIANT EQUATIONS ON HALF EUCLIDEAN SPACE 认领 引用 被引量：1
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作者 Aobing Li Yan Yan Li 《Acta Mathematica Scientia》 SCIE 2009年第4期1105-1112,共8页
We establish a Harnack type inequality on half Euclidean space for general conformally invariant fully nonlinear elliptic equations of second order.
关键词 Harnack conformally invariant elliptic
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M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds 认领 引用 被引量：1
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作者 Yun Miao Liqun Qi Yimin Wei 《Communications in Mathematical Research》 CSCD 2020年第3期336-353,共18页
We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-e... We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity. 展开更多
关键词 M-eigenvalue Riemann curvature tensor Ricci tensor conformal invariant canonical form
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A Global Rigidity Theorem for the Length of Concircular Curvature Tensor on the Locally Conformally Symmetric Riemannian Manifold 认领 引用
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作者 Shipei HU 《Journal of Mathematical Research with Applications》 CSCD 2020年第2期187-195,共9页
In this paper, we study the locally conformally symmetric closed Riemannian manifold, and establish a global rigidity theorem for the length of the concircular curvature vector.
关键词 conformally symmetric Riemannian curvature tensor concircular curvature vector Weyl tensor Schouten tensor
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Inflation with Conformally Coupled Scalar Field 认领 引用
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作者 WANG Wenfu 《Chinese Physics Letters》 SCIE CAS 1995年第12期766-768,共3页
In a Robertson-Walker geometry conformally coupled to a scalar field with inflation potential V(φ)=M4-(1/4)λ φ4,we investigate the classical evolution of a universe.The exact solutions in the model have been ... In a Robertson-Walker geometry conformally coupled to a scalar field with inflation potential V(φ)=M4-(1/4)λ φ4,we investigate the classical evolution of a universe.The exact solutions in the model have been found.It is shown that in the region where the value of the φ field is 0<φ<φmax,(φmax is the solution of V(φ)=0),there is inflation.This model can lead to successful inflation with λ~10-9,rather than 10-13 as previously reported. 展开更多
关键词 exact scalar conformally
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The Minimal Submanifolds in a Locally Symmetric and Conformally Flat Riemannian Manifold 认领 引用
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作者 舒世昌 《Chinese Quarterly Journal of Mathematics》 1993年第4期71-76,共6页
In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N+p.When N+pis a space S1+p of constant curvature,our theo... In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N+p.When N+pis a space S1+p of constant curvature,our theorems reduce to the theorems of[1],[2]. 展开更多
关键词 Locally symmetric conformally flat minimal submanifold
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Conformally symmetric wormhole solutions supported by non-commutative geometry in f(Q,T)gravity 认领 引用
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作者 Chaitra Chooda Chalavadi V Venkatesha +1 位作者 N S Kavya S V Divya Rashmi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2024年第2期111-124,共14页
This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole... This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results. 展开更多
关键词 traversable wormhole f(Q T)gravity energy conditions non-commutative geometry conformal motion
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On the Dynamical 4D BTZ Black Hole Solution in Conformally Invariant Gravity 认领 引用
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作者 Reinoud J. Slagter 《Journal of Modern Physics》 2020年第10期1711-1730,共20页
We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The me... We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The metric is written as  where the dilaton field ω contains all the scale dependencies and where  represents the “un-physical” spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and singular free  out of a BTZ-type solution for . In the vacuum situation, an exact time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2 + 1)-dimensional BTZ spacetime as well as for the uplifted (3 + 1)-dimensional BTZ spacetime. While  resembles the standard BTZ solution with its horizons,  is flat. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem of how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues. This research shows the power of conformally invariant gravity and can be applied to bridge the gap between general relativity and quantum field theory in the vicinity of the horizons of black holes. 展开更多
关键词 Scalar-Gauge Field Baňados-Teitelboim-Zanelli Black Hole Conformal Invariance Dilaton Field Eddington-Finkelstein Coordinate Black Hole Complementarity Antipodal Identification
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Construction of Initial Data Sets for Einstein-Scalar and Einstein-Maxwell Equations by Conformally Covariant Split System 认领 引用
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作者 Xiaohui TIAN Naqing XIE 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2026年第1期59-70,共12页
By using the implicit function,the authors prove the existence of solutions of the conformally covariant split system on compact three-dimensional Riemannian manifolds.They give rise to certain initial data for the Ei... By using the implicit function,the authors prove the existence of solutions of the conformally covariant split system on compact three-dimensional Riemannian manifolds.They give rise to certain initial data for the Einstein-scalar system and the Einstein-Maxwell system. 展开更多
关键词 Constraint equations Conformally covariant split Initial data Einsteinscalar Einstein-Maxwell
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Yamabe-Harmonic Flow on Locally Conformally Flat Manifolds 认领 引用
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作者 Zihao Wang 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2026年第7期1768-1784,共17页
In this paper we introduce a new geometric flow consisting of the Yamabe flow coupled with harmonic heat flow of a function on a closed manifold M,or shortly Yamabe-harmonic flow.It is define by To begin with we estab... In this paper we introduce a new geometric flow consisting of the Yamabe flow coupled with harmonic heat flow of a function on a closed manifold M,or shortly Yamabe-harmonic flow.It is define by To begin with we establish the short-time extsience via conformal transformation for any smooth initial data.Furthermore we derive interior-in-time derivative estimates for the Riemannian curvature and Lapse function and obtain the global existence of Yamabe-harmonic flow.Moreover,compact gradient Yamabe-harmonic solitons are proved to be manifolds with R=ϕ=Constant.Eventually we obtain the classification of singularities by blow-up rate of AC curvature,which is analogous to that of Ricci-harmonic flow and Ricci-connection flow.The relationship between singularity models and solitons shall appear in forthcoming work. 展开更多
关键词 Yamabe-harmonic flow locally conformally flat manifold gradient estimate global existence soliton singularities classification
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Classification of the Conformally Flat Centroaffine Hypersurfaces with Vanishing Centroaffine Shape Operator 认领 引用
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作者 Miaoxin LEI Ruiwei XU Peibiao ZHAO 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2025年第2期163-180,共18页
Cheng-Hu-Moruz(2017)completely classified the locally strongly convex centroaffine hypersurfaces with parallel cubic form based on the Calabi product(called the type I Calabi product for short)proposed by Li-Wang(1991... Cheng-Hu-Moruz(2017)completely classified the locally strongly convex centroaffine hypersurfaces with parallel cubic form based on the Calabi product(called the type I Calabi product for short)proposed by Li-Wang(1991).In the present paper,the authors introduce the type II Calabi product(in case λ1=2λ2),complementing the type I Calabi product(in caseλ1≠2λ2),and achieve a classification of the locally strongly convex centroaffine hypersurfaces in Rn+1 with vanishing centroaffine shape operator and Weyl curvature tensor by virtue of the types I and II Calabi product.As a corollary,3-dimensional complete locally strongly convex centroaffine hypersurfaces with vanishing centroaffine shape operator are completely classified,which positively answers the centroaffine Bernstein problems III and V by Li-Li-Simon(2004). 展开更多
关键词 Centroaffine hypersurface Centroaffine shape operator Calabi product Locally conformally flat Calabi hypersurface
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融合最大池化的Conformer中文语音识别 认领 引用 被引量：2
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作者 胡从刚 杨立鹏 +2 位作者 孙永奇 陈华龙 韩可可 《计算机工程》 CAS CSCD 北大核心 2026年第1期105-115,共11页
语音识别旨在通过先进的算法与信号处理技术,赋予机器理解人类语音的能力,使得人与机器之间的交流更加便捷、顺畅。目前,大多数端到端语音识别的研究工作主要围绕Conformer模型进行优化。针对Conformer编码器对语音细粒度局部特征提取... 语音识别旨在通过先进的算法与信号处理技术,赋予机器理解人类语音的能力,使得人与机器之间的交流更加便捷、顺畅。目前,大多数端到端语音识别的研究工作主要围绕Conformer模型进行优化。针对Conformer编码器对语音细粒度局部特征提取能力不足的问题,提出一种融合最大池化(MP)的Conformer中文语音识别模型。首先,将编码器卷积模块中门控线性单元的输出在时间维度上进行MP,以提取多帧语音信号对应一个字符的细粒度局部特征。然后,将池化后的特征与逐通道卷积(DWC)提取的粗粒度局部特征以逐元素相加的方式进行融合,以增加语音局部特征的信息量,从而提高Conformer模型的语音识别准确率。最后,在公开的中文数据集Aishell-1上的实验结果表明:采用贪心搜索方式进行解码,所提模型可以将基线模型的字错误率(CER)从5.58%降低至5.32%;采用注意力重打分方式进行解码,所提模型可以将基线模型的CER从5.06%降低至4.92%。 展开更多
关键词 语音识别 细粒度局部特征 Conformer模型 最大池化 逐通道卷积
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A novel Angle-Constrained Optimization method of Conformal Lattice Structures 认领 引用 被引量：1
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作者 Jun Yan Weibin Xu +2 位作者 Fuhao Wang Sixu Huo Kun Yan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2026年第2期269-295,共27页
Conformal truss-like lattice structures face significant manufacturability challenges in additive manufac-turing due to overhang angle limitations.To address this problem,we propose a novel angle-constrained optimizat... Conformal truss-like lattice structures face significant manufacturability challenges in additive manufac-turing due to overhang angle limitations.To address this problem,we propose a novel angle-constrained optimization method grounded in the global adjustment of nodal coordinates.First,a build direction is selected to minimize the number of violating struts.Then,an angular-constraint matrix is assembled from strut direction vectors,and analytical sensitivities with respect to nodal coordinates are derived to enable efficient constrained optimization under nonlinear angular inequality constraints.Numerical studies on two complex curved-surface lattices demonstrate that all overhang violations are eliminated while only minor changes are induced in global stiffness and strength.In particular,the maximum displacement of an ergonomic insole varies by only 2.87%after optimization.The results confirm the method’s versatility and engineering robustness,providing a practical approach for additive manufacturing-oriented lattice structure design. 展开更多
关键词 Conformal lattice structures additive manufacturing structural optimization complex structures
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Conformal ultra-thin,ultra-uniform metal films fabricated on non-planar substrates for advanced optoelectronics 认领 引用
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作者 Heyan Wang Jianghai He +5 位作者 Yingzheng Ren Huan Liu Yibin Jin Yilei Zhang Zhengang Lu Jiubin Tan 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2026年第3期826-839,共14页
Transparent conducting films are indispensable to modern optoelectronic devices due to their unique combination of high transparency and electrical conductivity.While existing fabrication methods—such as physical vap... Transparent conducting films are indispensable to modern optoelectronic devices due to their unique combination of high transparency and electrical conductivity.While existing fabrication methods—such as physical vapor deposition and solution-based synthesis—are well-established for flat substrates,producing high-quality transparent conductors on non-planar surfaces remains a significant challenge,largely due to difficulties in achieving conformal coverage,nanoscale uniformity,and consistent optoelectrical performance.In this study,we report a conformal deposition model with metal co-doping method on curved surfaces that can produce ultra-thin(≤10 nm),ultra-uniform(±0.5 nm),and ultra-smooth metal films.This work sets a new benchmark for conformal sub-10 nm metal films,whose optoelectrical performance rivals that of planar counterparts,achieving an average visible transmittance of∼88%and sheet resistance of∼8.1Ω·sq-1 with capping layers.In addition,the process can be further extended to a range of optical dielectrics,enabling precise production of advanced conformal coatings.These findings provide practical pathways for optoelectronic applications,including curved transparent electrodes,three-dimensional optical-to-microwave devices,and next-generation smart glasses. 展开更多
关键词 conformal ultra-thin metal curved transparent conducting films high transparency conformal deposition method metal co-doping
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High-resolution robotic electrohydrodynamic printing on rough,freeform surfaces via a self-stabilized electric-field technique 认领 引用
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作者 Jiaying Ge Dong Ye +5 位作者 Junmin Wen Shuang Fu Panpan Wang Hao Wu Yanqiao Pan YongAn Huang 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2026年第3期736-757,共22页
3D conformal printing has emerged as one of the most promising strategies for constructing micropatterns or microstructures on large-area curved surfaces,enabling innovative applications such as electromagnetic metama... 3D conformal printing has emerged as one of the most promising strategies for constructing micropatterns or microstructures on large-area curved surfaces,enabling innovative applications such as electromagnetic metamaterials and electronic devices.The robotic conformal electrohydrodynamic(EHD)printing(RE-printing)technique is highly appealing in this respect because of its capability for submicron-scale patterning and compatibility with a broad range of ink viscosities.However,maintaining a steady electric field to ensure uniform deposition on curved and rough surfaces is challenging.Here,we propose an eye-inlaid printhead with a'neighborhood'path compensation algorithm and a self-stabilizing electric field mechanism to significantly improve the accuracy of RE printing and find that a steady electric field strength,rather than a constant printing height,affects the uniformity of EHD-printed patterns more.This printhead integrates a camera for tangent plane positioning alongside a laser displacement sensor for measuring normal displacement and facilitates precise 3D positioning.The path compensation algorithm can maintain the electric field strength during the printing process by calculating the average local nozzle-to-substrate distance through in situ measurements of the printing height.This approach can not only stabilize the electric field but also reduce the robotic vibration caused by a fluctuating path on rough surfaces,reducing the electric field strength fluctuations from 20%to 5%and the vibration amplitude from 55µm to nearly 0µm compared with those of the traditional'point-to-point'path compensation technique.In addition,it can adaptively correct substrate model errors,frame deviations,and robot motion inaccuracies.The mean absolute deviation of the nozzle-to-substrate distance can be reduced to20µm,presenting an enhancement in printing precision by 77.23%compared with that of the'point-to-point'path compensation strategy.As a result,this approach achieves consistent line width and electrical resistance on curved substrates,supporting high-resolution conformal printing on surfaces with curvature radii as small as 1 mm and resolutions up to 5µm.Finally,de-icing heaters have been conformally fabricated on an airplane wing,and their performance has been confirmed through subsequent de-icing trials.This approach promises a versatile solution for the RE printing of large-area 3D conformal electronic devices. 展开更多
关键词 conformal printing electrohydrodynamic printing curved electronics robotic fabrication path compensation
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