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THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS
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作者 肖存涛 邱华 姚正安 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期973-983,共11页
In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small in... In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution. 展开更多
关键词 regularized MHD equations fractional Laplacian global well-posedness analyticity decay rate
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TIME ANALYTICITY FOR THE HEAT EQUATION ON GRADIENT SHRINKING RICCI SOLITONS
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作者 Jiayong WU 《Acta Mathematica Scientia》 SCIE CSCD 2022年第4期1690-1700,共11页
On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sh... On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers. 展开更多
关键词 Gradient shrinking Ricci soliton heat equation time analyticity
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Analyticity of Semigroups Generated by Singular Differential Matrix Operators
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作者 Ould Ahmed Mahmoud Sid Ahmed Adel Saddi 《Applied Mathematics》 2010年第4期283-287,共5页
In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is... In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is discussed. 展开更多
关键词 DISSIPATIVE OPERATORS Positive OPERATORS Spectrum ANALYTIC SEMIGROUPS Evolution Equations
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Analyticity of Semigroups generated by Degenerate Mixed Differential Operators
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作者 Adel Saddi 《Advances in Pure Mathematics》 2011年第3期42-48,共7页
In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analy... In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analytic semigroups on an appropriate Hilbert space . To illustrate the results an example is discussed. 展开更多
关键词 ADJOINT Interface DISSIPATIVE Operators ANALYTIC SEMIGROUPS
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On the Radius of Spatial Analyticity for the Inviscid Boussinesq Equations
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作者 CHENG Feng XU Chao-Jiang 《Journal of Partial Differential Equations》 CSCD 2020年第3期235-248,共14页
In this paper,we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations.If the initial datum is real-analytic,the solution remains real-analytic on the existence interval.By an induc... In this paper,we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations.If the initial datum is real-analytic,the solution remains real-analytic on the existence interval.By an inductive method we can obtain a lower bound on the radius of spatial analyticity of the smooth solution. 展开更多
关键词 Boussinesq equations analyticity radius of analyticity
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Analyticity of thermoelastic plates with dynamical boundary conditions 被引量:5
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作者 张琼 黄发伦 《Science China Mathematics》 SCIE 2003年第5期631-640,共10页
We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is... We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is analytic, hence exponentially stable. 展开更多
关键词 THERMOELASTICITY C 0 semigroup analyticity exponential stability
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The analyticity of solutions to a class of degenerate elliptic equations 被引量:2
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作者 LI ChunHe School of Mathematical Science,University of Electronic Science and Technology of China,Chengdu 610054,China 《Science China Mathematics》 SCIE 2010年第8期2061-2068,共8页
In the present paper,the analyticity of solutions to a class of degenerate elliptic equations is obtained.A kind of weighted norms are introduced and under such norms some degenerate elliptic operators are of weak coe... In the present paper,the analyticity of solutions to a class of degenerate elliptic equations is obtained.A kind of weighted norms are introduced and under such norms some degenerate elliptic operators are of weak coerciveness. 展开更多
关键词 analyticity DEGENERATE ELLIPTIC equations weighted NORM WEAK COERCIVENESS
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Analyticity of the Sine Family with L^P-Maximal Regularity for Second Order Cauchy Problems
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作者 Yong Zhong HUANG Meng Cheng WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第3期561-568,共8页
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining th... If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 展开更多
关键词 analyticity second order Cauchy problem maximal regularity PROPAGATOR
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Analyticity of Mild Solution for the 3D Incompressible Magneto-hydrodynamics Equations in Critical Spaces
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作者 Sheng WANG Yu Bing REN Fu Yi XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第11期1731-1741,共11页
The Cauchy problem for the 3D incompressible magneto-hydrodynamics equations in crit- cal spaces is considered. We first prove the global well-posedness of mild solution for the system in some time dependent spaces. F... The Cauchy problem for the 3D incompressible magneto-hydrodynamics equations in crit- cal spaces is considered. We first prove the global well-posedness of mild solution for the system in some time dependent spaces. Furthermore, we obtain analyticity of the solution. 展开更多
关键词 Lobal well-posedness analyticity mild solutions 3D incompressible magneto-hydrody- namics equations
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On the Radius of Analyticity of Solutions to 3D Navier-Stokes System with Initial Data in L^(p)
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作者 Ruilin HU Ping ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2022年第5期749-772,共24页
Given initial data u0 ∈ L^(p)(R^(3)) for some p in [3,18/5 [,the auhtors first prove that3 D incompressible Navier-Stokes system has a unique solution μ=μL+v with μL=^(def)e^(t△)μ_(0) and ν∈L^(∞)([0,T];H^(5/2... Given initial data u0 ∈ L^(p)(R^(3)) for some p in [3,18/5 [,the auhtors first prove that3 D incompressible Navier-Stokes system has a unique solution μ=μL+v with μL=^(def)e^(t△)μ_(0) and ν∈L^(∞)([0,T];H^(5/2)-^(6/p)∩L^(1)([0,T];H^(9/2-6/p) for some positive time T.Then they derive an explicit lower bound for the radius of space analyticity of v,which in particular extends the corresponding results in [Chemin,J.-Y.,Gallagher,I.and Zhang,P.,On the radius of analyticity of solutions to semi-linear parabolic system,Math.Res.Lett.,27,2020,1631-1643,Herbst,I.and Skibsted,E.,Analyticity estimates for the Navier-Stokes equations,Adv.in Math.,228,2011,1990-2033] with initial data in H^(s)(R^(3)) for s ∈ [1/2,3/2[. 展开更多
关键词 Incompressible Navier-Stokes equations Radius of analyticity Littlewood-Paley theory
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Wave Energy System Combined by a Heaving Box and a Perforated Flexible Membrane Wall
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作者 Sarat Chandra Mohapatra C.Guedes Soares 《哈尔滨工程大学学报(英文版)》 2026年第1期110-121,共12页
An analytical model of a floating heaving box integrated with a vertical flexible porous membrane placed right next to the box applications to wave energy extraction and breakwater systems is developed under the reduc... An analytical model of a floating heaving box integrated with a vertical flexible porous membrane placed right next to the box applications to wave energy extraction and breakwater systems is developed under the reduced wave equation.The theoretical solutions for the heave radiating potential to the assigned physical model in the corresponding zones are attained by using the separation of variables approach along with the Fourier expansion.Applying the matching eigenfunction expansion technique and orthogonal conditions,the unknown coefficients that are involved in the radiated potentials are determined.The attained radiation potential allows the computation of hydrodynamic coefficients of the heaving buoy,Power Take-Off damping,and wave quantities.The accuracy of the analytical solution for the hydrodynamic coefficients is demonstrated for different oblique angles with varying numbers of terms in the series solution.The current analytical analysis findings are confirmed by existing published numerical boundary element method simulations.Several numerical results of the hydrodynamic coefficients,power capture,power take-off optimal damping,and transmission coefficients for numerous structural and physical aspects are conducted.It has been noted that the ideal power take-off damping increases as the angle of incidence rises,and the analysis suggests that the ability to capture waves is more effective in shallower waters compared to deeper ones. 展开更多
关键词 Analytical model Heaving buoy Flexible membrane perforated wall Boundary element method code Power take-off Power capture
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The analyticity of abstract parabolic and correct systems 被引量:2
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作者 郑权 《Science China Mathematics》 SCIE 2002年第7期859-865,共7页
Let A be the matrix associated with an abstract parabolic system in the sense of Shilov or correct system in the sense of Petrovskii. We show that if the spectrum of its symbol is contained in a sector including some ... Let A be the matrix associated with an abstract parabolic system in the sense of Shilov or correct system in the sense of Petrovskii. We show that if the spectrum of its symbol is contained in a sector including some negative real axis, then A generates an analytic regularized semigroup. The corresponding result related to numerical range conditions is also showed. Moreover, these results are applied to matrices of partial differential operators on many function spaces. 展开更多
关键词 PARABOLIC system CORRECT system analytic REGULARIZED semigroup functional calculus Fourier multiplier.
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A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential
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作者 Chaojiang Xu Yan Xu 《Analysis in Theory and Applications》 CSCD 2024年第1期22-37,共16页
In this note,we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials.We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time va... In this note,we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials.We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L2 initial datum for positive time.So that the smoothing effect of Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat equation. 展开更多
关键词 Spatially homogeneous Landau equation analytic smoothing effect soft potentials
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基于FAHP-TOPSIS法的地下空间开发地质适宜性评价
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作者 李浩民 瞿婧晶 张其琪 《科学技术与工程》 北大核心 2025年第30期13187-13196,共10页
为了客观评价地下空间开发地质适宜性并为评价工作提供一种新思路和参考,提出了一种基于三角模糊数的模糊层次分析法(fuzzy analytic hierarchy process based on triangular fuzzy numbers,FAHP)和优劣解距离法(technique for order pr... 为了客观评价地下空间开发地质适宜性并为评价工作提供一种新思路和参考,提出了一种基于三角模糊数的模糊层次分析法(fuzzy analytic hierarchy process based on triangular fuzzy numbers,FAHP)和优劣解距离法(technique for order preference by similarity to ideal solution,TOPSIS)相结合的评价方法。通过地质调查研究构建基于土体工程地质性质、水文地质条件、不良地质作用、地形地貌等影响因素为主的层次分析关系模型。基于专家判别利用FAHP计算各评价因素的权重,以各评价指标层的分级临界值作为典型评价样本,利用TOPSIS法对适宜性等级进行非等分划分,基于区间值优化的TOPSIS法建立最终评价模型,通过ArcGIS的空间分析功能等确定每个评价单元适宜性等级。该方法与传统方法相比一定程度上减少了评价过程中专家评判的过多主观影响,评价过程更倾向于定量化,结果更为客观。利用该方法对无锡市区浅层地下空间开发地质适宜性进行评价,评价结果与实际工程经验相符,证明了该方法的有效性,因此该方法对地下空间开发适宜性评价工作具有一定借鉴意义。 展开更多
关键词 FAHP(fuzzy analytic hierarchy process) TOPSIS(technique for order preference by similarity to an ideal solution) 城市地下空间 地质适宜性评价
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Smart cities,smart systems:A comprehensive review of system dynamics model applications in urban studies in the big data era 被引量:2
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作者 Gift Fabolude Charles Knoble +1 位作者 Anvy Vu Danlin Yu 《Geography and Sustainability》 2025年第1期25-36,共12页
This paper addresses urban sustainability challenges amid global urbanization, emphasizing the need for innova tive approaches aligned with the Sustainable Development Goals. While traditional tools and linear models ... This paper addresses urban sustainability challenges amid global urbanization, emphasizing the need for innova tive approaches aligned with the Sustainable Development Goals. While traditional tools and linear models offer insights, they fall short in presenting a holistic view of complex urban challenges. System dynamics (SD) models that are often utilized to provide holistic, systematic understanding of a research subject, like the urban system, emerge as valuable tools, but data scarcity and theoretical inadequacy pose challenges. The research reviews relevant papers on recent SD model applications in urban sustainability since 2018, categorizing them based on nine key indicators. Among the reviewed papers, data limitations and model assumptions were identified as ma jor challenges in applying SD models to urban sustainability. This led to exploring the transformative potential of big data analytics, a rare approach in this field as identified by this study, to enhance SD models’ empirical foundation. Integrating big data could provide data-driven calibration, potentially improving predictive accuracy and reducing reliance on simplified assumptions. The paper concludes by advocating for new approaches that reduce assumptions and promote real-time applicable models, contributing to a comprehensive understanding of urban sustainability through the synergy of big data and SD models. 展开更多
关键词 Urban sustainability Smart cities System dynamics models Big data analytics Urban system complexity Data-driven urbanism
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Integration of data science with the intelligent IoT(IIoT):Current challenges and future perspectives 被引量:2
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作者 Inam Ullah Deepak Adhikari +3 位作者 Xin Su Francesco Palmieri Celimuge Wu Chang Choi 《Digital Communications and Networks》 2025年第2期280-298,共19页
The Intelligent Internet of Things(IIoT)involves real-world things that communicate or interact with each other through networking technologies by collecting data from these“things”and using intelligent approaches,s... The Intelligent Internet of Things(IIoT)involves real-world things that communicate or interact with each other through networking technologies by collecting data from these“things”and using intelligent approaches,such as Artificial Intelligence(AI)and machine learning,to make accurate decisions.Data science is the science of dealing with data and its relationships through intelligent approaches.Most state-of-the-art research focuses independently on either data science or IIoT,rather than exploring their integration.Therefore,to address the gap,this article provides a comprehensive survey on the advances and integration of data science with the Intelligent IoT(IIoT)system by classifying the existing IoT-based data science techniques and presenting a summary of various characteristics.The paper analyzes the data science or big data security and privacy features,including network architecture,data protection,and continuous monitoring of data,which face challenges in various IoT-based systems.Extensive insights into IoT data security,privacy,and challenges are visualized in the context of data science for IoT.In addition,this study reveals the current opportunities to enhance data science and IoT market development.The current gap and challenges faced in the integration of data science and IoT are comprehensively presented,followed by the future outlook and possible solutions. 展开更多
关键词 Data science Internet of things(IoT) Big data Communication systems Networks Security Data science analytics
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Fast and Accurate Prediction of Electromagnetic and Temperature Fields for SPMSM Equipped with Unequally Thick Magnetic Poles 被引量:2
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作者 Feng Liu Xiuhe Wang +1 位作者 Lingling Sun Hongye Wei 《CES Transactions on Electrical Machines and Systems》 2025年第2期199-211,共13页
With the continuous upgrading of traditional manufacturing industries and the rapid rise of emerging technology fields,the performance requirements for the permanent magnet synchronous motors(PMSMs)have become higher ... With the continuous upgrading of traditional manufacturing industries and the rapid rise of emerging technology fields,the performance requirements for the permanent magnet synchronous motors(PMSMs)have become higher and higher.The importance of fast and accurate electromagnetic thermal coupling analysis of such motors becomes more and more prominent.In view of this,the surfacemounted PMSM(SPMSM)equipped with unequally thick magnetic poles is taken as the main object and its electromagnetic thermal coupling analytical model(ETc AM)is investigated.First,the electromagnetic analytical model(EAM)is studied based on the modified subdomain method.It realizes the fast calculation of key electromagnetic characteristics.Subsequently,the 3D thermal analytical model(TAM)is developed by combining the EAM,the lumped parameter thermal network method(LPTNM),and the partial differential equation of heat flux.It realizes the fast calculation of key thermal characteristics in 3D space.Further,the information transfer channel between EAM and TAM is built with reference to the intrinsic connection between electromagnetic field and temperature field.Thereby,the novel ETcAM is proposed to realize the fast and accurate prediction of electromagnetic and temperature fields.Besides,ETcAM has a lot to commend it.One is that it well accounts for the complex structure,saturation,and heat exchange behavior.Second,it saves a lot of computer resources.It offers boundless possibilities for initial design,scheme evaluation,and optimization of motors.Finally,the validity,accuracy,and practicality of this study are verified by simulation and experiment. 展开更多
关键词 Electromagnetic field and temperature field Electromagnetic thermal coupling analytical model(ETcAM) Fast and accurate prediction SPMSM Unequally thick magnetic poles
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Geometric size and forming force prediction in incremental flanging:A new analytical model 被引量:1
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作者 Chong TIAN Dawei ZHANG +1 位作者 Guangcan YANG Shengdun ZHAO 《Chinese Journal of Aeronautics》 2025年第2期519-540,共22页
A new analytical model for geometric size and forming force prediction in incremental flanging(IF)is presented in this work.The complex deformation characteristics of IF are considered in the modeling process,which ca... A new analytical model for geometric size and forming force prediction in incremental flanging(IF)is presented in this work.The complex deformation characteristics of IF are considered in the modeling process,which can accurately describe the strain and stress states in IF.Based on strain analysis,the model can predict the material thickness distribution and neck height after IF.By considering contact area,strain characteristics,material thickness changes,and friction,the model can predict specific moments and corresponding values of maximum axial forming force and maximum horizontal forming force during IF.In addition,an IF experiment involving different tool diameters,flanging diameters,and opening hole diameters is conducted.On the basis of the experimental strain paths,the strain characteristics of different deformation zones are studied,and the stable strain ratio is quantitatively described through two dimensionless parameters:relative tool diameter and relative hole diameter.Then,the changing of material thickness and forming force in IF,and the variation of minimum material thickness,neck height,maximum axial forming force,and maximum horizontal forming force with flanging parameters are studied,and the reliability of the analytical model is verified in this process.Finally,the influence of the horizontal forming force on the tool design and the fluctuation of the forming force are explained. 展开更多
关键词 Incremental flanging Analytical model Strain characteristic Geometric size Forming force
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Hydraulic fracturing-based analytical method for determining seepage characteristics at tunnel-gasketed joints 被引量:1
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作者 GONG Chen-jie CHENG Ming-jin +2 位作者 FAN Xuan PENG Yi-cheng DING Wen-qi 《Journal of Central South University》 2025年第4期1520-1534,共15页
Waterproof performance of gaskets between segments is the focus of shield tunnels.This paper proposed an analytical method for determining seepage characteristics at tunnel-gasketed joints based on the hydraulic fract... Waterproof performance of gaskets between segments is the focus of shield tunnels.This paper proposed an analytical method for determining seepage characteristics at tunnel-gasketed joints based on the hydraulic fracturing theories.First,the mathematical model was established,and the seepage governing equation and boundary conditions were obtained.Second,three dimensionless parameters were introduced for simplifying the expressions,and the seepage governing equations were normalized.Third,analytical expressions were derived for the interface opening and liquid pressure.Moreover,the influencing factors of seepage process at the gasketed interface were analyzed.Parametric analyses revealed that,in the normalized criterion of liquid viscosity,the liquid tip coordinate was influenced by the degree of negative pressure in the liquid lag region,which was related to the initial contact stress.The coordinate of the liquid tip affected the liquid pressure distribution and the interface opening,which were analyzed under different liquid tip coordinate conditions.Finally,under two limit states,comparative analysis showed that the results of the variation trend of the proposed method agree well with those of previous research.Overall,the proposed analytical method provides a novel solution for the design of the waterproof in shield tunnels. 展开更多
关键词 shield tunnels segment joints seepage characteristics hydraulic fracture analytical solution
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Deformation analysis of ground and existing tunnel induced by overlapped curved shield tunneling 被引量:1
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作者 Yingnan Liu Huayang Lei +2 位作者 Liang Shi Gang Zheng Mengting Wang 《Journal of Rock Mechanics and Geotechnical Engineering》 2025年第2期795-809,共15页
The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield... The deformation caused by tunnel excavation is quite important for safety,especially when it is adjacent to the existing tunnel.Nevertheless,the investigation of deformation characteristics in overlapped curved shield tunneling remains inadequate.The analytical solution for calculating the deformation of the ground and existing tunnel induced by overlapped curved shield tunneling is derived by the Mirror theory,Mindlin solution and Euler-Bernoulli-Pasternak model,subsequently validated through both finite element simulation and field monitoring.It is determined that the overcutting plays a crucial role in the ground settlement resulting from curved shield tunneling compared to straight shield tunneling.The longitudinal settlement distribution can be categorized into five areas,with the area near the tunnel surface experiencing the most dramatic settlement changes.The deformation of the existing tunnel varies most significantly with turning radius compared to tunnel clearance and grouting pressure,especially when the turning radius is less than 30 times the tunnel diameter.The tunnel crown exhibits larger displacement than the tunnel bottom,resulting in a distinctive‘vertical egg'shape.Furthermore,an optimized overcutting mode is proposed,involving precise control of the extension speed and angular velocity of the overcutting cutter,which effectively mitigates ground deformation,ensuring the protection of the existing tunnel during the construction. 展开更多
关键词 Overlapped curved shield tunneling Analytical solution Ground deformation Existing tunnel Overcutting mode
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