This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a f...This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.展开更多
Low-frequency vibroseis acquisition has become a routine operation in land seismic surveys,given the advantages of low-frequency signals in characterizing geological structures and enhancing the imaging of deep explor...Low-frequency vibroseis acquisition has become a routine operation in land seismic surveys,given the advantages of low-frequency signals in characterizing geological structures and enhancing the imaging of deep exploration targets.The two key points of low-frequency sweep design techniques include controlling the distortion and improving the output energy during the low-frequency stage.However,the vibrators are limited by the maximum fl ow provided by the hydraulic systems at the low-frequency stage,causing difficulty in satisfying exploration energy requirements.Initially,a theoretical analysis of the low-frequency acquisition performance of vibrators is conducted.A theoretical maximum output force below 10 Hz is obtained by guiding through theoretical formulas and combining actual vibrator parameters.Then,the signal is optimized according to the surface characteristics of the operation area.Finally,detailed application quality control and operational procedures are established.The new low-frequency sweep design method has overcome the maximum flow limitations of the hydraulic system,increased the low-frequency energy,and achieved broadband acquisition.The designed signal has been tested and applied on various types of ground surfaces in the Middle East desert region,yielding good performance.The proposed low-frequency sweep design method holds considerable value for the application of conventional vibroseis in low-frequency acquisition.展开更多
Swept blades are widely utilized in transonic compressors/fans and provide high load,high through-flow,high efficiency,and adequate stall margin.However,there is limited quantitative research on the mechanism of the e...Swept blades are widely utilized in transonic compressors/fans and provide high load,high through-flow,high efficiency,and adequate stall margin.However,there is limited quantitative research on the mechanism of the effect of swept blades on the flow field,resulting in a lack of direct quantitative guidance for the design and analysis of swept blades in fans/compressors.To better understand this mechanism,this study employs a reduced-dimensional force equilibrium method to analyze more than 1500 swept cascades data.Results verify that circumferential fluctuation terms are responsible for inducing radial migration in the inlet airflow field of the swept blade,resulting in variations in the incidence angle and consequently leading to changes in the characteristics of the swept blade.Thus,a combination of simple functions and machine learning is utilized to model the circumferential fluctuation terms and quantify the sweep mechanism.The prediction accuracy of the model is high,with coefficient of determination greater than 0.95 on the test set.When the model is applied in a meridional flow analysis program,the calculation accuracy of the program for the incidence angle is improved by 0.4°and 0.6°at the design and off-design conditions respectively,compensating for the program’s original deficiencies.Meanwhile,the model can also provide quantitative guidance for the design of swept blades,thereby reducing the number of design iterations and improving design efficiency.展开更多
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.展开更多
基金supported by the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NNSF of China(12371312)+1 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the project cooperation between Guangxi Normal University and Yulin Normal University.
文摘This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.
基金The authors would like to express their sincere appreciation to the research project of CNPC Geophysical Key Lab(2022DQ0604-4)National Natural Science Foundation of China(Grant No.42074141).
文摘Low-frequency vibroseis acquisition has become a routine operation in land seismic surveys,given the advantages of low-frequency signals in characterizing geological structures and enhancing the imaging of deep exploration targets.The two key points of low-frequency sweep design techniques include controlling the distortion and improving the output energy during the low-frequency stage.However,the vibrators are limited by the maximum fl ow provided by the hydraulic systems at the low-frequency stage,causing difficulty in satisfying exploration energy requirements.Initially,a theoretical analysis of the low-frequency acquisition performance of vibrators is conducted.A theoretical maximum output force below 10 Hz is obtained by guiding through theoretical formulas and combining actual vibrator parameters.Then,the signal is optimized according to the surface characteristics of the operation area.Finally,detailed application quality control and operational procedures are established.The new low-frequency sweep design method has overcome the maximum flow limitations of the hydraulic system,increased the low-frequency energy,and achieved broadband acquisition.The designed signal has been tested and applied on various types of ground surfaces in the Middle East desert region,yielding good performance.The proposed low-frequency sweep design method holds considerable value for the application of conventional vibroseis in low-frequency acquisition.
基金supported by the National Natural Science Foundation of China(No.52376021)。
文摘Swept blades are widely utilized in transonic compressors/fans and provide high load,high through-flow,high efficiency,and adequate stall margin.However,there is limited quantitative research on the mechanism of the effect of swept blades on the flow field,resulting in a lack of direct quantitative guidance for the design and analysis of swept blades in fans/compressors.To better understand this mechanism,this study employs a reduced-dimensional force equilibrium method to analyze more than 1500 swept cascades data.Results verify that circumferential fluctuation terms are responsible for inducing radial migration in the inlet airflow field of the swept blade,resulting in variations in the incidence angle and consequently leading to changes in the characteristics of the swept blade.Thus,a combination of simple functions and machine learning is utilized to model the circumferential fluctuation terms and quantify the sweep mechanism.The prediction accuracy of the model is high,with coefficient of determination greater than 0.95 on the test set.When the model is applied in a meridional flow analysis program,the calculation accuracy of the program for the incidence angle is improved by 0.4°and 0.6°at the design and off-design conditions respectively,compensating for the program’s original deficiencies.Meanwhile,the model can also provide quantitative guidance for the design of swept blades,thereby reducing the number of design iterations and improving design efficiency.
文摘Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
