In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniq...In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniqueness results for steady symmetric transonic shock solutions to the nonisentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a symmetric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.展开更多
In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,...In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,and particularly,we obtain slant kink-wave solutions for the inhomogeneous Burgers(InhB)type equation.Next,we prove the integrability of the InhB equation in the sense of Lax pair.Furthermore,we study the spreading rate of the moving domain occupied by mass for the 1D Cauchy problem with compact support initial density.We find that the expanding domain grows exponentially in time,provided that the solutions exist and smooth at all time.Finally,we extend the corresponding results of the inhomogeneous pressureless Euler equations to the radially symmetric multi-dimensional case.展开更多
Wind turbine blades in cold regions are susceptible to icing due to meteorological conditions,significantly affecting the turbine's energy capture efficiency and operational safety.Precise calculation of droplet c...Wind turbine blades in cold regions are susceptible to icing due to meteorological conditions,significantly affecting the turbine's energy capture efficiency and operational safety.Precise calculation of droplet collection efficiency(DCE)is essential for accurate icing prediction.This study examines existing methods for calculating DCE and identifies limitations during glaze ice formation.An enhanced method based on the Euler Wall Film(EWF)model is introduced to address these limitations,incorporating splashing and rebound phenomena during glaze ice formation on wind turbine blades.The method's reliability is validated using data from the classic symmetric airfoil,NACA0012.Through the control variable method,this research examines DCE variations under different incoming velocities,medium volume droplet diameters(MVDs),and temperatures.The study also analyzes the distinctions between the improved method and the existing Eulerian method.Results indicate that both impact range and maximum DCE increase with higher incoming velocity and MVD,while temperature exhibits minimal influence on DCE.Variations between the calculation methods reveal differences in water droplet splashing intensity,primarily influenced by droplet kinetic energy and liquid film thickness.The splashing phenomenon gradually decreases as incoming velocity and MVD increase.展开更多
Microring resonators,as essential components of photonic integrated circuits,offer compact size,wavelength selectivity,and strong resonance effects,making them invaluable in optical computing,on-chip interconnects,and...Microring resonators,as essential components of photonic integrated circuits,offer compact size,wavelength selectivity,and strong resonance effects,making them invaluable in optical computing,on-chip interconnects,and quantum photonics.The proposal of the pulley-type microring enhances the coupling strength,but also brings about issues such as mode mismatch and the excitation of higher-order modes.Here,a lithium niobate microring resonator coupled with a pulley bus waveguide based on modified Euler curves is proposed.This Euler-modified pulley bus minimizes mode mismatch at bending junctions,effectively suppressing higher-order mode excitation.The design achieves a high Q factor(exceeding 105)and strong coupling efficiency(83%)within a compact structure of 70μm radius.Due to its simple structure and ease of fabrication,the Euler-modified pulley-type microring holds practical value for applications requiring high-quality microring resonators.展开更多
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported in part by NSFC(Grant Nos.12271205,12171498).
文摘In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uniqueness results for steady symmetric transonic shock solutions to the nonisentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a symmetric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.
基金Supported by the Henan Natural Science Foundation(242300421397)the Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions(25ZX013)+2 种基金the Scientific Research Team Plan of Zhengzhou University of Aeronautics(23ZHTD01003)the National Natural Science Foundation of China(11971475)the FLASS Internationalization and Exchange Scheme(FLASS/IE−D09/19-20−FLASS).
文摘In this paper,we consider the inhomogeneous pressureless Euler equations.First,we present a class of self-similar analytical solutions to the 1D Cauchy problem and investigate the large-time behavior of the solutions,and particularly,we obtain slant kink-wave solutions for the inhomogeneous Burgers(InhB)type equation.Next,we prove the integrability of the InhB equation in the sense of Lax pair.Furthermore,we study the spreading rate of the moving domain occupied by mass for the 1D Cauchy problem with compact support initial density.We find that the expanding domain grows exponentially in time,provided that the solutions exist and smooth at all time.Finally,we extend the corresponding results of the inhomogeneous pressureless Euler equations to the radially symmetric multi-dimensional case.
基金supported by the National Natural Science Foundation of China(Grant No.51879125)。
文摘Wind turbine blades in cold regions are susceptible to icing due to meteorological conditions,significantly affecting the turbine's energy capture efficiency and operational safety.Precise calculation of droplet collection efficiency(DCE)is essential for accurate icing prediction.This study examines existing methods for calculating DCE and identifies limitations during glaze ice formation.An enhanced method based on the Euler Wall Film(EWF)model is introduced to address these limitations,incorporating splashing and rebound phenomena during glaze ice formation on wind turbine blades.The method's reliability is validated using data from the classic symmetric airfoil,NACA0012.Through the control variable method,this research examines DCE variations under different incoming velocities,medium volume droplet diameters(MVDs),and temperatures.The study also analyzes the distinctions between the improved method and the existing Eulerian method.Results indicate that both impact range and maximum DCE increase with higher incoming velocity and MVD,while temperature exhibits minimal influence on DCE.Variations between the calculation methods reveal differences in water droplet splashing intensity,primarily influenced by droplet kinetic energy and liquid film thickness.The splashing phenomenon gradually decreases as incoming velocity and MVD increase.
基金supported by the National Key Research and Development Program of China(Grant No.2024YFB2808300)the National Natural Science Foundation of China(Grant Nos.62293523,62288101,62305156,92463304,92463308,12304421,and 12341403)+2 种基金Zhangjiang Laboratory(Grant No.ZJSP21A001)Program of Jiangsu Natural Science Foundation(Grant Nos.BK20230770 and BK20232033)Guangdong Major Project of Basic and Applied Basic Re-search(Grant No.2020B0301030009).
文摘Microring resonators,as essential components of photonic integrated circuits,offer compact size,wavelength selectivity,and strong resonance effects,making them invaluable in optical computing,on-chip interconnects,and quantum photonics.The proposal of the pulley-type microring enhances the coupling strength,but also brings about issues such as mode mismatch and the excitation of higher-order modes.Here,a lithium niobate microring resonator coupled with a pulley bus waveguide based on modified Euler curves is proposed.This Euler-modified pulley bus minimizes mode mismatch at bending junctions,effectively suppressing higher-order mode excitation.The design achieves a high Q factor(exceeding 105)and strong coupling efficiency(83%)within a compact structure of 70μm radius.Due to its simple structure and ease of fabrication,the Euler-modified pulley-type microring holds practical value for applications requiring high-quality microring resonators.
