In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced...In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.展开更多
In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assume...In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.展开更多
The existence, uniqueness and regularity of solutions to the Cauchy problem posed for a nonhomogeneous viscous Burger's equation were shown in Chung, Kim and Slemrod [1] by assuming suitable conditions on initial ...The existence, uniqueness and regularity of solutions to the Cauchy problem posed for a nonhomogeneous viscous Burger's equation were shown in Chung, Kim and Slemrod [1] by assuming suitable conditions on initial data. Moreover, they derived the asymptotic behaviour of solutions of the Cauchy problem by imposing additional conditions on initial data. In this article, we obtain the same asymptotic behaviour of solutions to the Cauchy problem without imposing additional condition on initial data.展开更多
According to the vibration characteristics of the round window, a mechani- cal model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are deri...According to the vibration characteristics of the round window, a mechani- cal model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are derived by the variational prin- ciple. Combined with the Bessel function, an analytical solution of the round window displacement is obtained by MATHEMATICA. Combined with clinical characteristics of round window membrane lesion, the effect of sound transmission due to thickening of the round window membrane caused by the otitis media, shrinkage of the round window membrane area caused by otosclerosis, and hardening of the round window membrane itself is analyzed. The results show that with thickening of the round window membrane, the displacement of the round window membrane is decreased. In the meantime, with hardening of the round window membrane and shrinkage of the membrane area, the max- imum displacement Of the round window membrane is gradually reduced, leading to a decrease in sound transmission. Thus, the analyticM analysis can avoid interference of environment and the technical level of personnel, and it can evaluate transmission per- formance of the round window membrane efficiently, providing a theoretical basis for the reverse excitation of artificial prosthesis.展开更多
Based on the Pennes’ bioheat transfer equation, a simplified one-dimensional bioheat transfer model of the cylindrical living tissues in the steady state has been set up for application in limb and whole body heat tr...Based on the Pennes’ bioheat transfer equation, a simplified one-dimensional bioheat transfer model of the cylindrical living tissues in the steady state has been set up for application in limb and whole body heat transfer studies, and by using the Bessel’s equation, its corresponding analytic solution has been derived in this paper. With the obtained analytic solution, the effects of the thermal conductivity, the blood perfusion, the metabolic heat generation, and the coefficient of heat transfer on the temperature distribution in living tissues are analyzed. The results show that the derived analytic solution is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment.展开更多
The Birkhoffian mechanics is more general than the Hamilton mechanics,but only some dynamical systems can be realized as a Birkhoffian formulation.This paper proposes a novel Birkhoffian formulation for the classical ...The Birkhoffian mechanics is more general than the Hamilton mechanics,but only some dynamical systems can be realized as a Birkhoffian formulation.This paper proposes a novel Birkhoffian formulation for the classical Bessel equation.Based on the first method of Santilli,the Birkhoffian formulation of Bessel equation is established under the assumption that the Birkhoffian describes the total physical energy of the corresponding conservative systems.Zero and n-th order classical Bessel equations are studied to verify the effectiveness of the proposed formulation.展开更多
基金the National Natural Science Foundation of China (No. 11074170)the Independent Research Program of State Key Laboratory of Machinery System and Vibration (SKLMSV) (No. MSV-MS-2008-05)the Visiting Scholar Program of SKLMSV (No. MSV-2009-06)
文摘In 2D fast multipole method for scattering problems,square quadrature rule is used to discretize the Bessel integral identity for diagonal expansion of 2D Helmholtz kernel,and numerical integration error is introduced. Taking advantage of the relationship between Euler-Maclaurin formula and trapezoidal quadrature rule,and the relationship between trapezoidal and square quadrature rule,sharp computable bound with analytical form on the error of numerical integration of Bessel integral identity by square quadrature rule is derived in this paper. Numerical experiments are presented at the end to demonstrate the accuracy of the sharp computable bound on the numerical integration error.
基金supported by National Basic Research Programm of China (Grant No.2006CB805902)National Natural Science Foundation of China (Grant No. 10871096)
文摘In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.
基金S.Engu was supported by Council of Scientific and Industrial Research,India (File no. 25 (0302)/19/EMR-Ⅱ)。
文摘The existence, uniqueness and regularity of solutions to the Cauchy problem posed for a nonhomogeneous viscous Burger's equation were shown in Chung, Kim and Slemrod [1] by assuming suitable conditions on initial data. Moreover, they derived the asymptotic behaviour of solutions of the Cauchy problem by imposing additional conditions on initial data. In this article, we obtain the same asymptotic behaviour of solutions to the Cauchy problem without imposing additional condition on initial data.
基金Project supported by the National Natural Science Foundation of China(Nos.11272200 and11572186)
文摘According to the vibration characteristics of the round window, a mechani- cal model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are derived by the variational prin- ciple. Combined with the Bessel function, an analytical solution of the round window displacement is obtained by MATHEMATICA. Combined with clinical characteristics of round window membrane lesion, the effect of sound transmission due to thickening of the round window membrane caused by the otitis media, shrinkage of the round window membrane area caused by otosclerosis, and hardening of the round window membrane itself is analyzed. The results show that with thickening of the round window membrane, the displacement of the round window membrane is decreased. In the meantime, with hardening of the round window membrane and shrinkage of the membrane area, the max- imum displacement Of the round window membrane is gradually reduced, leading to a decrease in sound transmission. Thus, the analyticM analysis can avoid interference of environment and the technical level of personnel, and it can evaluate transmission per- formance of the round window membrane efficiently, providing a theoretical basis for the reverse excitation of artificial prosthesis.
文摘Based on the Pennes’ bioheat transfer equation, a simplified one-dimensional bioheat transfer model of the cylindrical living tissues in the steady state has been set up for application in limb and whole body heat transfer studies, and by using the Bessel’s equation, its corresponding analytic solution has been derived in this paper. With the obtained analytic solution, the effects of the thermal conductivity, the blood perfusion, the metabolic heat generation, and the coefficient of heat transfer on the temperature distribution in living tissues are analyzed. The results show that the derived analytic solution is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment.
基金Supported by the National Natural Science Foundation of China(11702119,11502071)the Natural Science Foundation of Jiangsu Province(BK20170565)
文摘The Birkhoffian mechanics is more general than the Hamilton mechanics,but only some dynamical systems can be realized as a Birkhoffian formulation.This paper proposes a novel Birkhoffian formulation for the classical Bessel equation.Based on the first method of Santilli,the Birkhoffian formulation of Bessel equation is established under the assumption that the Birkhoffian describes the total physical energy of the corresponding conservative systems.Zero and n-th order classical Bessel equations are studied to verify the effectiveness of the proposed formulation.
