In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inver...In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.展开更多
Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equatio...Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.展开更多
Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are i...Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the in.homogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.展开更多
The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere ...The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scintillations in the cross sections of vortex and nonvortex beams differs widely. Despite the scintillation index of vortex beams has been calculated only for the simplest LG10 mode, the obtained results are quite general, because they demonstrate the main properties inherent in scintillations of vortex beams of any type.展开更多
Simple single-lens equivalent systems for graded-index (GRIN) lenses in inhomogeneous medium obtained using matrix optics are proposed in this letter. Due to its simplicity, the equivalent optical system enables qui...Simple single-lens equivalent systems for graded-index (GRIN) lenses in inhomogeneous medium obtained using matrix optics are proposed in this letter. Due to its simplicity, the equivalent optical system enables quick analysis of the imaging properties of GRIN lens rod immersed in inhomogeneous medium. This facilitates the optical analysis of complicated optoelectronics systems in inhomogeneous medium utilizing GRIN lens rods.展开更多
This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the...This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.展开更多
Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radiall...Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.展开更多
基金Shanghai Youth Science FoundationSupported in Part by Shanghai ScienceTechnology Development Foundation
文摘In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.
文摘Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.
基金National Science&Technology Pillar Program under Grant No.2015BAK17B06Natural Science Foundation of Heilongjiang Province,China under Grant No.A201310+1 种基金Scientific Research Starting Foundation for Post Doctorate of Heilongjiang Province,China under Grant No.LBH-Q13040the Fundamental Research Funds for the Central Universities of China under Grant No.HEUCF150203
文摘Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the in.homogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.
基金supported in part by the Division of Physical Sciences of RAS “Fundamental Problems of Photonics and Physics of New Optical Materials.”
文摘The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scintillations in the cross sections of vortex and nonvortex beams differs widely. Despite the scintillation index of vortex beams has been calculated only for the simplest LG10 mode, the obtained results are quite general, because they demonstrate the main properties inherent in scintillations of vortex beams of any type.
文摘Simple single-lens equivalent systems for graded-index (GRIN) lenses in inhomogeneous medium obtained using matrix optics are proposed in this letter. Due to its simplicity, the equivalent optical system enables quick analysis of the imaging properties of GRIN lens rod immersed in inhomogeneous medium. This facilitates the optical analysis of complicated optoelectronics systems in inhomogeneous medium utilizing GRIN lens rods.
基金supported by the National Natural ScienceFoundation of China Grant(11871416,12171057)the Natural Science Foundation of Shandong Province Grant(ZR2019MA027)。
文摘This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.
基金Scientific Research Fund of Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2017QJGJ06the National Science and Technology Pillar Program under Grant No.2015BAK17B06+2 种基金the Earthquake Industry Special Science Research Foundation Project under Grant No.201508026-02the Fundamental Research Funds for the Central Universities under Grant No.HEUCF170202the program for Innovative Research Team in China Earthquake Administration
文摘Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.