Mode matching method is used to analyze the scattering characteristics of thecircular-to-circular groove waveguide junction. Matching the electric fields and magnetic fields atthe boundary of the junction, and multipl...Mode matching method is used to analyze the scattering characteristics of thecircular-to-circular groove waveguide junction. Matching the electric fields and magnetic fields atthe boundary of the junction, and multiplying the mode functions of the circular waveguide andcircular groove waveguide on both sides of the boundary equation, the scattering matrix equation isobtained, the scattering coefficients can be obtained from the equation. Then the scatteringcharacteristics of the iris with circular window in circular groove waveguide are analyzed. At lastthe convergent problem is discussed; when choosing a suitable mode group, convergent numericalresults are obtained, and the frequency response of the iris' scattering coefficients is also given.展开更多
Suction bucket foundations can be divided into four compartments by cruciform internal bulkheads,thereby yielding better capacity in certain conditions than those without internal bulkheads.As yet,no systematic study ...Suction bucket foundations can be divided into four compartments by cruciform internal bulkheads,thereby yielding better capacity in certain conditions than those without internal bulkheads.As yet,no systematic study has been conducted regarding the effects of cruciform internal bulkheads on the capacities of suction bucket foundations.In this study,we established a large number of finite element models of suction bucket foundations with and without cruciform internal bulkheads and of solid embedded circular foundations.We found the uniaxial capacities and failure modes of suction bucket foundations with various depth ratios to remain basically unaffected by internal bulkheads in uniform clays.However,in inhomogeneous clay with high strength heterogeneity,we observed the uniaxial moment and horizontal capacities and corresponding failure modes of suction bucket foundations with a low depth ratio to be obviously affected by internal bulkheads.In this case,the uniaxial moment capacities,in particular,as well as the horizontal capacities of suction bucket foundations with cruciform internal bulkheads become obviously greater than those without internal bulkheads.Under combined loading,we found the failure envelopes of suction bucket foundations with and without cruciform internal bulkheads and of solid circular foundation to also be basically consistent in uniform clays.However,in inhomogeneous clay with high strength heterogeneity,cruciform internal bulkheads can obviously change the shapes of the failure envelopes of bucket foundations with a small depth ratio.We conclude that when the acting vertical load or foundation depth is relatively small,suction bucket foundations with cruciform internal bulkheads can be subjected to larger moment and horizontal loads in soft clays with high strength heterogeneity.展开更多
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman tr...A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.展开更多
The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric con...The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.展开更多
For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the fo...For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we have r( f, n) = r( g, n) or r( f, n) ≠ r( g, n).Our method is to use elliptic curves and the corresponding new forms.展开更多
文摘Mode matching method is used to analyze the scattering characteristics of thecircular-to-circular groove waveguide junction. Matching the electric fields and magnetic fields atthe boundary of the junction, and multiplying the mode functions of the circular waveguide andcircular groove waveguide on both sides of the boundary equation, the scattering matrix equation isobtained, the scattering coefficients can be obtained from the equation. Then the scatteringcharacteristics of the iris with circular window in circular groove waveguide are analyzed. At lastthe convergent problem is discussed; when choosing a suitable mode group, convergent numericalresults are obtained, and the frequency response of the iris' scattering coefficients is also given.
基金supported by the National Natural Science Foundation of China(Nos.51479133,51109157)the Elite Scholar Program of Tianjin University(2017XRG0040)
文摘Suction bucket foundations can be divided into four compartments by cruciform internal bulkheads,thereby yielding better capacity in certain conditions than those without internal bulkheads.As yet,no systematic study has been conducted regarding the effects of cruciform internal bulkheads on the capacities of suction bucket foundations.In this study,we established a large number of finite element models of suction bucket foundations with and without cruciform internal bulkheads and of solid embedded circular foundations.We found the uniaxial capacities and failure modes of suction bucket foundations with various depth ratios to remain basically unaffected by internal bulkheads in uniform clays.However,in inhomogeneous clay with high strength heterogeneity,we observed the uniaxial moment and horizontal capacities and corresponding failure modes of suction bucket foundations with a low depth ratio to be obviously affected by internal bulkheads.In this case,the uniaxial moment capacities,in particular,as well as the horizontal capacities of suction bucket foundations with cruciform internal bulkheads become obviously greater than those without internal bulkheads.Under combined loading,we found the failure envelopes of suction bucket foundations with and without cruciform internal bulkheads and of solid circular foundation to also be basically consistent in uniform clays.However,in inhomogeneous clay with high strength heterogeneity,cruciform internal bulkheads can obviously change the shapes of the failure envelopes of bucket foundations with a small depth ratio.We conclude that when the acting vertical load or foundation depth is relatively small,suction bucket foundations with cruciform internal bulkheads can be subjected to larger moment and horizontal loads in soft clays with high strength heterogeneity.
文摘A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.
基金Supported by National Natural Science Foundation of China under Grant Nos. 60711120203, 60890193STPAA of Guangzhou City under Grant No. 2060
文摘The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.
基金the National Natural Science Foundation of China (Grant No. 19871917).
文摘For two given ternary quadratic forms f( x, y, z) and g( x, y, z), let r( f, n) and r( g,n) be the numbers of representations of n represented by f( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we have r( f, n) = r( g, n) or r( f, n) ≠ r( g, n).Our method is to use elliptic curves and the corresponding new forms.
