共查询到19条相似文献,搜索用时 78 毫秒
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本文用数值方法求解含有椭圆积分的二阶微分方程,讨论了均匀带电圆环内点电荷的非线性振荡及其运动特征. 相似文献
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关于夫琅禾费椭圆孔衍射积分的精确解 总被引:2,自引:1,他引:1
对于椭圆孔的衍射积分问题,在众多的理论光学书籍和文献中,人们只作定性讨论,没有严格解。本文试图从衍射积分公式出发,选取合适的正交曲线坐标系,并巧妙地利用贝塞尔函数,从而得到夫琅禾费椭圆扎衍时积分的精确解。 相似文献
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在柱状边界条件下将对柱侧面的曲面积分表示成一维积分,同时还给出了椭圆积分的计算方法,由对空间立体角积分的算例可知,其计算的速度有了显着的提高。 相似文献
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椭圆包层光纤场的迭代近似解与漏模损耗计算 总被引:1,自引:1,他引:0
试图理论上处理椭圆包层各向异性光纤复杂的折射率分布。数学过程包括折射率分布的级数展开、δ-涵数的导数和积分以及用格林函数求解方程的迭代技术。给出了椭圆包层各向异性光纤漏模损耗的解析表达式。数值结果表明椭圆包层各向异性光纤的漏模损耗比领结型光纤小,比阶跃型各向异性光纤大;偏心率越大越有利于制造单模单偏光纤。 相似文献
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运用欧拉-拉格朗日方程给出了Kerr时空赤道面上的零测地线方程并求出两个首次积分,结合零测地线所满足的恒等式求得轨道微分方程.通过把被积函数化成部分分式,以及解出被积函数中的一个四次方程并对根进行排序,可把轨道微分方程的解表示成第一类椭圆积分和第三类椭圆积分. 相似文献
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边界元素法中有关积分的计算方法(Ⅰ)柱状边界条件下对空间立体角积分的计算 总被引:1,自引:0,他引:1
利用任意闭合曲面对曲面外任一点所张立体角为零的特点将柱状边界条件下对柱侧面的积分转变为对柱底面的积分,并将其表示成椭圆积分的形式。 相似文献
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研究了一维光格中旋量玻色-爱因斯坦凝聚体的高阶非线性作用下的孤子激发,得出了用椭圆积分表示的明孤子解和特定参数条件下的暗孤子解析解,并求得了能量表达式. 相似文献
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The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number. 相似文献
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Magnetostatic self and interaction energies can be computed via demagnetization factors whenever the magnetic state is close to a uniform state, e.g. in the presence of a strong applied field, or when the dimensions involved are within the single-domain limit. We derive analytical expressions for the demagnetization factors of cylindrical shells and rings with rectangular and square cross-sections. The factors are given either as a combination of elliptic integrals or as a series expansion in powers of the dimensionless ratio between inner and outer radii. Limiting cases are analysed for particular ranges of the shape parameters. We also investigate the ring with a square cross-section, and the elliptic ring, where analytical expressions are provided only for small eccentricity. Finally, we introduce the dipolar coupling integral encoding magnetostatic interactions between a magnetized cylinder and a thin coating on its lateral surface. 相似文献
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对于通以恒定电流的有限长螺线管,首先用柱函数展开法推导出矢势的表达式,再利用磁感应强度与矢势的关系式,得出积分形式的磁场表达式.然后用直接积分的方法计算出磁场分布的级数表达式.最后讨论了某些特殊位置处的磁场. 相似文献
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《Journal of computational physics》2008,227(2):1523-1543
The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number. 相似文献
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对于通以恒定电流的有限长厚壁螺线管,用柱函数展开法推导出矢势的表达式,再根据磁感应强度与矢势的关系式得出磁场的积分形式表达式.用直接积分的方法,计算出厚壁螺线管内部和外部的磁场分布的级数表达式.另外还用本文得出的公式求得中轴线上的磁场. 相似文献
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Equations that simulate the magnetic induction and current density distributions in half-space in view of the power I-V characteristic are derived. The magnetization front velocity is determined for a given mean rate of external magnetic field variation at the boundary of the sample. An integral condition for the electrical resistance (nonlinearly depending on the magnetic field) under which the magnetic flux penetrates into the sample with a finite rate is found. An analytical solution that simulates the power variation of the magnetic field at the boundary is given. The Bean generalized model describing the current density distribution near the critical current is considered. It is shown that solutions like shock waves may arise beyond the applicability domain of the Bean model. 相似文献
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We work out finite-dimensional integral formulae for the scalar product of genus one states of the groupG Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the
elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the
Bethe Ansatz for the commuting Hamiltonians building up the connection and quantizing the quadratic Hamiltonians of the elliptic
Hitchin system. 相似文献