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相关概念视频

Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Gauss's Law: Planar Symmetry01:27

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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Torsion of Noncircular Members01:16

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Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
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Singularity Functions for Bending Moment01:18

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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扭曲的旋高斯斯谢尔模型束,概括的ABCD系统和多维的赫尔米特多项式.

Milo W Hyde, Benjamin C Wilson, Santasri R Bose-Pillai

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    概括
    此摘要是机器生成的。

    这项研究引入了多维的Hermite多项式 (MDHPs),以更有效地表示扭曲状部分连贯束的交叉光谱密度 (CSD). 实验验证证证实了光学系统中这种新的理论方法的准确性.

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    科学领域:

    • 光学是什么?光学是什么?光学是什么?
    • 数学物理 数学物理

    背景情况:

    • 在光学系统中,部分连贯束,特别是扭曲的旋转束,至关重要.
    • 描述这些光束的交叉光谱密度 (CSD) 的现有方法可能是计算密集的.
    • 对于理论和实验光学研究来说,对高效和准确的数学表示的需求至关重要.

    研究的目的:

    • 为了获得一个新的理论框架,用于交叉光谱密度 (CSD) 函数的扭曲旋部分连贯束.
    • 引入和使用多维赫尔米特多项式 (MDHPs) 来表示CSD函数.
    • 为拟议的理论模型提供计算方法和实验验证.

    主要方法:

    • 使用多维赫米特多项式 (MDHPs) 来导出交叉光谱密度 (CSD) 函数.
    • 开发用于计算MDHPs的递归关系.
    • 实现 MATLAB 代码以生成任意顺序的 MDHP.
    • 通过不对称光学系统传播的扭曲束的光谱密度的实验测量.

    主要成果:

    • 通过使用MDHPs建立了一个用于扭曲旋部分连贯束的CSD函数的新配方.
    • MDHP在传统的单维Hermite多项式上表现出显著的符号和计算优势.
    • 提供用于生成MDHP的MATLAB代码,以促进实际应用.
    • 实验结果与衍生的理论CSD函数的预测一致,证实了它的有效性.

    结论:

    • 使用MDHP提供了一种有效且具有计算优势的方法来表征扭曲状部分连贯束的CSD.
    • 由此衍生的理论模型经过实验验证,为光学系统分析提供了可靠的工具.
    • 这项工作促进了对光学系统中部分连贯光束传播的理解和数学描述.