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Related Concept Videos

Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

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In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has...
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A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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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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Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
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Related Experiment Video

Updated: May 6, 2026

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
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Scattering of multi-Gaussian Schell-model beams on a random medium.

Yuanyuan Zhang, Daomu Zhao

    Optics Express
    |October 24, 2013
    PubMed
    Summary

    This study examines how multi-Gaussian Schell-model beams scatter in random media. Beam properties and scatterer characteristics significantly affect far-zone spectral density and coherence.

    Area of Science:

    • Optics and Photonics
    • Wave Scattering Theory

    Background:

    • Multi-Gaussian Schell-model (MGSM) beams are widely used in optical systems.
    • Understanding beam propagation through random media is crucial for applications like free-space optical communication.

    Purpose of the Study:

    • To investigate the scattering of MGSM beams from random media.
    • To analyze the far-zone spectral properties of scattered MGSM beams.

    Main Methods:

    • Utilizing the angular spectrum representation of plane waves.
    • Applying the first-order Born approximation for scattering analysis.
    • Calculating far-zone normalized spectral density and spectral degree of coherence.

    Main Results:

    • The normalized spectral density is influenced by beam profile boundary (M), transverse width, and source correlation width.

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  • The spectral degree of coherence is affected by beam parameters and scatterer properties.
  • Scattering effects are analyzed within the first-order Born approximation.

    • Conclusions:

    • The scattering characteristics of MGSM beams in random media depend on both the source parameters and the medium's properties.
    • The findings provide insights into the propagation of partially coherent beams through turbulent or inhomogeneous environments.