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Related Concept Videos

Deflection of a Beam01:19

Deflection of a Beam

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.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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.
The M/EI...
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

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...
Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

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 areas.
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

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Rejection of Fluorescence Background in Resonance and Spontaneous Raman Microspectroscopy
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Published on: May 18, 2011

Nonlinear beam interactions in 1D discrete Kerr systems.

J Meier, G Stegeman, D Christodoulides

    Optics Express
    |June 5, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Researchers studied parallel beam interactions in discrete Kerr systems using AlGaAs waveguides. They observed linear responses and spatial soliton interactions, influenced by absorption and asymmetry at high intensities.

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    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
    12:18

    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

    Published on: August 5, 2013

    Area of Science:

    • Nonlinear optics
    • Quantum optics
    • Materials science

    Background:

    • Discrete Kerr systems exhibit unique light-matter interactions.
    • Waveguide arrays allow for controlled studies of nonlinear phenomena.
    • AlGaAs waveguides offer specific optical properties at 1550 nm.

    Purpose of the Study:

    • Investigate parallel beam interactions in 1D discrete Kerr systems.
    • Characterize the transition from linear response to soliton formation.
    • Analyze the effects of multiphoton absorption and input asymmetry on beam interactions.

    Main Methods:

    • Experimental setup using coupled channel waveguides in AlGaAs.
    • Operation at 1550 nm, near the half-bandgap energy.
    • Systematic variation of input intensity and relative phase.
    • Recording of output intensity patterns.

    Main Results:

    • Observed linear response for low input intensities.
    • Demonstrated spatial soliton formation and interactions (moderate to strong localization).
    • Investigated high-intensity effects including multiphoton absorption and asymmetric inputs.

    Conclusions:

    • Parallel beams in discrete Kerr systems exhibit rich nonlinear behavior.
    • Spatial solitons readily form and interact within these waveguide arrays.
    • Multiphoton absorption and input asymmetry significantly modify beam interactions at high intensities.