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Related Concept Videos

Propagation of Waves01:07

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Reflection of Waves01:07

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.

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Fabrication of Zero Mode Waveguides for High Concentration Single Molecule Microscopy
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Published on: May 12, 2020

Variable-transformed collocation method for field propagation through waveguiding structures.

A Sharma, A Taneja

    Optics Letters
    |October 2, 2009
    PubMed
    Summary
    This summary is machine-generated.

    Variable transformation enhances numerical accuracy in collocation methods. Specific transformations significantly improve field-propagation algorithm accuracy by over 2 orders of magnitude.

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    Area of Science:

    • Numerical analysis
    • Computational physics
    • Algorithm optimization

    Background:

    • Collocation methods are widely used for solving differential equations.
    • Numerical accuracy is crucial for the reliability of field-propagation algorithms.
    • Existing methods may suffer from limitations in sample point distribution.

    Purpose of the Study:

    • To investigate the impact of variable transformation on numerical accuracy in collocation methods.
    • To identify specific transformations that enhance field-propagation algorithm performance.
    • To quantify the improvement in numerical accuracy achievable through these transformations.

    Main Methods:

    • Applying variable transformations to redistribute sample points in the collocation method.
    • Developing and analyzing field-propagation algorithms utilizing transformed sample points.
    • Comparing numerical accuracy with and without variable transformations.

    Main Results:

    • Variable transformation effectively redistributes sample points, improving numerical accuracy.
    • Specific transformations lead to significant enhancements in accuracy, exceeding 2 orders of magnitude.
    • The proposed approach offers a substantial improvement over standard collocation methods.

    Conclusions:

    • Variable transformation is a powerful technique for enhancing numerical accuracy in collocation-based field-propagation.
    • The identified transformations provide a practical method for achieving high-accuracy numerical solutions.
    • This work has implications for various scientific and engineering fields relying on accurate field simulations.