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Related Concept Videos

Method of Superposition01:20

Method of Superposition

The method of superposition is a crucial technique in structural engineering, used to analyze the effect of multiple loads on beams. This approach involves calculating the deflection and slope for each load on a beam separately, and then summing these effects to determine the overall impact. It is applicable only when the beam material remains within its elastic limit, ensuring that deformations are linearly elastic.
When applying the method of superposition, each type of load—whether...
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
Design Example: Maintaining Level of an Embankment01:19

Design Example: Maintaining Level of an Embankment

Constructing a roadway embankment over uneven terrain requires precise leveling to ensure stability and proper drainage. Surveyors use a leveling instrument and staff to calculate ground elevations and determine the required fill material at each point along the embankment alignment.The process begins by positioning a leveling instrument near a benchmark with a known elevation. A backsight reading establishes the instrument height, which serves as a reference for subsequent measurements. A...
Calculation of Volume of Solids by Integration01:27

Calculation of Volume of Solids by Integration

Volume calculation often begins with simple geometric solids. For example, the volume of a rectangular box is obtained by multiplying the area of its base by its height. This straightforward approach relies on the fact that the cross-sectional area of the box remains constant throughout its length. Many real-world objects, however, do not have uniform cross-sections, and their volumes cannot be determined using elementary geometric formulas.To address this limitation, the Slicing Method...
Superposition Theorem01:18

Superposition Theorem

The superposition principle is a fundamental concept stating that in a linear circuit, the voltage across (or current through) an element can be determined by summing the individual contributions of each independent source acting in isolation. When dealing with linear circuits containing multiple independent sources, this principle serves as a valuable tool for analysis. To apply the superposition principle effectively, one should focus on a single independent source at a time while...
Multimachine Stability01:25

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Related Experiment Video

Updated: Jun 12, 2026

Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices
10:18

Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices

Published on: January 27, 2017

New calculational technique for multilayer stacks.

C Schwartz, L F Desandre

    Applied Optics
    |May 22, 2010
    PubMed
    Summary
    This summary is machine-generated.

    A novel R-matrix propagation method enhances calculations for multilayer stacks, overcoming numerical instability issues with evanescent waves. This impedance-based technique offers a stable alternative to the characteristic matrix method for optical and electromagnetic simulations.

    More Related Videos

    Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition
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    Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition

    Published on: March 13, 2018

    Related Experiment Videos

    Last Updated: Jun 12, 2026

    Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices
    10:18

    Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices

    Published on: January 27, 2017

    Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition
    09:12

    Production of Single Tracks of Ti-6Al-4V by Directed Energy Deposition to Determine the Layer Thickness for Multilayer Deposition

    Published on: March 13, 2018

    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics
    • Materials Science

    Background:

    • The characteristic matrix technique is widely used for analyzing multilayer optical and electromagnetic stacks.
    • This method suffers from numerical instability when evanescent waves are present, limiting its applicability.
    • Developing stable and accurate computational methods is crucial for designing advanced optical and electromagnetic devices.

    Purpose of the Study:

    • Introduce a new calculational technique for multilayer stacks that addresses numerical instability.
    • Provide a stable alternative to the characteristic matrix method, particularly for scenarios involving evanescent waves.
    • Offer guidance on selecting the appropriate technique for specific multilayer stack problems.

    Main Methods:

    • Developed a new technique based on R-matrix propagation algorithms.
    • Propagated the impedance of the multilayer stack instead of the admittance.
    • Derived the relationship between the new R-matrix method and the characteristic matrix technique.

    Main Results:

    • The R-matrix propagation technique effectively avoids numerical instability issues associated with evanescent waves.
    • Established clear criteria for choosing between the R-matrix and characteristic matrix techniques.
    • Demonstrated the implementation of the R-matrix propagation technique through several illustrative examples.

    Conclusions:

    • The R-matrix propagation method offers a numerically stable and reliable approach for analyzing multilayer stacks with evanescent waves.
    • This new technique expands the capabilities for simulating complex optical and electromagnetic systems.
    • The provided guidance will aid researchers in selecting the most suitable computational method for their specific applications.