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Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
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Related Experiment Video

Updated: Jun 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Structure of a general pure Mueller matrix.

J W Hovenier

    Applied Optics
    |October 22, 2010
    PubMed
    Summary

    This study explores the relationship between pure Mueller matrices and Jones matrices, revealing a fundamental structure within Mueller matrices. The findings simplify understanding how radiation polarization changes are represented mathematically.

    Area of Science:

    • Optics and Photonics
    • Mathematical Physics
    • Polarimetry

    Background:

    • Mueller matrices describe the polarization state of light.
    • Jones matrices represent polarization transformations.
    • Understanding the relationship between these matrices is crucial for optical system analysis.

    Purpose of the Study:

    • To elucidate the relationship between pure Mueller matrices and 2x2 Jones matrices.
    • To derive explicit expressions for Mueller matrix changes based on Jones matrix operations.
    • To reveal the inherent structural properties of pure Mueller matrices.

    Main Methods:

    • Mathematical derivation of relationships between Mueller and Jones matrices.
    • Analysis of matrix transformations including transpose, complex conjugate, and Hermitian conjugate.

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    Setting Limits on Supersymmetry Using Simplified Models
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    Last Updated: Jun 7, 2026

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    Setting Limits on Supersymmetry Using Simplified Models
    07:46

    Setting Limits on Supersymmetry Using Simplified Models

    Published on: November 15, 2013

  • Identification of interrelations among elements of pure Mueller matrices.

    • Main Results:

    • Pure Mueller matrices possess a simple, elegant structure.
    • Interrelations involve squares or products of matrix elements.
    • Explicit formulas are provided for Mueller matrix changes from elementary Jones matrix operations.

    Conclusions:

    • The derived structure simplifies the analysis of pure Mueller matrices.
    • This work provides a unified framework for understanding Mueller matrix properties.
    • The findings facilitate advancements in polarimetry and optical metrology.