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Related Concept Videos

Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

404
Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is...
404
Construction of Root Locus01:15

Construction of Root Locus

373
The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
For positive gain values, the root locus exists on the real axis to the left of an odd number of finite open-loop poles or zeros. The root locus starts at the open-loop poles and traces the paths of the closed-loop poles as the gain...
373
Properties of the Root Locus01:05

Properties of the Root Locus

272
The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on...
272
Root-Locus Method01:19

Root-Locus Method

445
A cruise control system in a car is designed to maintain a specified speed automatically by adjusting the gas pedal. The system continuously measures the vehicle's speed and makes fine adjustments to the pedal to achieve this goal. The root locus method is particularly useful for understanding how the cruise control system's behavior changes under varying conditions, such as when the car goes uphill, downhill, or faces strong wind resistance.
This system can be represented by a block...
445
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

312
The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
312
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.3K
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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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Extended Planckian locus.

Elaheh Daneshvar, Graham Finlayson, Michael H Brill

    Optics Express
    |December 19, 2025
    PubMed
    Summary
    This summary is machine-generated.

    This study extends Planck and Wien formulas to negative temperatures, revealing continuity at infinite temperatures but a discontinuity at zero. This research strengthens theoretical foundations for lighting indices like correlated color temperature.

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    Area of Science:

    • Color science
    • Thermodynamics
    • Radiometry

    Background:

    • The Planckian locus and Wien locus describe black body radiator colors at different temperatures.
    • These loci are crucial for understanding everyday illuminations and color temperature.
    • Existing models do not fully encompass negative temperature color properties.

    Purpose of the Study:

    • To extend the Planck and Wien formulas to include negative temperatures.
    • To analyze the behavior of these extended loci, particularly at temperature limits.
    • To provide a stronger theoretical basis for lighting indices.

    Main Methods:

    • Mathematical extension of Planck and Wien formulas to negative temperatures.
    • Analysis of the resulting chromaticity diagram loci.
    • Investigation of locus continuity and discontinuities at temperature limits (0 and ∞).

    Main Results:

    • The extended Wien locus intersects the spectral locus at 360 nm.
    • Continuity is observed between positive and negative infinite color temperatures.
    • A significant discontinuity exists at positive and negative zero color temperatures.

    Conclusions:

    • The extended Wien locus offers a more complete representation of color temperature, including negative values.
    • The findings enhance the theoretical underpinnings of correlated color temperature and related lighting metrics.
    • This work improves the practical applicability of color temperature calculations in illumination science.