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Fault Types01:18

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When analyzing a single line-to-ground fault from phase A to ground at a three-phase bus, it is important to consider the fault impedance. This impedance is zero for a bolted fault, equal to the arc impedance for an arcing fault, and represents the total fault impedance for a transmission-line insulator flashover. To derive sequence and phase currents, fault conditions are translated from the phase domain to the sequence domain.
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The number e is a fundamental constant in calculus, playing a central role in describing continuous change, particularly exponential growth. It is most naturally defined through its relationship with the natural logarithm, which is the inverse of the exponential function with base e. This relationship allows e to be characterized using basic principles of differentiation rather than as an arbitrary numerical constant.A key property of the natural logarithm function, ln x, is that its derivative...
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Limits are a key mathematical concept for understanding how functions behave as their input approaches specific values, particularly when the function is undefined. They help reveal trends and discontinuities by examining the values a function approaches rather than its actual value.One-sided limits focus on the direction from which a value is approached. When a function behaves differently depending on whether the input approaches from the left or the right, the two one-sided limits may not...
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Naked-Eye Visual Warning of ppmv-Level Fault-Free Humidity Upper Limit.

Xiaoyan Wei1, Tianyou Qin2, Siyu Wang1

  • 1State Key Lab of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun, P. R. China.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|January 29, 2026
PubMed
Summary

This study introduces a novel, portable sensor for detecting parts per million by volume (ppmv)-level humidity. The new technology offers a rapid, visual warning system for critical applications, enhancing system reliability.

Keywords:
colorimetric humidity sensinghumidity detectionhydrochromic molecular switchesnaked‐eye detection

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Area of Science:

  • Materials Science
  • Chemical Engineering
  • Sensor Technology

Background:

  • Accurate monitoring of parts per million by volume (ppmv)-level fault-free humidity upper limit (FFHUL) is critical for high-tech manufacturing and aerospace.
  • Existing ppmv-FFHUL warning systems are limited by gradual response modes, complexity, cost, and portability.

Purpose of the Study:

  • To develop a portable, low-cost solution for precise ppmv-level humidity threshold modulation and warning.
  • To introduce an "enzyme-like" construction method and a "leap change" response mode for advanced humidity sensing.

Main Methods:

  • Utilized synergistic supramolecular interactions between auxiliary mediums to create an "enzyme-like" microenvironment.
  • Engineered a humidity-sensitive component with spatially fixed sensitizing functional groups.
  • Developed a paper-like material enabling high-contrast, naked-eye readout.

Main Results:

  • The developed material exhibits paper-like flexibility and facile fabrication.
  • Achieved high-contrast readout of ppmv-FFHUL by naked eye.
  • Provided a visual pre-alert signal 20% ahead of the critical humidity value.

Conclusions:

  • The proposed method offers a portable, low-cost solution for ppmv-level humidity warning labels.
  • The "enzyme-like" construction and "leap change" response mode present an innovative approach for trace-level monitoring materials.
  • This technology enhances system reliability in critical fields through early warning and rapid screening.