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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Phase Transitions02:31

Phase Transitions

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Inductance: Single-Phase And Three-Phase Line01:28

Inductance: Single-Phase And Three-Phase Line

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Understanding the inductance of transmission lines is crucial for efficient design and operation in electrical power systems. This discussion delves into the inductance characteristics of single-phase two-wire and three-phase three-wire transmission lines with equal phase spacing.
Single-Phase Two-Wire Line:
A single-phase line consists of two solid cylindrical conductors, denoted as x and y. Each conductor carries phasor currents ix and iy, respectively. Given that the sum of these currents is...
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Capacitance: Single-Phase And Three-Phase Line01:25

Capacitance: Single-Phase And Three-Phase Line

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In electrical power systems, understanding the capacitance of transmission lines is fundamental for efficient operation.
Single-Phase Lines
Consider a single-phase, two-wire transmission line with equal phase spacing energized by a voltage source. One conductor carries a uniform positive charge, while the other carries an equal negative charge. The capacitance C of the line can be derived from the voltage V between the conductors. For a one-meter section of the line, the capacitance is given...
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Phase Changes01:19

Phase Changes

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Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
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Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

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Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass...
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Updated: Feb 6, 2026

Electrochemical Etching and Characterization of Sharp Field Emission Points for Electron Impact Ionization
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Electrochemical Etching and Characterization of Sharp Field Emission Points for Electron Impact Ionization

Published on: July 12, 2016

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Sharp Phase Field Method.

Alphonse Finel1, Yann Le Bouar1, Benoît Dabas1

  • 1Laboratoire d'Etude des Microstructures, ONERA, CNRS, Université Paris-Saclay, 92320 Châtillon, France.

Physical Review Letters
|August 8, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a novel, intrinsically discrete phase field model. It enhances computational efficiency for predicting microstructural evolution with high accuracy and rotational invariance.

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Area of Science:

  • Computational materials science
  • Materials physics
  • Mathematical modeling

Background:

  • Phase field modeling is a general framework for predicting microstructural evolution.
  • Traditional phase field models require fine grid spacing for accuracy, limiting computational efficiency.
  • Discretization schemes can introduce grid-dependent artifacts like interface pinning.

Purpose of the Study:

  • To develop a new, intrinsically discrete phase field formulation.
  • To improve the numerical capabilities and computational efficiency of phase field modeling.
  • To accurately model interfacial kinetic properties and rotational invariance.

Main Methods:

  • Developed an intrinsically discrete phase field formulation.
  • Resolved interfaces with a single grid point, avoiding grid pinning.
  • Ensured accurate rotational invariance in the numerical scheme.

Main Results:

  • The new formulation significantly improves numerical capabilities.
  • Interfacial kinetic properties are reproduced with high accuracy.
  • The model successfully simulates coupled conserved and nonconserved fields.

Conclusions:

  • The intrinsically discrete phase field model offers a more efficient and accurate approach.
  • This method overcomes limitations of traditional grid-based phase field models.
  • It provides a robust framework for simulating complex microstructural evolutions.