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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

46.6K
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 Diagram01:19

Phase Diagram

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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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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.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
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Two-Dimensional (2D) NMR: Overview01:12

Two-Dimensional (2D) NMR: Overview

1.1K
The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse....
1.1K
Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
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Related Experiment Video

Updated: Nov 16, 2025

Three-Dimensional Phase Resolved Functional Lung Magnetic Resonance Imaging
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Three-Dimensional Phase Resolved Functional Lung Magnetic Resonance Imaging

Published on: June 21, 2024

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Three-dimensional spatially resolved phase graph framework.

Xiang Gao1, Valerij G Kiselev1, Thomas Lange1

  • 1Department of Radiology, Medical Physics, Medical Center University of Freiburg, University of Freiburg, Freiburg, Germany.

Magnetic Resonance in Medicine
|February 20, 2021
PubMed
Summary
This summary is machine-generated.

A new open-source framework simulates magnetic resonance imaging (MRI) pulse sequences in 3D, enabling efficient analysis of signal modulation and image artifacts for advanced applications like MR fingerprinting.

Keywords:
3D gradientsextended phase graphmagnetic resonance fingerprintingmagnetic spectroscopic imagingrecursive magnetization evolution

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Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Computational Physics
  • Biomedical Engineering

Background:

  • Accurate simulation of complex MRI pulse sequences is crucial for developing advanced imaging techniques.
  • Existing methods may struggle with arbitrary pulse sequences, 3D gradient orientations, and anisotropic diffusion.

Purpose of the Study:

  • To introduce an open-source, spatially resolved phase graph framework for simulating arbitrary MRI pulse sequences in 3D.
  • To generalize the extended phase graph algorithm for non-periodic sequences and estimate 3D signal modulation.

Main Methods:

  • Extended the recursive magnetization-evolution algorithm to include anisotropic diffusion.
  • Developed a novel 3D k-space grid-merging method for efficient computation and memory management.
  • Implemented a post-simulation module for tracking and visualizing signal evolution in k-space and image domains.

Main Results:

  • The grid-merging algorithm demonstrated high computational efficiency in simulating frequency responses of steady-state sequences.
  • The framework successfully visualized magnetization evolution in PRESS-based spectroscopic imaging sequences.
  • Validated through applications in MR fingerprinting, diffusion-weighted imaging, and spectroscopic imaging.

Conclusions:

  • The proposed simulation framework provides a validated tool for analyzing signal evolution in both frequency and spatial domains.
  • This open-source framework enhances the simulation capabilities for complex MRI sequences and artifact analysis.