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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

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...
Phase Diagram01:19

Phase Diagram

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).
Phase Diagram01:24

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
Phase Transitions02:31

Phase Transitions

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 occupy...
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

Design Example: Creating a Hydraulic Model of a Dam Spillway

Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.

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Related Experiment Video

Updated: May 11, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

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Published on: December 7, 2021

Visualization of system dynamics using phasegrams.

Christian T Herbst1, Hanspeter Herzel, Jan G Svec

  • 1Department of Cognitive Biology, Laboratory of Bioacoustics, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria. christian.herbst@univie.ac.at

Journal of the Royal Society, Interface
|May 24, 2013
PubMed
Summary
This summary is machine-generated.

A novel phasegram tool visualizes system dynamics by mapping time to identify vibratory regimes like chaos. This method aids signal classification in physics, biology, and medicine without needing system parameters.

Keywords:
Poincaré sectionattractor visualizationbioacousticsphasegramsliding-window analysissystem dynamics

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Area of Science:

  • Nonlinear dynamics
  • Signal processing
  • Data visualization

Background:

  • Traditional analysis methods for oscillating systems often require known parameters or lack temporal resolution.
  • Visualizing complex system dynamics, such as chaos, remains a challenge.

Purpose of the Study:

  • To introduce a new tool, the phasegram, for the visualization and analysis of system dynamics.
  • To demonstrate the phasegram's utility in analyzing both classical nonlinear systems and biological signals.

Main Methods:

  • The phasegram combines sliding-window analysis with nonlinear dynamics visualization techniques.
  • Time is mapped to the x-axis, with vibratory regimes identified by horizontal line stability.
  • The method is automatically constructed from time-series data, requiring no prior system parameter knowledge.

Main Results:

  • Phasegrams effectively identify periodic oscillations, subharmonics, and chaotic regimes.
  • The tool provides a time-varying bifurcation diagram interpretation.
  • Successful application demonstrated on the logistic map, Lorenz system, and voice signals.

Conclusions:

  • Phasegrams offer a powerful, parameter-free approach for analyzing oscillating systems.
  • The tool shows significant potential for signal classification across various scientific disciplines.
  • Phasegrams can serve as a quantitative foundation for further research in physics, acoustics, biology, and medicine.