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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.
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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Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Measuring Active and Passive Tameness Separately in Mice
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Active phase separation: A universal approach.

Fabian Bergmann1, Lisa Rapp1, Walter Zimmermann1

  • 1Theoretische Physik I, Universität Bayreuth, 95440 Bayreuth, Germany.

Physical Review. E
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Summary
This summary is machine-generated.

Active phase separation is a common phenomenon in systems out of equilibrium, like cell populations. The classical Cahn-Hilliard (CH) model surprisingly describes these nonequilibrium systems, linking diverse biological and ecological examples.

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Area of Science:

  • Non-equilibrium statistical mechanics
  • Mathematical biology
  • Soft matter physics

Background:

  • Phase separation is a fundamental process in physics and chemistry, typically studied in systems at thermal equilibrium.
  • Many biological and ecological systems exhibit collective behaviors driven by internal dynamics, operating far from equilibrium.
  • Understanding the collective dynamics and emergent structures in these non-equilibrium systems is a key challenge.

Purpose of the Study:

  • To identify active phase separation as a generic phenomenon in non-equilibrium systems with conservation constraints.
  • To demonstrate that the classical Cahn-Hilliard (CH) equation can describe system-spanning properties of active phase separation near onset.
  • To establish a general mathematical framework linking the CH equation to specific models of active phase separation.

Main Methods:

  • Theoretical analysis of non-equilibrium systems with conservation laws.
  • Application of the Cahn-Hilliard (CH) model to active phase separation phenomena.
  • Development of a general reduction scheme to connect generic CH equation with system-specific models.

Main Results:

  • Active phase separation is identified as a universal demixing phenomenon in diverse non-equilibrium systems, including cell polarization, chemotaxis, self-propelled particles, and ecological communities.
  • The study shows that the classical Cahn-Hilliard (CH) equation accurately describes the system-spanning properties of active phase separation near its onset.
  • A general reduction scheme is introduced, establishing a mathematical link between the CH equation and specific active phase separation models, exemplified by cell polarization and chemotactic cell communities.

Conclusions:

  • The classical Cahn-Hilliard (CH) equation provides a surprisingly effective framework for describing active phase separation in non-equilibrium systems.
  • The developed reduction scheme offers a powerful tool for analyzing and understanding collective behaviors in a wide range of active matter systems.
  • The findings bridge the gap between equilibrium and non-equilibrium descriptions of phase separation, with implications for biology, ecology, and physics.