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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
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A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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This study introduces a universal theory for active nematic liquid crystals, revealing two instabilities that cause defect proliferation. It identifies three distinct nonequilibrium steady states, including a novel defect-ordered nematic phase.

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Area of Science:

  • Active matter physics
  • Soft condensed matter theory
  • Liquid crystal dynamics

Background:

  • Active nematic liquid crystals exhibit complex behaviors driven by self-propelled constituents.
  • Understanding defect formation and ordering in these systems is crucial for predicting their collective dynamics.

Purpose of the Study:

  • To develop a universal phenomenological continuum theory for dense, overdamped active nematic liquid crystals.
  • To investigate the instabilities and nonequilibrium steady states arising from this theory.

Main Methods:

  • Construction of a general continuum theory based on fundamental principles.
  • Analysis of bifurcations and stability of theoretical solutions.
  • Characterization of defect proliferation and ordering phenomena.

Main Results:

  • The theory predicts two distinct instabilities: one driven by shear forces and another by active torques.
  • Focusing on the active torque bend instability, three nonequilibrium steady states were identified.
  • A novel defect-ordered nematic phase with polar ordering of +½ disclinations was discovered.

Conclusions:

  • The developed theory provides a universal framework for active nematics, independent of microscopic details.
  • The identified instabilities and steady states offer insights into defect dynamics and emergent ordering in active matter.
  • The findings connect theoretical predictions to experimental observations and other active nematic models.