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Tommy Dessup1, Thibaud Maimbourg1, Christophe Coste1

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This summary is machine-generated.

Confined interacting particles form zigzag patterns. Short-range forces can destabilize these structures, but longer-range interactions, like Coulomb forces, ensure stability. This study clarifies pattern formation conditions.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Soft matter physics

Background:

  • Particles in quasi-one-dimensional channels exhibit diverse equilibrium patterns.
  • These patterns depend on interparticle interactions and transverse confinement potentials.
  • Observed configurations include linear, zigzag, and distorted zigzag arrangements.

Purpose of the Study:

  • To clarify the conditions governing the existence of different particle configurations.
  • To analyze the linear stability of the zigzag pattern.
  • To determine the interaction range for zigzag pattern stability.

Main Methods:

  • Linear stability analysis of the zigzag pattern.
  • Calculation of the critical interaction range for instability.
  • Investigation of finite size effects.

Main Results:

  • An acoustic transverse mode destabilizes zigzag patterns for short-range interactions.
  • Zigzag patterns are unconditionally stable for Coulomb interactions.
  • The linear stability analysis accurately describes the domain of existence for distorted zigzag patterns.

Conclusions:

  • A criterion for instability onset in the thermodynamic limit is established.
  • A biphasic model explains characteristics of distorted zigzag patterns.
  • Finite size effects introduce significant complexity to pattern formation.