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Reconfigurable Microfluidic Channel with Pin-discretized Sidewalls
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Dimensional crossover in surface growth on rectangular substrates.

Ismael S S Carrasco1,2, Tiago J Oliveira1

  • 1Universidade Federal de Viçosa, Departamento de Física, 36570-900 Viçosa, MG, Brazil.

Physical Review. E
|June 19, 2026
PubMed
Summary
This summary is machine-generated.

Dimensional crossovers in interface growth were observed across multiple universality classes. Simulations show a transition from two-dimensional (2D) to one-dimensional (1D) scaling in roughness and height distributions for systems with large aspect ratios.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Statistical Physics

Background:

  • Interface growth phenomena are crucial in various physical systems.
  • Dimensional crossovers in the Kardar-Parisi-Zhang (KPZ) class were recently reported.
  • Understanding these crossovers in other universality classes is essential.

Purpose of the Study:

  • To investigate dimensional crossovers in interface growth for Edwards-Wilkinson (EW), Mullins-Herring (MH), and Villain-Lai-Das Sarma (VLDS) universality classes.
  • To analyze the impact of substrate aspect ratio on scaling behavior.
  • To explore crossovers in height distributions and steady-state regimes.

Main Methods:

  • Extensive numerical simulations were employed.
  • Analysis focused on interface roughness scaling with time and system dimensions.
  • Height distributions and steady-state properties were examined.

Main Results:

  • Dimensional crossovers from 2D to 1D scaling were observed in roughness for all studied classes with large aspect ratios (R=Ly/Lx).
  • A crossover in height distribution from 2D to 1D was found for the VLDS class.
  • Steady-state roughness and VLDS height distributions showed interpolation between 2D and 1D behavior with increasing R.

Conclusions:

  • Interface growth exhibits dimensional crossovers across multiple universality classes, not just KPZ.
  • Substrate geometry, particularly aspect ratio, significantly influences scaling behavior and crossover phenomena.
  • The findings provide a comprehensive understanding of dimensional crossover effects in diverse interface growth models.