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Self-repelling bipedal exploration process.

Hor Dashti-N1, M N Najafi2, Hyunggyu Park1

  • 1School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea.

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|December 24, 2021
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Summary
This summary is machine-generated.

This study examines a biped spider walk model, revealing distinct behaviors based on leg distance (d) and path self-crossing parameters. The research identifies a crossover in movement regimes, impacting walker distance and growth process dynamics.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • The study investigates a novel two-leg (biped) spider walk model with self-repelling properties.
  • Local stochastic movements are governed by two control parameters: βd for leg distance and βh for path self-crossing statistics.

Purpose of the Study:

  • To analyze the long-time behavior of the biped spider walk under varying control parameters.
  • To identify and characterize different dynamical regimes and their impact on system properties.

Main Methods:

  • Statistical analysis of a biped spider walk model with a modified probability measure for local movements.
  • Investigation of crossovers between small and large βd regimes for long-time dynamics.
  • Mapping the system to a growth process represented by a height field.

Main Results:

  • A crossover between two distinct large-time regimes (small and large βd) was observed.
  • In the small βd regime, walkers maintain a fixed average distance; in the large βd regime, distance decays logarithmically with time.
  • Roughness and average height of the associated growth process exhibit different power-law behaviors (t vs. log t) in the two regimes.

Conclusions:

  • The biped spider walk model exhibits complex dynamics with a clear crossover behavior dependent on control parameters.
  • The fractal dimension and winding angle consistently reflect this crossover, indicating a unified change in system properties.
  • The findings provide insights into the statistical mechanics of self-repelling walks and related growth processes.