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TITLE Self-repelling bipedal exploration process
KIAS AUTHORS Park, Hyunggyu,Dashti-N, Hor,Park, Hyunggyu
ARCHIVE arXiv:2107.05303
ABSTRACT A self-repelling two-leg (biped) spider walk is considered where the local stochastic movements are governed by two independent control parameters fid and fih, so that the former controls the distance (d) between the legs positions, and the latter controls the statistics of self-crossing of the traversed paths. The probability measure for local movements is supposed to be the one for the "true self-avoiding walk" multiplied by a factor exponentially decaying with d. After a transient behavior for short times, a variety of behaviors have been observed for large times depending on the value of fid and fih. Our statistical analysis reveals that the system undergoes a crossover between two (small and large fid) regimes identified in large times (t). In the small fid regime, the random walkers (identified by the position of the legs of the spider) remain on average in a fixed nonzero distance in the large time limit, whereas in the second regime (large fid), the absorbing force between the walkers dominates the other stochastic forces. In the latter regime, d decays in a power-law fashion with the logarithm of time. When the system is mapped to a growth process (represented by a height field which is identified by the number of visits for each point), the roughness and the average height show different behaviors in two regimes, i.e., they show a power law with respect to t in the first regime and log t in the second regime. The fractal dimension of the random walker traces and the winding angle are shown to consistently undergo a similar crossover.
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