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Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
08:19

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion

Published on: January 15, 2016

Vicious walks with long-range interactions.

Igor Goncharenko1, Ajay Gopinathan

  • 1School of Natural Sciences, University of California, Merced, California 95343, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We studied vicious walks with long-range interactions using renormalized field theory. Our findings reveal distinct scaling behaviors for survival and reunion probabilities across different dimensions and interaction parameters.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • The asymptotic behavior of vicious walks with short-range interactions is well-understood.
  • Realistic processes often involve long-range potentials decaying as r^(-d-σ) in d dimensions.

Purpose of the Study:

  • To investigate the impact of long-range potentials on the survival and reunion probabilities of vicious walks.
  • To calculate the exponents governing the decay of survival probability for all σ and d parameters.

Main Methods:

  • Renormalized field theory techniques were employed.
  • A double expansion in ε=2-d and δ=2-d-σ was used to calculate exponents to first order.

Main Results:

  • Identified distinct scaling regions in the σ-d plane for survival and reunion probabilities.
  • Calculated the exponents describing the decay of survival probability for all parameter values.
  • Determined the leading logarithmic corrections to these probabilities.

Conclusions:

  • Long-range interactions significantly alter the scaling behavior of vicious walks compared to short-range interactions.
  • The study provides a comprehensive analysis of survival and reunion probabilities in systems with long-range potentials.