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Continuously variable survival exponent for random walks with movable partial reflectors.

R Dickman1, D ben-Avraham

  • 1Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970, Belo Horizonte, MG, Brazil. dickman@cedro.fisica.ufmg.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2001
PubMed
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This study explores a random walk with a movable reflector, revealing how its survival probability changes continuously with the reflector's properties. This offers insights into complex systems with many absorbing states.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • Random walks are fundamental models in physics and mathematics.
  • Systems with absorbing boundaries and mobile elements exhibit complex behaviors.
  • Nonuniversal kinetic critical behavior is observed in various physical models.

Purpose of the Study:

  • To investigate a one-dimensional lattice random walk with an absorbing boundary and a movable partial reflector.
  • To analyze the impact of the reflector's properties on the walker's survival probability.
  • To elucidate a mechanism for nonuniversal kinetic critical behavior.

Main Methods:

  • Iteration of the transition matrix.
  • Asymptotic analysis of the probability generating function.

Related Experiment Videos

  • Mathematical modeling of a one-dimensional lattice random walk.

    • Main Results:

    • The critical exponent governing survival probability varies continuously between 1/2 and 1.
    • This variation is dependent on the reflector's reflection probability (r).
    • A mechanism for nonuniversal kinetic critical behavior is proposed.

    Conclusions:

    • The model provides a mechanism for nonuniversal kinetic critical behavior.
    • The study demonstrates continuous variation in critical exponents based on system parameters.
    • Findings are relevant to models with infinite absorbing configurations.