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Related Experiment Videos

Trapping and survival probability in two dimensions.

L K Gallos1, P Argyrakis, K W Kehr

  • 1Department of Physics, University of Thessaloniki, GR-54006 Thessaloniki, Greece.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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This study quantifies the crossover in particle survival probability during random walks with traps. The findings reveal the crossover

Area of Science:

  • Statistical Physics
  • Probability Theory
  • Computational Physics

Background:

  • Particles in random walks can get trapped, affecting their survival probability.
  • Previous models offered approximations for early (Rosenstock) and late (Donsker-Varadhan) times.
  • The exact crossover point between these regimes was previously unknown.

Purpose of the Study:

  • To quantitatively determine the crossover in survival probability for particles on a lattice with traps.
  • To develop a method for locating this crossover based on a scaling hypothesis.
  • To analyze the survival probability as a function of steps and trap concentration.

Main Methods:

  • Utilized a scaling ansatz based on the mean number of visited sites (S(n)).
  • Employed Monte Carlo simulations and a 'slithering' snake algorithm for self-interacting random walks.

Related Experiment Videos

  • Analyzed survival probability (Phi(n,c)) as a function of steps (n) and trap concentration (c).

    • Main Results:

    • Successfully located the crossover point, which was previously only postulated.
    • The crossover location depends on both the number of steps (n) and trap concentration (c).
    • The crossover occurs at low survival probabilities, characteristic of longer walks.

    Conclusions:

    • A novel method for quantitatively determining the crossover in survival probability has been established.
    • The findings provide a more complete understanding of particle behavior in random environments.
    • This research bridges early-time approximations and asymptotic behaviors in random walk theory.