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First-contact time to a patch in a multidimensional potential well.

Le Yang1, David Sept, A E Carlsson

  • 1Department of Physics, Washington University, St. Louis, Missouri 63130, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
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We derived a simple formula for predicting the first-contact time of a diffusing particle escaping a potential well. This formula accurately models escape dynamics across various dimensions and applications, including biopolymer interactions.

Area of Science:

  • Statistical physics
  • Physical chemistry
  • Biophysics

Background:

  • Particle escape from potential wells is crucial in chemical, physical, and biological processes.
  • Escape often involves locating specific regions within complex potential landscapes.

Purpose of the Study:

  • To develop a general formula for first-contact time in particle escape dynamics.
  • To validate the formula through simulations and apply it to multi-dimensional systems and biopolymer interactions.

Main Methods:

  • Analytical theory development combining high-symmetry and zero-potential cases.
  • Computational simulations for validating theoretical predictions.
  • Extension of theory to calculate inter-particle first-contact times.

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Main Results:

  • A simple, dimension-independent formula for first-contact time was derived.
  • The formula accurately predicts the dependence of escape time on well depth and patch size.
  • The extended theory successfully modeled first-contact time for two biopolymer filaments.

Conclusions:

  • The derived formula provides a powerful tool for understanding and predicting particle escape dynamics.
  • The findings have broad applicability in diverse scientific fields, from materials science to molecular biology.
  • The study offers a unified approach to first-contact time calculations in complex systems.