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Denis S Grebenkov1

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We analyzed how multiple diffusing particles reaching a target affect reaction triggers. Finite residence times create particle coupling, influencing the mean first passage time for simultaneous arrival.

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Area of Science:

  • Physical Chemistry
  • Chemical Physics
  • Biophysics

Background:

  • The first passage problem is crucial for understanding diffusion-limited reactions.
  • Reversible target-binding kinetics with finite residence times introduce complex particle interactions.
  • Simultaneous particle arrival on a target can initiate significant events.

Purpose of the Study:

  • To investigate the first passage time for multiple particles with reversible target-binding kinetics.
  • To determine the mean first passage time (MFPT) for the simultaneous arrival of 'm' particles.
  • To analyze the impact of adsorption and desorption rates on particle behavior.

Main Methods:

  • Analytical computation of the mean first passage time (MFPT).
  • Mapping the problem to higher-dimensional surface-mediated diffusion.
  • Solving coupled partial differential equations for particle dynamics.

Main Results:

  • Finite residence times lead to intricate temporal coupling between independent particles.
  • Analytical solutions for the MFPT were derived for two independent particles.
  • The influence of adsorption and desorption rates on MFPT was quantified.

Conclusions:

  • The study provides insights into multi-particle diffusion with reversible binding.
  • Understanding particle coupling is key for predicting reaction initiation.
  • The findings are relevant for chemical reactions and biophysical events.