Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Order statistics of the trapping problem.

S B Yuste1, L Acedo

  • 1Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

First-encounter time of two diffusing particles in two- and three-dimensional confinement.

Physical review. E·2022
Same author

Pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres.

Physical review. E·2021
Same author

Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains.

Physical review. E·2020
Same author

First-encounter time of two diffusing particles in confinement.

Physical review. E·2020
Same author

Structural properties of additive binary hard-sphere mixtures.

Physical review. E·2020
Same author

Standard and fractional Ornstein-Uhlenbeck process on a growing domain.

Physical review. E·2019

This study provides an exact solution for the time moments until particles are trapped on a lattice. It reveals how trapping time moments scale with particle number and trap concentration, offering insights into diffusion processes.

Area of Science:

  • Statistical Physics
  • Mathematical Physics
  • Diffusion Processes

Background:

  • Understanding particle diffusion and trapping is crucial in various scientific fields.
  • Previous models often lacked exact solutions for moments of trapping times.

Purpose of the Study:

  • To derive an exact expression for the mth moment of the time until the first j particles are trapped.
  • To analyze the behavior of these moments for large numbers of diffusing particles on a lattice with traps.

Main Methods:

  • The study derives an exact answer in terms of the probability that no particle is trapped by time t.
  • The Rosenstock approximation is employed to evaluate this probability.
  • Asymptotic expressions are derived for the one-dimensional lattice case.

Related Experiment Videos

Main Results:

  • An exact formula for the mth moment is presented.
  • For a wide range of trap concentrations, the mth moment scales as x(-m) and variance as x(-2), where x = ln(2/d)(1-c)ln N.
  • Rigorous asymptotic expressions with dominant and corrective terms are provided for 1D lattices.

Conclusions:

  • The derived formulas offer precise predictions for trapping times in diffusion-limited processes.
  • The scaling behavior provides a universal description for trapping phenomena across different dimensions and concentrations.
  • The study advances the analytical understanding of diffusion with traps.