English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Diffusive search for a static target is a common problem in statisticalphysics with numerous applications in chemistry and biology. We look at thisproblem from a different perspective and investigate the statistics ofencounters between the diffusing particle and the target. While an exactsolution of this problem was recently derived in the form of a spectralexpansion over the eigenbasis of the Dirichlet-to-Neumann operator, the latteris generally difficult to access for an arbitrary target. In this paper, wepresent three complementary approaches to approximate the probability densityof the rescaled number of encounters with a small target in a bounded confiningdomain. In particular, we derive a simple fully explicit approximation, whichdepends only on a few geometric characteristics such as the surface area andthe harmonic capacity of the target, and the volume of the confining domain. Wediscuss the advantages and limitations of three approaches and check theiraccuracy. We also deduce an explicit approximation for the distribution of thefirst-crossing time, at which the number of encounters exceeds a prescribedthreshold. Its relations to common first-passage time problems are discussed.

Statistics of diffusive encounters with a small target: Three complementary approaches