Stochastic cloaking: concealing a region from diffusive particles

TL;DR

This paper introduces stochastic cloaking, a method to hide regions from diffusing particles by manipulating diffusivity, with near-perfect performance under the Ito interpretation, advancing cloaking techniques into thermodynamics.

Contribution

The paper presents the concept of stochastic cloaking for diffusive particles and analyzes its effectiveness under different stochastic calculus interpretations, especially Ito.

Findings

Near-perfect cloaking achieved with Ito interpretation

Performance improved by regularising singularities

Simulation results demonstrate effective concealment of inner region

Abstract

We introduce "stochastic cloaking," where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different interpretations of the Langevin equation affect the cloaking performance of an annular single-layer invisibility cloak of smoothly varying diffusivity in two dimensions. Near-perfect cloaking is achieved under the Ito convention, indicated by the cloak preventing particles from accessing an inner core without disturbing the particle density outside the cloak. The cloak's performance can be further improved by regularising its singular behaviour. We believe our demonstration of stochastic cloaking is a significant milestone, comparable to earlier developments that extended cloaking from optics and acoustics to thermodynamics.