Accelerating solutions to the diffusion equation

TL;DR

This paper presents methods to accelerate solutions to the diffusion equation, demonstrating that the maximum diffusion density evolves with acceleration described by Airy functions in both 1D and 3D cases.

Contribution

The authors introduce a novel approach to accelerate diffusion solutions and construct a modified form that preserves the accelerating behavior.

Findings

Diffusive solutions exhibit acceleration characterized by Airy functions.

Acceleration observed in both one-dimensional and three-dimensional systems.

A modified diffusion solution retains the accelerating features.

Abstract

We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive accelerating behavior for one--dimensional systems, as well as for a general three--dimensional case. We also construct a modulated modified form of the diffusion solution that retains the accelerating features.