Asymmetric Diffusion 

• Edwards B, Camacho M, Engheta N. “Achieving Asymmetry and trapping in diffusion with spatiotemporal metamaterials” Nature Communications (11), 1-7, 2020.

Introduction

Diffusion is the natural consequence of random motion. Between the diffusion equation and the wave equation, the majority of the physics we experience in our daily lives can be explained. Both thermal and electrostatics can be explained as diffusion-based systems.

Similar to waves, in most systems diffusion is both reciprocal and symmetric. A thermos is equally good at keeping a hot drink hot as it is keeping a cold drink cold. It is very strange when we encounter a system in which diffusion appears to be asymmetric. Without careful analysis, such devices appear dangerously close to perpetual motion machines.

In this work, we created a metamaterial system in which diffusion was not symmetric. Diffusion is based on two quantities: capacity and conductance. We found that by sinusoidally varying these properties with time, we could create systems that were governed by the convection-diffusion equation. In other words, while the material of interest (charge or heat) would diffuse, it would also behave as if it were being blown by a wind, potentially even accumulating at the edge of the system.

By itself, accumulation is surprising as we expect things to spread out in a diffusive system. However, given the sinusoidal undulation of the material parameters, we could imagine that somehow that material wants to flow in the direction of the underlying wave. However, it gets stranger because the direction of the apparent breeze does not depend on the direction of the undulation. Rather, it depends on the phase difference between how we vary the capacity and conductance of the material.

Controlling the heat capacity for a material is difficult. However it is relatively straight forward to make a variable capacitor. Taking our inspiration from