Researchers have developed diffusive metamaterials that manipulate the flow of particles or energy in an analogous way to how optical metamaterials control light. These new materials, operating in the diffusion regime, allow for guiding, concentrating, or diverting particles or heat with unprecedented precision. The key to their function lies in a duality between the material's geometry and the physical properties of diffusion, enabling the design of structures that mimic behaviors observed in biological systems to optimize transport. This breakthrough paves the way for a new class of materials with applications in fields as diverse as thermal engineering, medicine, and catalysis.

Traditionally, diffusion control has been achieved by altering the chemical composition or porosity of materials. However, this approach has limitations in terms of precision and adaptability. Diffusive metamaterials overcome these barriers by employing "space engineering" that shapes the trajectories of diffusing particles. This is accomplished through periodic or aperiodic micro-scale structures, which create an effective medium with anisotropic and inhomogeneous diffusive properties. The analogy with optics allows for the application of established wave control design principles to the manipulation of diffusive phenomena, accelerating the development of these new materials.

The methodology used is based on exploiting physical-geometric duality, where variations in the material's geometry (e.g., the shape and size of pores or channels) directly translate into changes in effective diffusion coefficients. This enables inverse design, where a desired diffusive behavior is specified, and the necessary geometry to achieve it is deduced. Experiments have demonstrated the ability of these metamaterials to create "diffusive lenses" that focus heat or particles, as well as "diffusive invisibility cloaks" that hide objects from diffusion flow. These capabilities have significant implications for thermal management in electronic devices, controlled drug delivery, and improving efficiency in catalytic reactions.