diffusesuch

Diffusesuch is a theoretical construct used to describe diffusion processes that operate across multiple domains, combining physical diffusion with diffusion through interconnected networks. In this framework, a substance, signal, or influence spreads not only through a medium by local dispersion but also across social, technological, or infrastructural networks, yielding a diffuse, cross-domain distribution pattern. The term is used primarily in interdisciplinary modeling to capture coupled diffusion phenomena where local dispersion interacts with nonlocal propagation paths.

Modeling diffusesuch involves coupled dynamics that integrate a local diffusion term with a nonlocal network term. A typical formulation uses a partial differential equation for the physical layer, such as D(x) ∇^2 u(x,t), together with a graph-Laplacian term κ Lu(x,t) on the network layer, or a set of interdependent equations linking spatial fields and node states. Parameters like diffusion coefficients, network weights, and coupling strengths control the balance between physical and network diffusion and shape the resulting patterns.

Applications of diffusesuch concepts span environmental science, epidemiology, information diffusion, and urban planning. They are used to model scenarios where a contaminant, disease, or message spreads through a physical medium and concurrently through connected networks, producing broader and more complex dissemination patterns than either diffusion channel alone.

Limitations include challenges in parameter identifiability, sensitivity to network structure, and data requirements for validating cross-domain models. Diffusesuch approaches also demand careful specification of interlayer couplings and may rely on simplifying assumptions to remain tractable. See also diffusion, nonlocal diffusion, network diffusion, and multi-layer networks.