Classical and Quantum Models of Diffusion

The objective of the paper is twofold: first, to review the classical diffusion models and show the approximations at the origin of the parabolic character of the classical equations; second, to demonstrate a connection between the quantum and classical models of diffusion. As diffusion is inherently related to the motion of constituents, the consistent models are framed within the dynamics of mixtures. The derivation of diffusion equations is then determined based on the related, pertinent approximations.

Successive waves in pandemic infections: physical diffusion theory and data comparisons

We establish the principal that the prediction, timing and magnitude of second and more distinct waves of infection can be based on the well - known physics and assumptions of classical diffusion theory. This model is fundamentally different from the commonly used SEIR and R0 fitting methods. Driven by data, we seek a working approximation for the observed orders of magnitude for the timing and rate of second and more waves. The dynamic results and characteristics are compared to the data and enable predictions of timescales and maximum expected rates where diffusive effects dominate.The important point is this simple physical model allows understanding of the dominant processes, provides prediction estimates, and is based the solutions derived from existing, consistent and well-known physical principles. The medical system and health policy implications of such inexorable diffusive spread are that any NPI and other countermeasures deployed for and after the rapid first peak must recognize that large residual infection waves will then likely occur.

Flipping the Diffusion of Innovations Paradigm: Embracing the Positive Deviance Approach to Social Change

The classical diffusion of the innovations paradigm has faced criticism for reifying outside-in, expert-driven approaches to solving problems and for overlooking and rejecting local solutions. In this article, we argue that diffusion scholars should pay more attention to approaches such as positive deviance (PD) that enable communities to discover the wisdom they already have and then to act on it. PD is an asset-based approach that identifies what is going right in a community to amplify it, as opposed to focusing on what is going wrong in a community and fixing it with outside expertise. In the PD approach, the change is led by internal change agents who, with access to no special resources, present the social behavioural proof to their peers that problems can be solved. Given that the solutions are generated locally, they are more likely to sustain and be owned by potential adopters.