Space-Time Innovation Diffusion Based on Physical Analogy

To predict the diffusion of innovations quantitatively, a diffusion equation based on the analogy between physical systems is presented. Referring to physical systems of heat propagation, which are based on the concepts of heat transfer, convection, and radiation, we propose that patterns of innovation diffusion can be classified. To compute the diffusion distribution with respect to time and space, we consider a variety of concepts such as the adoption ratio, adoption capacity ratio, and innovation diffusivity. These concepts are formulated on the basis of a discussion and carefully performed comparison between concepts drawn from the extant social science literature (e.g., neighboring effects, hierarchical effects, etc.) and mathematical models used in natural sciences. The innovation diffusion equation is subsequently derived from these concepts. Lastly, as applications to the proposed analogy, we model two innovation diffusion processes.

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