In this paper we consider the spread of modern technological innovations. We contrast social learning and threshold heterogeneity models of innovation diffusion, and show how the typical temporal evolution of the distribution of adopters may be consistent with either explanation. Noting the likelihood that each model contains some useful independent explanatory power, we introduce a combined model. We also consider a spatially-structured population in which the spread of an innovation by social influence is modelled as a reaction-diffusion system, and show that the typical spatiotemporal evolution of the distribution is also consistent with a heterogeneity explanation. Additional contextual information is required to estimate the relative importance of social learning and of economic inequalities in observed adoption lags.

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Starting from Fick’s train of thought, which led to the formulation of his law governing diffusion in a solid or liquid medium, we first consider the limits of applicability of this law to solid medium-single penetrant systems. We then take up the question of proper formulation, in combination with simple but physically meaningful modeling, of diffusion behavior deviating from this law, because of (i) concentration dependence (ii) time dependence or (iii) space dependence, of the relevant transport parameters (which include the sorption, no less than the diffusion, coefficient). Examples of application to real systems are offered in each case. We conclude that progress in such studies depends on following Fick’s mode of thinking rather than on adhering to the formalism of his law.

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This paper considers permeation through microporous or nanoporous inorganic membranes under the influence of an applied pressure gradient. In general membrane permeation may be considered as a diffusive process, driven by the gradient of chemical potential (which depends on both composition and pressure). The relative importance of these two factors varies greatly for different types of system. The general features of such processes are reviewed and the diffusional behavior of selected systems is examined. (membrane permeation, osmosis, diffusion, zeolite membrane, DDR-3, SAPO-34)