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When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.

We report, for the first time, the experimental observation of solitary waves in an axisymmetric Taylor-Couette flow. The solitary waves result from a parity-breaking bifurcation which occurs near the onset of Eckhaus instability for Taylor vortex flow in a wide-gap, counterrotating system (radius ratio η=0.5 and speed ratio μ=-0.2). Our results agree quantitatively with a recent theoretical calculation by Riecke and Paap