Force-driven parallel shear flow in a spatially periodic domain is shown to be linearly unstable
with respect to both the Reynolds number and the domain aspect ratio. This finding is confirmed
by computer simulations, and a simple expression is derived to determine stable flow conditions.
Periodic extensions of Couette and Poiseuille flows are unstable at Reynolds numbers two orders
of magnitude smaller than their aperiodic equivalents because the periodic boundaries impose
fundamentally different constraints. This instability has important implications for designing computational models of nonlinear dynamic processes with periodicity.
Monitoring the attention of others is fundamental to social cognition. Most of the literature on the topic assumes that our social cognitive machinery is tuned specifically to the gaze direction of others as a proxy for attention. This standard assumption reduces attention to an externally visible parameter. Here we show that this assumption is wrong and a deeper, more meaningful representation is involved. We presented subjects with two cues about the attentional state of a face: direction of gaze and emotional expression. We tested whether people relied predominantly on one cue, the other, or both. If the traditional view is correct, then the gaze cue should dominate. Instead, people employed a variety of strategies, some relying on gaze, some on expression, and some on an integration of cues. We also assessed people’s social cognitive ability using two, independent, standard tests. If the traditional view is correct, then social cognitive ability, as assessed by the independent tests, should correlate with the degree to which people successfully use the gaze cue to judge the attention state of the face. Instead, social cognitive ability correlated best with the degree to which people successfully integrated the cues together, instead of with the use of any one specific cue. The results suggest a rethink of a fundamental component of social cognition: monitoring the attention of others involves constructing a deep model that is informed by a combination of cues. Attention is a rich process and monitoring the attention of others involves a similarly rich representation.
