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We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
Width control on event-scale deposition and evacuation of sediment in bedrock-confined channels
(2020)
In mixed bedrock-alluvial rivers, the response of the system to a flood event can be affected by a number of factors, including coarse sediment availability in the channel, sediment supply from the hillslopes and upstream, flood sequencing and coarse sediment grain size distribution. However, the impact of along-stream changes in channel width on bedload transport dynamics remains largely unexplored. We combine field data, theory and numerical modelling to address this gap. First, we present observations from the Daan River gorge in western Taiwan, where the river flows through a 1 km long 20-50 m wide bedrock gorge bounded upstream and downstream by wide braidplains. We documented two flood events during which coarse sediment evacuation and redeposition appear to cause changes of up to several metres in channel bed elevation. Motivated by this case study, we examined the relationships between discharge, channel width and bedload transport capacity, and show that for a given slope narrow channels transport bedload more efficiently than wide ones at low discharges, whereas wider channels are more efficient at high discharges. We used the model sedFlow to explore this effect, running a random sequence of floods through a channel with a narrow gorge section bounded upstream and downstream by wider reaches. Channel response to imposed floods is complex, as high and low discharges drive different spatial patterns of erosion and deposition, and the channel may experience both of these regimes during the peak and recession periods of each flood. Our modelling suggests that width differences alone can drive substantial variations in sediment flux and bed response, without the need for variations in sediment supply or mobility. The fluctuations in sediment transport rates that result from width variations can lead to intermittent bed exposure, driving incision in different segments of the channel during different portions of the hydrograph.