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The Delay circuit, on the other hand, shows a large increase (overshoot) in fluorescence, which also decays towards a steady level, although this level is not the same as that reached by the basic circuit.
The GFP concentrations in the Delay circuit in both models show a sharp increase ("overshoot") followed by a gradual decline to the same steady state value (takes longer time than TetR due to slower degradation rate, as shown in Supporting Information S2, Fig. S9).
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In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot.
The hybrid integrator is designed to obtain improved low-frequency disturbance rejection properties under double-integrator (PI2D-like) control, but without the unwanted increase of overshoot otherwise resulting from adding an extra linear integrator.
While the broadening could be due to a decreasing value of x, we found that this same decrease would lead to increasing enthalpy overshoots on heating, contrary to the experimental observations.
Consequently, attempts to apply any interface-sharpening techniques to stop the progressively more severe smearing interfaces for a longer simulation time may result in an overshoot increase and in some cases convergence to a non-physical solution occurs.
On increasing the length of delay, the extent of overshoot increases, but the steady state remains constant (not shown here).
Hence, it is clear that both plasmid size difference and translational efficiency of later cistrons are not the major contributing factors to the increased gene expression (Overshoot) in the Delay circuit.
The magnitude of the overshoot increases with shear rate.
For PMSE layers, it is also often noted that an "overshoot", or increase in echo strength, occurs at the end of the heating period, possibly because the charge state of the aerosol particles is temperature dependent (e.g. Havnes et al. 2004; Biebricher et al 2006).
The experiments with simple gene circuits also show the overshoot and increase in population heterogeneity.
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