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Theory is developed to predict the flows induced by small-amplitude two-dimensional vertically propagating internal wavepackets under the influence of rotation. While the long wave response originally predicted by Bretherton [J. Fluid Mech. 36, 785-803 (1969)] dominates if the influence of background rotation is negligible, the induced waves are found to be evanescent if the Coriolis parameter is sufficiently large. Explicitly, evanescent induced flows dominate if the Coriolis parameter is greater than the forcing frequency, which is set by the ratio of the vertical group velocity of the wavepacket divided by the vertical scale of modulation of the wavepacket. The predicted structure of the induced flow is confirmed by numerical simulations. For an up- and rightward propagating Gaussian wavepacket that dominantly induces a long wave response, the flow is rightward across the upper flank and leftward across the lower flank of the wavepacket. In contrast, the induced flow for a dominantly evanescent response is negative over the middle of the wavepacket. This qualitative change in structure is anticipated to influence the modulational stability of moderately large amplitude wavepackets.

Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model idealizes chemical interactions, allowing rigorous reasoning about the computational power of chemical kinetics. Here we focus on function computation with CRNs, where we think of the initial concentrations of some species as the input and the equilibrium concentration of another species as the output. Specifically, we are concerned with CRNs that are rate-independent (the computation must be correct independent of the reaction rate law) and composable ($f\circ g$ can be computed by concatenating the CRNs computing $f$ and $g$). Rate independence and composability are important engineering desiderata, permitting implementations that violate mass-action kinetics, or even "well-mixedness", and allowing the systematic construction of complex computation via modular design. We show that to construct composable rate-independent CRNs, it is necessary and sufficient to ensure that the output species of a module is not a reactant in any reaction within the module. We then exactly characterize the functions computable by such CRNs as superadditive, positive-continuous, and piecewise rational linear. Thus composability severely limits rate-independent computation unless more sophisticated input/output encodings are used., Appeared at Computational Methods in Systems Biology (CMSB) 2018 (best paper award) To appear in IEEE/ACM Transactions on Computational Biology and Bioinformatics

Biological regulatory networks depend upon chemical interactions to process information. Engineering such molecular computing systems is a major challenge for synthetic biology and related fields. The chemical reaction network (CRN) model idealizes chemical interactions, abstracting away specifics of the molecular implementation, and allowing rigorous reasoning about the computational power of chemical kinetics. Here we focus on function computation with CRNs, where we think of the initial concentrations of some species as the input and the eventual steady-state concentration of another species as the output. Specifically, we are concerned with CRNs that are rate-independent (the computation must be correct independent of the reaction rate law) and composable (\(f \circ g\) can be computed by concatenating the CRNs computing f and g). Rate independence and composability are important engineering desiderata, permitting implementations that violate mass-action kinetics, or even “well-mixedness”, and allowing the systematic construction of complex computation via modular design. We show that to construct composable rate-independent CRNs, it is necessary and sufficient to ensure that the output species of a module is not a reactant in any reaction within the module. We then exactly characterize the functions computable by such CRNs as superadditive, positive-continuous, and piecewise rational linear. Our results show that composability severely limits rate-independent computation unless more sophisticated input/output encodings are used.