Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization.

We investigate the transport of a solute past isolated sinks in a bounded domain when advection is dominant over diffusion, evaluating the effectiveness of homogenization approximations when sinks are distributed uniformly randomly in space. Corrections to such approximations can be non-local, non-smooth and non-Gaussian, depending on the physical parameters (a Péclet number Pe, assumed large, and a Damköhler number Da) and the compactness of the sinks. In one spatial dimension, solute distributions develop a staircase structure for large Pe , with corrections being better described with credible intervals than with traditional moments. In two and three dimensions, solute distributions are near-singular at each sink (and regularized by sink size), but their moments can be smooth as a result of ensemble averaging over variable sink locations. We approximate corrections to a homogenization approximation using a moment-expansion method, replacing the Green's function by its free-space form, and test predictions against simulation. We show how, in two or three dimensions, the leading-order impact of disorder can be captured in a homogenization approximation for the ensemble mean concentration through a modification to Da that grows with diminishing sink size.

Impaired cardiac energy metabolism in embryos lacking adrenergic stimulation.

As development proceeds from the embryonic to fetal stages, cardiac energy demands increase substantially, and oxidative phosphorylation of ADP to ATP in mitochondria becomes vital. Relatively little, however, is known about the signaling mechanisms regulating the transition from anaerobic to aerobic metabolism that occurs during the embryonic period. The main objective of this study was to test the hypothesis that adrenergic hormones provide critical stimulation of energy metabolism during embryonic/fetal development. We examined ATP and ADP concentrations in mouse embryos lacking adrenergic hormones due to targeted disruption of the essential dopamine ß-hydroxylase (Dbh) gene. Embryonic ATP concentrations decreased dramatically, whereas ADP concentrations rose such that the ATP/ADP ratio in the adrenergic-deficient group was nearly 50-fold less than that found in littermate controls by embryonic day 11.5. We also found that cardiac extracellular acidification and oxygen consumption rates were significantly decreased, and mitochondria were significantly larger and more branched in adrenergic-deficient hearts. Notably, however, the mitochondria were intact with well-formed cristae, and there was no significant difference observed in mitochondrial membrane potential. Maternal administration of the adrenergic receptor agonists isoproterenol or l-phenylephrine significantly ameliorated the decreases in ATP observed in Dbh-/- embryos, suggesting that α- and ß-adrenergic receptors were effective modulators of ATP concentrations in mouse embryos in vivo. These data demonstrate that adrenergic hormones stimulate cardiac energy metabolism during a critical period of embryonic development.