Turning waves and breakdown for incompressible flows

We consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (\al,f_0(\al)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time $t^*$ where the solution of the free boundary problem parameterized as (\al,f(\al,t)) blows-up: \|\da f\|_{L^\infty}(t^*)=\infty. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down.Comment: 15 page

Environmental enrichment results in both brain connectivity efficiency and selective improvement in different behavioral tasks

Exposure to environmental enrichment (EE) has been a useful model for studying the effects of experience on brain plasticity, but to date, few is known about the impact of this condition on the brain functional networks that probably underlies the multiple behavioral improvements. Hence, we assessed the effect of an EE protocol in adult Wistar rats on the performance in several behavioral tasks testing different domains (Open field (OP): locomotor activity; Elevated-zero maze (EZM): anxiety-related behaviors; 5-choice serial reaction time task (5-CSRTT): attentional processes; 4-arm radial water maze (4-RAWM): spatial memory) in order to check its effectiveness in a wide range of functions. After this, we analyzed the functional brain connectivity underlying each experimental condition through cytochrome C oxidase (COx) histochemistry. Our EE protocol reduced both locomotor activity in the OP and anxiety-related behaviors in the EZM. On the other hand, enriched rats showed more accuracy in the 4-RAWM, whereas 5-CSRTT performance was not significantly ameliorated by EE condition. In relation to COx functional connectivity, we found that EE reduced the number of strong positive correlations both in basal and training conditions, suggesting a modulating effect on specific brain connections. Our results suggest that EE seems to have a selective effect on specific brain regions, such as prefrontal cortex and hippocampus, leading to a more efficient brain connectivity.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. PPIT.UMA.B1.2017/3