Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterising the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares-of-polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterising the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach

Managing a Common Renewable Resource in Asymmetric Information

The clear definition of property rights is not a sufficient condition to prevent congestion effects in commons. In this paper we present how interesting can be the coordination among owners in the preservation of the common good. Our approach takes into account economic dynamics and incentive mechanisms in a hidden information context. We consider a natural resource which is being used up for a continuum of producers on a common property regime. We also consider that each producer has an individual performance index which is a hidden information of the rest of players. We introduce coordination in the sense of a global maximization of the joint profit. If there is no coordination among the producers, their behavior leads to complete rent dissipation. We focus our model in the case of the producers convinced to coordinate their actions in order to preserve their own economic sustainability. Under perfect information we find that the exclusion of at subset of producers can appear and how it is endogenously determined. Under asymmetric information we propose a quantity-transfer contract which lead us to the previous stationary disposal stock of the resource without exclusion.Commons, Natural Resources, Dynamics, Asymmetric Information, Contracts, Environmental Economics and Policy,

Embryonic Exposure to the Synthetic-Progesterone Levonorgestrel (LNG) Results in Hyperactive Behavior in Zebrafish (\u3ci\u3eDanio rerio\u3c/i\u3e)

Exposure to endocrine-disrupting chemicals has been associated with an increased risk of anxiety-like behavior at various life stages. Levonorgestrel (LNG), a synthetic contraceptive, could potentially alter steroidal regulated brain development based on the findings of this thesis. In-silico measurements were used for comparing LNG, which had been found in surface water, to chemical databases to predict the bioavailability, half-life, and estrogen binding potential. Zebrafish (Danio rerio) for illuminating the effects of LNG exposure during early zebrafish embryonic development, similar to fetal development, on behavior was investigated. Our data suggests exposure in a dose-dependent manner of LNG can potentially alter steroid-mediated early development as indicated by displaying an anxiety-like behavioral phenotype in both the locomotive and thigmotaxis behavioral assays at 5 days post-fertilization. Furthermore, embryonic zebrafish displayed an increase in heart rate phenotype at 2 dpf. Altogether, this thesis uncovered LNG sensitive period of development in embryonic zebrafish

Benefits of Counseling Services for Elementary School Students

The aim of this capstone study was to identify how elementary school counseling services benefits students, academically and emotionally. The interest in this study was a yearning to gain deeper insight into elementary school counseling and how their services impacts students. Through research and field study it has proven that elementary school counseling has been beneficial for young students. Understanding the role of the elementary school counselor is vital to comprehend the services school counselors provide. The collaboration counselors have with teachers, administration, parents and most importantly, the students, reflect how beneficial the counseling sessions are and the conflicts that may arise