On the Long Time Behavior of the Quantum Fokker-Planck equation

We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispersion estimates in the cases were no equilibrium state exists

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

We consider a one dimensional transport model with nonlocal velocity given by the Hilbert transform and develop a global well-posedness theory of probability measure solutions. Both the viscous and non-viscous cases are analyzed. Both in original and in self-similar variables, we express the corresponding equations as gradient flows with respect to a free energy functional including a singular logarithmic interaction potential. Existence, uniqueness, self-similar asymptotic behavior and inviscid limit of solutions are obtained in the space $\mathcal{P}_{2}(\mathbb{R})$ of probability measures with finite second moments, without any smallness condition. Our results are based on the abstract gradient flow theory developed in \cite{Ambrosio}. An important byproduct of our results is that there is a unique, up to invariance and translations, global in time self-similar solution with initial data in $\mathcal{P}_{2}(\mathbb{R})$, which was already obtained in \textrm{\cite{Deslippe,Biler-Karch}} by different methods. Moreover, this self-similar solution attracts all the dynamics in self-similar variables. The crucial monotonicity property of the transport between measures in one dimension allows to show that the singular logarithmic potential energy is displacement convex. We also extend the results to gradient flow equations with negative power-law locally integrable interaction potentials

Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure

We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and V\'azquez, where the pressure is obtained as a Riesz potential associated to the density. We take advantage of the displacement convexity of the Riesz potential in one dimension to show a functional inequality involving the entropy, entropy dissipation, and the Euclidean transport distance. An argument by approximation shows that this functional inequality is enough to deduce the exponential convergence of solutions in self-similar variables to the unique steady states

Observations on the Overwintering Potential of the Striped Cucumber Beetle (Coleoptera: Chrysomelidae) in Southern Minnesota

The striped cucumber beetle, Acalymma vittatum (Fabricius) (Coleoptera: Chrysomelidae), is an important pest of cucurbit crops. However, the overwinter- ing capacity of this pest in temperate regions is poorly understood. In this study, the in-field survival of A. vittatum was examined during three consecutive winters. In addition, the supercooling points of A. vittatum were determined as an index of cold hardiness for adults. During each winter, the survival of adults decreased significantly through time, with no individuals surviving until spring. By comparing the supercooling points and in-field survival of adults to soil temperatures, it appears that winter temperatures in Minnesota are cold enough to induce freezing of the beetles. Moreover, a considerable amount of mortality occurred before minimum monthly soil temperatures dropped below the supercooling point of overwintering individuals, suggesting the occurrence of prefreeze mortality. An improved understanding of the response of A. vittatum to winter temperatures in temperate regions may aid in early season management of this pest

Sweetened beverages, snacks and overweight: findings from the Young Lives cohort study in Peru

OBJECTIVE: To determine the association between consumption of snacks and sweetened beverages and risk of overweight among children. DESIGN: Secondary analysis of the Young Lives cohort study in Peru. SETTING: Twenty sentinel sites from a total of 1818 districts available in Peru. SUBJECTS: Children in the younger cohort of the Young Lives study in Peru, specifically those included in the third (2009) and the fourth (2013) rounds. RESULTS: A total of 1813 children were evaluated at baseline; 49·2 % girls and mean age 8·0 (sd 0·3) years. At baseline, 3·3 (95 % CI 2·5, 4·2) % reported daily sweetened beverage consumption, while this proportion was 3·9 (95 % CI 3·1, 4·9) % for snacks. Baseline prevalence of overweight was 22·0 (95 % CI 20·1, 23·9) %. Only 1414 children were followed for 4·0 (sd 0·1) years, with an overweight incidence of 3·6 (95 % CI 3·1, 4·1) per 100 person-years. In multivariable analysis, children who consumed sweetened beverages and snacks daily had an average weight increase of 2·29 (95 % CI 0·62, 3·96) and 2·04 (95 % CI 0·48, 3·60) kg more, respectively, than those who never consumed these products, in approximately 4 years of follow-up. Moreover, there was evidence of an association between daily consumption of sweetened beverages and risk of overweight (relative risk=2·12; 95 % CI 1·05, 4·28). CONCLUSIONS: Daily consumption of sweetened beverages and snacks was associated with increased weight gain v. never consuming these products; and in the case of sweetened beverages, with higher risk of developing overweight

Structure preserving schemes for mean-field equations of collective behavior

In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang-Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic Problem