Measuring the mixing efficiency in a simple model of stirring:some analytical results and a quantitative study via Frequency Map Analysis

We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate numerically the break down of invariant curves as $T$ increases and we give a quantitative estimate of the efficiency of the mixing.Comment: 10 figure

Esclerosi de varices esofàgiques

L'hemorràgia digestiva per varices esofàgiques constitueix una de les complicacions més greus dels pacients amb hipertensió portal, l'etiologia més freqüent dels quals és la cirrosi hepàtica. S'avalua que la mortalitat dels pacients que sagnen per varices esofàgiques és de l'ordre del 20% i que el 50% dels pacients amb antecedents d'hemorràgia per varices sagnaran novament en el curs de l'any següent al darrer episodi..

Development of local strontium ranelate delivery systems and long term in vitro drug release studies in osteogenic medium

Funding Information: The authors acknowledge financial support from the Latvian Academy of Sciences though the ERANet under the frame of EuroNanoMed-II (Nanoforosteo, Project number: Z/14/1187) and the Riga Technical University and Riga Stardiņš University Cooperation Research Project No. RTU/RSU-18. Publisher Copyright: © 2018, The Author(s).It has been recognized that the operative stabilization of osteoporotic fractures should be followed up with an appropriate osteoporosis treatment in order to decrease the risk of repeated fractures. Despite the good clinical results of strontium ranelate (SrRan) towards the osteoporosis treatment, high drug doses and long treatment period cause an increased risk of serious side effects. Novel local SrRan/poly(lactic acid) (SrRan/PLA) delivery systems containing from 3.57 ± 0.28 wt% to 24.39 ± 0.91 wt% of active substance were developed. In order to resemble the naturally occurring processes, osteogenic media (OM) was used as a release medium for long term (121 days) in vitro drug release studies and UV/VIS method for the determination of SrRan content in OM was developed and validated. Biomimetic calcium phosphate precipitates were found on the surface and in the pores of prepared delivery system after microcapsule exposure to OM for 121 days as well as SrRan particles, indicating that the release of the drug have not been completed within 121 days. In vitro cell viability evaluation approved no cytotoxic effects of microcapsule suspensions and extracts.publishersversionPeer reviewe

Flow map parameterization methods for invariant tori in Hamiltonian systems

The goal of this paper is to present a methodology for the computation of invariant tori in Hamiltonian systems combining flow map methods, parameterization methods, and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one (avoiding Poincaré maps), parameterization methods reduce the cost of a single step of the derived Newton-like method to be proportional to the cost of a FFT. Symplectic properties lead to some magic cancellations that make the methods work. The multiple shooting version of the methods are applied to the computation of invariant tori and their invariant bundles around librational equilibrium points of the Restricted Three Body Problem. The invariant bundles are the first order approximations of the corresponding invariant manifolds, commonly known as the whiskers, which are very important in the dynamical organization and have important applications in space mission design.A.H. is supported by the grants PGC2018-100699-B-I00 (MCIU-AEI-FEDER, UE), 2017 SGR 1374 (AGAUR), MSCA 734557 (EU Horizon 2020), and MDM-2014-0445 (MINECO), and by the NSF under Grant No. 1440140 to found his residence at MSRI in Berkeley, California, during the Fall 2018 semester. J.M. Mondelo has been supported by the MINECO-AEI grant MTM2014-52209-C2-1-P and the MICINN-AEI grants MTM2016-80117-P, MTM2017-86795-C3-1-P, PID2019-104851GB-I00.Peer reviewe

Solar system models with a selected set of frequencies

The purpose of this paper is to develop a methodology to generate simplified models suitable for the analysis of the motion of a small particle, such as a spacecraft or an asteroid, in the Solar System. The procedure is based on applying refined Fourier analysis methods to the time–dependent functions that appear in the differential equations of the problem. The equations of the models obtained are quasi–periodic perturbations of the Restricted Three Body Problem that depend explicitly on natural frequencies of the Solar System. Some examples of these new models are given and compared with other ones found in the literature. For one of these new models, close to the Earth–Moon system, we have computed the dynamical substitutes of the collinear libration points.
The methodology developed in this paper can also be used for the analytical construction of simplified models of systems governed by differential equations which have a quasi–periodic (in time) external excitation and such that the form of the equations is rather cumbersome