Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1

In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.     

Global stability analysis of parametrically excited cylindrical shells through the evolution of basin boundaries

In the present study, the large-amplitude vibrations and stability of a perfect circular cylindrical shell subjected to axial harmonic excitation in the neighborhood of the lowest natural frequencies are investigated. Donnell's shallow shell theory is used and the shell spatial discretization is obtained by the Ritz method. An efficient low-dimensional model presented in previous publications is used to discretize the continuous system. The main purpose of this work is to discuss the use of basins of attraction as a measure of the reliability and safety of the structure. First, the nonlinear behavior of the conservative system is discussed and the basin structure and volume is understood from the topologic structure of the total energy and its evolution as a function of the system parameters. Then, the behavior of the forced oscillations of the harmonically excited shell is analyzed. First the stability boundaries in force control space are obtained and the bifurcation events connected with these boundaries are identified. Based on the bifurcation diagrams, the probability of parametric instability and escape are analyzed through the evolution and erosion of basin boundaries within a prescribed control volume defined by the manifolds. Usually, basin boundaries become fractal. This together with the presence of catastrophic subcritical bifurcations makes the shell very sensitive to initial conditions, uncertainties in system parameters, and initial imperfections. Results show that the analysis of the evolution of safe basins and the derivation of appropriate measures of their robustness is an essential step in the derivation of safe design procedures for multiwell systems.     

Near wall characterization of the flow over a two-dimensional steep smooth hill

Near-wall data for the strongly perturbed flow in a neutrally stable boundary layer encountering a steep, smooth, two-dimensional hill are presented. Observations were made on the centerplane of a water channel at thirteen stations relative to the hill by laser Doppler anemometry. The large reverse flow region that is formed on the lee of the hill was particularly scrutinized through seven measuring stations. Results are presented for the mean and turbulent properties of the flow. Wall shear stress was evaluated through fitting procedures that resorted to the near wall behavior of the velocity profile. Logarithmic fits as well as predictions through the Reynolds stress profiles are also presented.     

Non-linear flexural-flexural-torsional-extensional dynamics of beams—I. Formulation

The non-linear differential equations of motion, and boundary conditions, for Euler-Bernoulli beams able to experience flexure along two principal directions (and, thus, flexure in any direction in space), torsion and extension are formulated. The beam's material is assumed to be Hookean but its properties may vary along its span. The nonlinearities present in the differential equations include contributions from the curvature expression and from inertia terms. A set of differential equations with polynomial nonlinearities to cubic order, suitable for a perturbation analysis of the motion, is also developed and the validity of the inextensional approximation is assessed. The equations developed here reduce to those for an inextensional beam. In Part II of this paper, a specific example of application is analyzed and the results obtained are compared with those available in the literature where several non-linear terms have been neglected a priori.     

Harmonic non-linear response of beck's column to a lateral excitation

The non-linear response of a column with a follower force (Beck's column) subjected to a distributed periodic lateral excitation, or to a support excitation, is determined. An analytical solution for the response amplitude in terms of the loading and system parameters is obtained by a perturbation analysis of the differential equations of motion. Non-linear inertia and non-linear curvature terms are taken into account in the formulation of the differential equations.     

New Acetogenins from the Seeds of Annona coriacea

From the hexane and MeOH extracts of Annona coriacea Mart . (Annonaceae) seeds, two novel acetogenins, coriapentocins A and B ( 1 and 2 , resp.) were isolated. The known acetogenin bullacin ( 3 ) was also isolated from the hexane extract. The structures of compounds 1 – 3 were elucidated by NMR and MS analysis, and relative configurations were established by comparison with literature data.     

Functionalization of 2-(S)-isopropyl-5-iodo-pyrimidin-4-ones through Cu(I)-mediated 1,3-dipolar azide-alkyne cycloadditions

A series of 2-(S)-isopropyl-pyrimidinones functionalized at C5 with triazole rings, in which the substituents are found at N-1′ of the triazole ring, were synthesized. Through the azide-acetylene cycloaddition reaction, using CuI as a copper source and ultrasonic waves as an energy source it was possible to obtain products with yields ranging from 79% to 89% within 5 min or less. A preliminary study to gain further insight into the reaction was performed using in situ ReactIR technology.     

Automated two-dimensional separation flow system with electrochemical preconcentration, stripping, capillary electrophoresis and contactless conductivity detection for trace metal ion analysis

This paper describes the automation of a fully electrochemical system for preconcentration, cleanup, separation and detection, comprising the hyphenation of a thin layer electrochemical flow cell with CE coupled with contactless conductivity detection (CE-C?D). Traces of heavy metal ions were extracted from the pulsed-flowing sample and accumulated on a glassy carbon working electrode by electroreduction for some minutes. Anodic stripping of the accumulated metals was synchronized with hydrodynamic injection into the capillary. The effect of the angle of the slant polished tip of the CE capillary and its orientation against the working electrode in the electrochemical preconcentration (EPC) flow cell and of the accumulation time were studied, aiming at maximum CE-C?D signal enhancement. After 6 min of EPC, enhancement factors close to 50 times were obtained for thallium, lead, cadmium and copper ions, and about 16 for zinc ions. Limits of detection below 25 nmol/L were estimated for all target analytes but zinc. A second separation dimension was added to the CE separation capabilities by staircase scanning of the potentiostatic deposition and/or stripping potentials of metal ions, as implemented with the EPC-CE-C?D flow system. A matrix exchange between the deposition and stripping steps, highly valuable for sample cleanup, can be straightforwardly programmed with the multi-pumping flow management system. The automated simultaneous determination of the traces of five accumulable heavy metals together with four non-accumulated alkaline and alkaline earth metals in a single run was demonstrated, to highlight the potentiality of the system.     

VLE of CO2 + glycerol + (ethanol or 1-propanol or 1-butanol)

Vapour-liquid equilibrium of CO₂ + [0.00871 glycerol + 0.99129 (ethanol or 1-propanol or 1-butanol)] mixtures was measured at the temperatures of 313.15 K and 333.15 K, and close to the critical line, at pressures up to 12 MPa. On the liquid side, the bubble points measured for these ternary mixtures follow closely the behaviour of VLE reported by several authors for the corresponding binary mixtures without glycerol. On the vapour side, however, dew points for the ternary mixtures deviate significantly from VLE results for the binaries. A correlation of the results obtained for the CO₂ + glycerol + ethanol mixture with the Peng-Robinson equation of state, admitting quasi-binary behaviour, equally yields good agreement on the liquid side, and significant deviations on the vapour side.