Studying Dynamical Principles of Human Locomotion using Inverse Optimal Control

Human movement, as for example human gait, can be considered as an optimal realization of some given task. However, the criterion for which the naturally performed human motion is optimal, is generally not known. In this article we formulate an inverse optimal control problem to study the relevance of four different optimization criteria in human locomotion. As a walking model we use an actuated three dimensional spring loaded inverted pendulum (3D-SLIP), which is able to mirror the typical shape of the center of mass trajectory in human gait. Using a direct all-at-once approach, the weighting of the optimization criteria and the position of the footsteps are optimized in such a way, that the center of mass trajectory of the resulting optimal state fits real motion capture data as good as possible. Numerical experiments show, that whereas the so called capture point seems to have a great impact on human walking, minimization of the vertical center of mass movement does not show any relevance at all. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

M?ssbauer analysis of high-energy mechanical-milled sand fraction of a magnetic soil developing on basalt

A sample of the coarse sand fraction from the soil material of the A-horizon (0?C0.2 m from the soil surface) of a dusky red magnetic Oxisol was submitted to high-energy mechanical milling for different times. This assay aimed mainly at (a) monitoring the individualization of strongly aggregated mineral particles, and (b) measuring the effect of the milling pressure on the mineralogy changes of the material. These data are also intended to experimentally subside any physical model describing the mechanical behavior of the superficial soil layer that is subjected to intensive machine management, in agriculture fields. Powder X-ray data reveal that some mineralogical phases, notably gibbsite, disappear soon after the first few hours milling. The 298 K-transmission Mössbauer spectrum for the non-milled sand sample shows a qualitatively typical pattern for the sand fraction of basalt derived soils, with magnetically ordered sextets, assignable mainly to hematite and maghemite, and an intense central (super)paramagnetic Fe^3?+? doublet. For the milled samples, spectra revealed progressive spectral reduction of the magnetic hyperfine structure, with concomitant increase of relative subspectral areas due to (super)paramagnetic phases, as the milling time increased. This result is consistent with the reduction of measured saturation magnetization, from 4.96(8) J T^???1 kg^???1, for the non-milled sample, to 3.26(7) J T^???1 kg^???1, for the sample milled for 8 hours.     

Stability of Gasless Combustion Fronts in One-Dimensional Solids

For gasless combustion in a one-dimensional solid, we show a type of nonlinear stability of the physical combustion front: if a perturbation of the front is small in both a spatially uniform norm and an exponentially weighted norm, then the perturbation stays small in the spatially uniform norm and decays in the exponentially weighted norm, provided the linearized operator has no eigenvalues in the right half-plane other than zero. Using the Evans function, we show that the zero eigenvalue must be simple. Factors that complicate the analysis are: (1) the linearized operator is not sectorial, and (2) the linearized operator has good spectral properties only when the weighted norm is used, but then the nonlinear term is not Lipschitz. The result is nevertheless physically natural. To prove it, we first show that when the weighted norm is used, the semigroup generated by the linearized operator decays on a subspace complementary to the operator’s kernel, by showing that it is a compact perturbation of the semigroup generated by a more easily analyzed triangular operator. We then use this result to help establish that solutions stay small in the spatially uniform norm, which in turn helps establish nonlinear convergence in the weighted norm.     

Stepwise Halide‐Triggered Double and Triple Catenation of Self‐Assembled Coordination Cages

A simple self‐assembled [Pd₂ L ₄] coordination cage consisting of four carbazole‐based ligands was found to dimerize into the interpenetrated double cage [3 X@Pd₄ L ₈] upon the addition of 1.5 equivalents of halide anions (X=Cl^?, Br^?). The halide anions serve as templates, as they are sandwiched by four Pd^II cations and occupy the three pockets of the entangled cage structure. The subsequent addition of larger amounts of the same halide triggers another structural conversion, now yielding a triply catenated link structure in which each Pd^II node is trans‐coordinated by two pyridine donors and two halide ligands. This simple system demonstrates how molecular complexity can increase upon a gradual change of the relative concentrations of reaction partners that are able to serve different structural roles.     

Ultrasound‐assisted extraction method for the simultaneous determination of emerging contaminants in freshwater sediments

Sediments are the fate of several emerging organic contaminants, such as pharmaceuticals, personal care products and hormones, and therefore an important subject in environmental monitoring studies. In the present work, a simple and sensitive method was developed, validated and applied for the simultaneous extraction of atenolol, caffeine, carbamazepine, diclofenac, ibuprofen, naproxen, propranolol, triclosan, estrone, 17‐β‐estradiol and 17‐α‐ethinylestradiol using ultrasound‐assisted extraction from freshwater sediment samples followed by solid‐phase extraction clean‐up and liquid chromatography with tandem mass spectrometry detection. The solvent type and extraction pH were evaluated to obtain the highest recoveries of the compounds. The best method shows absolute recoveries between 54.0 and 94.4% at 50 ng/g concentration. The method exhibits good precision with relative standard deviation ranging from 1.0–16%. The detection and quantification limits ranged from 0.006–0.067 and 0.016–0.336 ng/g, respectively. The developed method was successfully applied to freshwater sediment samples collected from different sites in Jundiaí River basin of São Paulo State, Brazil. The compounds atenolol, caffeine, propranolol and triclosan were detected in all the sampling sites with concentrations of 13.8, 41.0, 28.5 and 176 ng/g, respectively.     

Instabilities of longitudinal convection rolls in couette flow

Summary An investigation has been made of the instabilities of longitudinal convection rolls in a Couette flow which is heated from below. The instabilities occur either as stationary waves or as waves which propagate along the convection rolls. Neutral stability curves are presented as a function of Rayleigh and Reynolds numbers for a Prandtl number of 0.7. The disturbance energy budget is given for selected values of the Rayleigh and Reynolds numbers.

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Zusammenfassung Die Instabilitäten von longitudinalen Konvektionsrollen in einer ebenen Couette-Strömung, die von unten erhitzt wird, sind untersucht worden. Die Instabilitäten nehmen entweder die Form von stehenden Wellen an oder von Wellen, die sich entlang der Konvektionsrollen fortpflanzen. Die Kurven für marginale Stabilität sind als Funktion der Rayleigh-und Reynoldszahl dargestellt worden im Fall der Prandtlzahl 0.7. Das Energiebudget der Störungen wird für ausgewählte Werte der Rayleigh-und Reynoldszahl angegeben.

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Dedicated to Professor Nikolaus Rott on the occasion of his 60th birthday.     

Heat transfer and stability properties of convection rolls in an internally heated fluid layer

Summary A study has been made of stationary two-dimensional convection in an internally heated, infinite Prandtl number, horizontal fluid layer bounded above and below by rigid plates of unequal temperature. Sufficient conditions for instability of the quiescent state, as well as post-instability, two-dimensional finite amplitude convective solutions, and heat transfer are obtained as a function of the two Rayleigh number parameters and the wavenumber. Investigation of the stability of the finite amplitude convective motion reveals a region in the dual Rayleigh number domain wherein stationary, two-dimensional convection represents a stable solution of the equations of motion.

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Zusammenfassung Eine Studie der stationären zweidimensionalen Konvektion in einer homogen erhitzten horizontalen Flüssigkeitsschicht wird gemacht im Fall einer unendlichen Prandtl-Zahl, wenn oben und unten feste Platten mit verschiedenen Temperaturen als Randbedingungen vorgegeben sind. Hinreichende Bedingungen für die Instabilität der statischen Schichtung und Lösungen für die voll entwickelte Instabilität in Form zweidimensionaler Konvektion endlicher Amplitude werden in Abhängigkeit von den zwei Rayleighzahl-Parametern und der Wellenzahl berechnet. Die Untersuchung der Stabilität der Konvektionsströmung endlicher Amplitude ergibt ein Gebiet innerhalb des durch die beiden Rayleighzahlen aufgespannten Raumes, im dem zweidimensionale stationäre Konvektion eine physikalisch realisierbare, stabile Lösung der Bewegungsgleichungen darstellt.