A Numerical Study of the Flow Around a Model Winged Seed in Auto-Rotation

In this study the flow around a winged-seed in auto-rotation is characterized using direct numerical simulations (DNS) at Reynolds number in the range 80–240, based on the descent speed and a characteristic chord length. In this range, the flow is approximately steady when observed from a reference frame fixed to the seed. For all cases, the flow structure consists of a wing tip vortex which describes a helical path, a vortex shed behind the nut of the seed and a stable leading edge vortex above the wing surface which merges with the tip vortex. With increasing Reynolds number, the leading edge vortex becomes more intense and gets closer to the wing surface. The simulation results also show the formation of a spanwise flow on the upper surface of the wing, moving fluid towards the wing tip in a region downstream and beneath the leading edge vortex. This spanwise flow is rather weak inside the core of the leading edge vortex, and the analysis of the streamlines show a very weak transport of vorticity along the vortex for the cases under consideration. The analysis of the flow suggests that the stabilization of the leading edge vortex is mainly due to non-inertial accelerations, although viscous effects may contribute, specially at lower Re. Furthermore, the leading edge vortex has been characterized by analysing the flow variables averaged along cross-sections of the vortex. While some quantities, like the spanwise velocity or the pressure inside the vortex, are rather insensitive to the threshold used to define the leading edge vortex, the same is not true for the circulation of the vortex or its averaged spanwise vorticity, due to the viscous nature of the vortex. Finally, it is observed that the spanwise vorticity scales with the angular rotation of the seed for the different Re.     

Eco-friendly synthesis,in vitro anti-proliferative evaluation,and 3D-QSAR analysis of a novel series of monocationic 2-aryl/heteroaryl-substituted 6-(2-imidazolinyl)benzothiazole mesylates

Abstract

Herein, we describe the synthesis of twenty-one novel water-soluble monocationic 2-aryl/heteroaryl-substituted 6-(2-imidazolinyl)benzothiazole mesylates 3a–3u and present the results of their anti-proliferative assays. Efficient syntheses were achieved by three complementary simple two-step synthetic protocols based on the condensation reaction of aryl/heteroaryl carbaldehydes or carboxylic acid. We developed an eco-friendly synthetic protocol using glycerol as green solvent, particularly appropriate for the condensation of thermally and acid-sensitive heterocycles such as furan, benzofuran, pyrrole, and indole. Screening of anti-proliferative activity was performed on four human tumour cell lines in vitro including pancreatic cancer (CFPAC-1), metastatic colon cancer (SW620), hepatocellular carcinoma (HepG2), and cervical cancer (HeLa), as well as in normal human fibroblast cell lines. All tested compounds showed strong to moderate anti-proliferative activity on tested cell lines depending on the structure containing aryl/heteroaryl moiety coupled to 6-(2-imidazolinyl)benzothiazole moiety. The most potent cytostatic effects on all tested cell lines with \(\hbox {IC}_{50}\) values ranging from 0.1 to 3.70 \(\upmu \hbox {M}\) were observed for benzothiazoles substituted with naphthalene-2-yl 3c, benzofuran-2-yl 3e, indole-3-yl 3j, indole-2-yl 3k, quinoline-2-yl 3s, and quinoline-3-yl 3t and derivatives substituted with phenyl 3a, naphthalene-1-yl 3b, benzothiazole-2-yl 3g, benzothiazole-6-yl 3h, N-methylindole-3-yl 3l, benzimidazole-2-yl 3n, benzimidazole-5(6)-yl 3o, and quinolone-4-yl 3u with \(\hbox {IC}_{50}\) values ranging from 1.1 to 29.1 \(\upmu \hbox {M}\). Based on obtained anti-proliferative activities, 3D-QSAR models for five cell lines were derived. Molecular volume, molecular surface, the sum of hydrophobic surface areas, molecular mass, and possibility of making dispersion forces were identified by QSAR analyses as molecular properties that are positively correlated with anti-proliferative activity, while compound’s capability to accept H-bond was identified as a negatively correlated property. Comparison of molecular properties identified for different cell lines enabled assumptions about similarity of mode of action through which anti-proliferative activities against different cell lines are accomplished. Novel compounds that are predicted to have enhanced activities in comparison with herein presented ones were designed using 3D-QSAR analysis as guideline.

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A comprehensive study of classification methods for medical diagnosis

In this model study, we developed a method to distinguish between breast cancer cells and normal epithelial cells, which is in principal suitable for online diagnosis by Raman spectroscopy. Two cell lines were chosen as model systems for cancer and normal tissue. Both cell lines consist of epithelial cells, but the cells of the MCF‐7 series are carcinogenic, where the MCF‐10A cells are normal growing. An algorithm is presented for distinguishing cells of the MCF‐7 and MCF‐10A cell lines, which has an accuracy rate of above 99%. For this purpose, two classification steps are utilized. The first step, the so‐called top‐level classifier searches for Raman spectra, which are measured in the nuclei region. In the second step, a wide range of discriminant models are possible and these models are compared. The classification rates are always estimated using a cross‐validation and a holdout‐validation procedure to ensure the ability of the routine diagnosis to work in clinical environments. Copyright © 2009 John Wiley & Sons, Ltd.     

Improved functional mapping of the human amygdala using a standard functional magnetic resonance imaging sequence with simple modifications

As the amygdala is involved in various aspects of emotional processing, its characterization using neuroimaging modalities, such as functional magnetic resonance imaging (fMRI), is of great interest. However, in fMRI, the amygdala region suffers from susceptibility artifacts that are composed of signal dropouts and image distortions. Various technically demanding approaches to reduce these artifacts have been proposed, and most require alterations beyond a mere change of the acquisition parameters and cannot be easily implemented by the user without changing the MR sequence code. In the present study, we therefore evaluated the impact of simple alterations of the acquisition parameters of a standard gradient-echo echo-planar imaging technique at 3 T composed of echo times (TEs) of 27 and 36 ms as well as section thicknesses of 2 and 4 mm while retaining a section orientation parallel to the intercommissural plane and an in-plane resolution of 2x2 mm(2). In contrast to previous studies, we based our evaluation on the resulting activation maps using an emotional stimulation paradigm rather than on MR raw image quality only. Furthermore, we tested the effects of spatial smoothing of the functional raw data in the course of postprocessing using spatial filters of 4 and 8 mm. Regarding MR raw image quality, a TE of 27 ms and 2-mm sections resulted in the least susceptibility artifacts in the anteromedial aspect of the temporal lobe. The emotional stimulation paradigm resulted in robust bilateral amygdala activation for the approaches with 2-mm sections only -- but with larger activation volumes for a TE of 36 ms as compared with that of 27 ms. Moderate smoothing with a 4-mm spatial filter represented a good compromise between increased sensitivity and preserved specificity. In summary, we showed that rather than applying advanced modifications of the MR sequence, a simple increase in spatial resolution (i.e., the reduction of section thickness) is sufficient to improve the detectability of amygdala activation.     

Entanglement in the Quantum Ising Model

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong, the entanglement grows at most logarithmically in the number of spins. The proof utilises a transformation to a model of classical probability called the continuum random-cluster model, and is based on a property of the latter model termed ratio weak-mixing. In an intermediate result, we establish an exponentially decaying bound on the operator norm of differences of the reduced density operator. Of special interest is the mathematical rigour of this work, and the fact that the proof applies equally to a large class of disordered interactions.     

Unitarily invariant convex functions on the state space of type I and type III von Neumann algebras

Properties of unitarily invariant convex functions, defined on subsets of positive linear forms of type I and type III IV¹-algebras have been investigated. We especially characterize those pairs of positive linear forms f, g for which Ψ(f) ? Ψ(g) holds for every unitarily invariant convex function Ψ and in which case we call f “more chaotic” than g.     

Quantum entropy and special relativity

We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.     

The general ising model

Harmonic analysis and the generalized GKS inequalities are applied to examine features of the general Ising model.