An improved known vicinity algorithm based on geometry test for particle localization in arbitrary grid

The known vicinity algorithm based on the geometry test for the particle localization problem in the hybrid Eulerian–Lagrangian model was extended and enhanced aiming at the connected grids with convex polygon/polyhedral cells. Such extensions were achieved by proposing novel improvements. Specifically, a new “side function”, to determine the relative position of the particle and the cell, was introduced to build a more formal test process. In addition, a binary search method was developed to accelerate the particle in cell test and trajectory/face intersection test for grids consisting of arbitrary polygon/polyhedral cells. Further, the particle location problem without the known vicinity position was established and solved by special boundary treatment through considering the internal/external boundary and larger particle displacement in one single Lagrangian step. The improved algorithm was applied to the particle location problem with both two dimensional and three dimensional Eulerian grids. Additionally, the proposed algorithm was compared with the previous ones to exhibit its higher efficiency and broader application. Sample cases focusing the water impingement computation for aircraft icing were solved by adopting this algorithm assisted by the Lagrangian particle dynamics model, and the computational results were verified by the experiments.     

A flow-injection mass spectrometry fingerprinting method for authentication and quality assessment of <Emphasis Type="Italic">Scutellaria lateriflora</Emphasis>-based dietary supplements

Scutellaria lateriflora, commonly known as skullcap, is used as an ingredient in numerous herbal products. However, it has been occasionally adulterated/contaminated with Teucrium canadense and/or Teucrium chamaedrys, commonly known as germander, due to the morphological similarities between the two genera. The latter contains hepatotoxic diterpenes. Despite the potential hepatotoxicity introduced by germander contamination, analytical methodologies for the authentication and quality assessment of S. lateriflora-based dietary supplements have not been reported. In this study, a flow-injection/mass spectrometry fingerprinting method in combination with principal component analysis was used to survey S. lateriflora-based dietary supplements sold in the USA.     

Differentiation of <Emphasis Type="BoldItalic">Panax quinquefolius</Emphasis> grown in the USA and China using LC/MS-based chromatographic fingerprinting and chemometric approaches

American ginseng (Panax quinquefolius) is one of the most commonly used herbal medicines in the world. Discriminating between P. quinquefolius grown in different countries is difficult using traditional quantitation methods. In this study, a liquid chromatographic mass spectrometry fingerprint combined with chemometric analysis was established to discriminate between American ginseng grown in the USA and China. Fifteen American ginseng samples grown in Wisconsin and 25 samples grown in China were used. The chromatographic fingerprints, representing the chemical compositions of the samples, made it possible to distinguish samples from the two locations. In addition, it was found that some ginsenosides varied widely from P. quinquefolius cultivated in these two countries. P. quinquefolius grown in the USA is higher in ginsenoside R_c, ginsenoside R_d, quinquenoside III/pseudo-ginsenoside RC₁, malonyl ginsenoside R_b1, and ginsenoside R_b2, but lower in ginsenoside R_b1 compared with P. quinquefolius grown in China. These ginsenosides may be responsible for the class separation seen using fingerprinting and chemometric approaches.     

Stability of an abstract system of coupled hyperbolic and parabolic equations

In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations $$\begin{array}{ll}\;\;u_{tt} = -Au + \gamma A^{\alpha} \theta,\\ \quad \theta_t = -\gamma A^{\alpha}u_t - kA^{\beta}\theta,\\ u(0) = u_0, \quad u_t(0) = v_0, \quad \theta(0) = \theta_0\end{array}$$ where A is a self-adjoint, positive definite operator on a Hilbert space H. For ${(\alpha,\beta) \in [0,1] \times [0,1]}$ , the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577–593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.     

An integrable coupled Alice–Bob modified Korteweg de-Vries system: Lax pairs,Bäcklund transformations,residual symmetries and exact solutions

ABSTRACT

A coupled Alice–Bob modified Korteweg de-Vries (mKdV) system is established from the mKdV equation in this paper, which is nonlocal and suitable to model two-place entangled events. The Lax integrability of the coupled Alice–Bob mKdV system is proved by demonstrating three types of Lax pairs. By means of the truncated Painlevé expansion, auto-Bäcklund transformation of the coupled Alice–Bob mKdV system and Bäcklund transformation between the coupled Alice–Bob mKdV system and the Schwarzian mKdV equation are demonstrated. Nonlocal residual symmetries of the coupled Alice–Bob mKdV system are researched. To obtain localized Lie point symmetries of residual symmetries, the coupled Alice–Bob mKdV system is extended to a system consisting six equations. Calculation on the prolonged system shows that it is invariant under the scaling transformations, space-time translations, phase translations and Galilean translations. One-parameter group transformation and one-parameter subgroup invariant solutions are obtained. The consistent Riccati expansion (CRE) solvability of the coupled Alice–Bob mKdV system is proved and some interaction structures between soliton–cnoidal waves are obtained by CRE. Moreover, Jacobi periodic wave solutions, solitary wave solutions and singular solutions are obtained by elliptic function expansion and exponential function expansion.     

Authentication of black cohosh (Actaea racemosa) dietary supplements based on chemometric evaluation of hydroxycinnamic acid esters and hydroxycinnamic acid amides

Analytical and Bioanalytical Chemistry - Ester and amide derivatives of hydroxycinnamic acids are found in black cohosh (Actaea racemosa) and other Actaea plants. These two compound groups were...     

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke (when the wake has not developed) with those of a later stroke (when the wake has developed). The following has been shown. (1) The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke (downstroke or upstroke), depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing ``impinges' on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. (2) The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke's starting vortex, tip vortices and attached leading edge vortex (these vortices form a downwash producing vortex ring). (3) The wake effect decreases the mean lift by 6%–18% (depending on wing kinematics at stroke reversal) and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing. The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science Fund of China(03A51049) The English text was polished by Xing Zhang     

Large aerodynamic forces on a sweeping wing at low Reynolds number

The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically. After an initial start from rest, the wing is made to execute an azimuthal rotation (sweeping) at a large angle of attack and constant angular velocity. The Reynolds number (Re) considered in the present note is 480 (Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root). During the constant-speed sweeping motion, the stall is absent and large and approximately constant lift and drag coefficients can be maintained. The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows. Soon after the initial start, a vortex ring, which consists of the leading-edge vortex (LEV), the starting vortex, and the two wing-tip vortices, is formed in the wake of the wing. During the subsequent motion of the wing, a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength. This prevents the LEV from shedding. As a result, the size of the vortex ring increases approximately linearly with time, resulting in an approximately constant time rate of the first moment of vorticity, or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wingspan. The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force. The project supported by the National Natural Science Foundation of China (10232010)     

Profiling the metabolic difference of seven tanshinones using high-performance liquid chromatography/multi-stage mass spectrometry with data-dependent acquisition

Tanshinones are a class of bioactive constituents in the roots of Salvia miltiorrhiza named Dan-Shen in Chinese, which possess diverse pharmacological activities. In this study, we employed a sensitive high-performance liquid chromatography/multi-stage mass spectrometry (HPLC/MS(n)) method with data-dependent acquisition and a dynamic exclusion program for the identification of phase I metabolites of seven tanshinones in rat bile after intravenous administration. These seven tanshinones are tanshinone IIA, sodium tanshinone IIA sulfonate (abbreviated as STS, a water-soluble derivate of tanshinone IIA), cryptotanshinone, 15,16-dihydrotanshinone I, tanshinone IIB, przewaquinone A and tanshinone I. Altogether 33 metabolites underwent monohydroxylation, dihydroxylation, dehydrogenation, D-ring hydrolysis or oxidation reactions in the C-4 or C-15 side chain which were characterized by analyzing the LC/MS(n) data. Different metabolic reactions for tanshinones were dependent on the degree of saturation and the substituent group in the skeleton. Dehydrogenation was the major metabolic modification for cryptotanshinone with saturated A and D rings. 15,16-Dihydrotanshinone I containing a saturated D ring was mainly metabolized through D-ring hydrolysis. For tanshinone IIA, possessing a saturated A ring, hydroxylation was the major metabolic pathway. When there was hydroxyl group substitution in the C-17 or C-18 position, such as przewaquinone A and tanshinone IIB, or sulfonic group substitution in the C-16 position, such as STS, higher metabolic stability than that of tanshinone IIA was shown and only trace metabolites were generated. Oxidation in the C-4 or C-15 side chain was a characteristic reaction for tanshinone IIA and hydroxylated tanshinone IIA. For tanshinone I, bearing unsaturated A and D rings simultaneously, no metabolites were detected.