Non‐linear stability for convection with quadratic temperature dependent viscosity

In this paper, we study the non‐linear stability of convection for a Newtonian fluid heated from below, where the viscosity of the fluid depends upon temperature. We are able to show that for Rayleigh numbers below a certain critical value, Ra_c, the rest state of the fluid and the steady temperature distribution remains non‐linearly stable, using the calculations of Diaz and Straughan (Continuum Mech. Thermodyn. 2004; 16 :347–352). The central contribution of this paper lies in a simpler proof of non‐linear stability, than the ones in the current literature, by use of a suitable maximum principle argument. Copyright © 2006 John Wiley & Sons, Ltd.     

对流占优的Sobolev方程的投影稳定化有限元方法

对于对流占优的Sobolev方程,提出了一种新的投影稳定化有限元方法,建立了半离散和全离散的投影稳定化格式,给出了解的稳定性和收敛性分析.该方法能够有效克服对流占优,与内罚方法相比,投影格式更简单,计算量更小,且得到的C—N格式是无条件稳定的,时间精度达到了二阶.最后,通过实验证明,数值结果与理论结果完全一致.     

带强迫项的高阶中立型微分方程的振动性

研究了一类强迫高阶非线性中立型时滞微分方程一切解振动的充分条件,建立了两个振动定理,推广和改进了已有结果.     

The pointwise estimates of solutions for a nonlinear convection diffusion reaction equation

This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal L~p,1≤ p ≤ +∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

Evaluation of linear and nonlinear convection schemes on multidimensional non‐orthogonal grids with applications to KVLCC2 tanker

Almost all evaluations of convection schemes reported in the literature are conducted using simple problems on uniform orthogonal grids; thus, having limited contribution when solving industrial computational fluid dynamics (CFD), where the grids are usually non‐orthogonal with distortions. Herein, several convection schemes are assessed in uniform and distorted non‐orthogonal grids with emphasis on industrial applications. Linear and nonlinear (TVD) convection schemes are assessed on analytical benchmarks in both uniform and distorted grids. To evaluate the performance of the schemes, four error metrics are used: dissipation, phase and L₁ errors, and the schemes' effective order of accuracy. Qualitative and quantitative deterioration of these error metrics as a function of the grid distortion metrics are investigated, and rigorous verifications are performed. Recommendations for effective use of the convection schemes based on the range of grid aspect ratio (AR), expansion ratio (ER) and skewness (Q) are included. A ship hydrodynamics case is studied, involving a Reynolds averaged Navier–Stokes simulation of a bare‐hull KVLCC2 tanker using linear and nonlinear convection schemes coupled with isotropic and anisotropic Reynolds‐stress (ARS) turbulence models using CFDShip‐Iowa v4. Predictions of local velocities and turbulent quantities from the midships to the nominal wake plane are compared with experimental fluid dynamics (EFD), and rigorous verification and validation analyses for integral forces and moments are performed for 0° and 12° drift angles. Best predictions are observed when coupling a second‐order TVD scheme with the anisotropic turbulence model. Further improvements are observed in terms of prediction of the vortical structures for 30° drift when using TVD2S‐ARS coupled with DES. Copyright © 2009 John Wiley & Sons, Ltd.     

HPLC–PDA identification and resolution of rufinamide forced degradation impurities: A congregated chemometric expedite optimization coupled with factorials and desirability

Rufinamide is used presently to treat Lenaux–Gastaut syndrome. A full factorial design and desirability approach was investigated for the optimization of hydrolytic stress via response surface curves (RSCs). The degradation impurities were identified and resolved using reversed-phase high-performance liquid chromatography (RP-HPLC) on the Qualisil® BDS C₈ column. Acetonitrile–water (29:71, v/v) was optimized for the mobile phase and used at a flow rate of 1.0 ml/min with detection at a wavelength of 230 nm. Rufinamide showed appreciable susceptibility to hydrolysis under acidic and alkaline stress, and substantial degradation in the neutral condition. It degraded much less under oxidative stress. Exposure towards thermal and photolytic stress conditions indicated appreciable stability. The developed method was subjected to validation as per the recommendations of the International Conference on Harmonization. The proposed method showed no influence from the excipients and the degradation products. As well as good precision and accuracy in determination, the method showed a linear response between 2 and 12 μg ml⁻¹. The method was extended for determination in a human plasma sample, which resulted in excellent recovery without interference from matrix effects. The combined use of desirability and design for the optimization of acidic and alkaline hydrolytic stress led to simple and rapid analysis.     

Validated Stability-Indicating GC-MS Method for Characterization of Forced Degradation Products of Trans-Caffeic Acid and Trans-Ferulic Acid

When dealing with simple phenols such as caffeic acid (CA) and ferulic acid (FA), found in a variety of plants, it is very important to have control over the most important factors that accelerate their degradation reactions. This is the first report in which the stabilities of these two compounds have been systematically tested by exposure to various different factors. Forced degradation studies were performed on pure standards (trans-CA and trans-FA), dissolved in different solvents and exposed to different oxidative, photolytic and thermal stress conditions. Additionally, a rapid, sensitive, and selective stability-indicating gas chromatographic-mass spectrometric method was developed and validated for determination of trans-CA and trans-FA in the presence of their degradation products. Cis-CA and cis-FA were confirmed as the only degradation products in all the experiments performed. All the compounds were perfectly separated by gas chromatography (GC) and identified using mass spectrometry (MS), a method that additionally elucidated their structures. In general, more protic solvents, higher temperatures, UV radiation and longer storage times led to more significant degradation (isomerization) of both trans-isomers. The most progressive isomerization of both compounds (up to 43%) was observed when the polar solutions were exposed to daylight at room temperature for 1 month. The method was validated for linearity, precision as repeatability, limit of detection (LOD) and limit of quantitation (LOQ). The method was confirmed as linear over tested concentration ranges from 1−100 mg L⁻¹ (r²s were above 0.999). The LOD and LOQ for trans-FA were 0.15 mg L⁻¹ and 0.50 mg L⁻¹, respectively. The LOD and LOQ for trans-CA were 0.23 mg L⁻¹ and 0.77 mg L⁻¹, respectively.     

Identification and characterization of forced degradation products and stability‐indicating assay for notoginsenosidefc by using UHPLC‐Q‐TOF‐MS and UHPLC‐MS/MS: Insights into stability profile and degradation pathways

Notoginsenoside Fc, a protopanaxadiol‐type saponin, shows multi‐pharmacological activities. Chemical stability evaluation plays a crucial role in drug development. In this study, the forced degradation behavior of Notoginsenoside Fc was investigated under hydrolytic and oxidative conditions. A specific ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry was developed for the separation, identification, and characterization of the degradation products of Notoginsenoside Fc. Fifty potential degradation products were formed via deglycosylation, dehydration, hydration, isomerization, side‐chain cleaving, oxidation, and superoxidation. Notoginsenoside Fc was subjected to different pH solutions, temperatures, and time periods to assess its stability. A sensitive ultra high performance liquid chromatography‐tandem mass spectrometry was developed for the quantification of Notoginsenoside Fc, notoginsenoside ST‐4, notoginsenoside Ft1, and relative quantification of notoginsenoside Ft2, 20(R)‐notoginsenoside Ft2, notoginsenoside SFt3, and notoginsenoside SFt4. The assay was linear over the concentration range (R² > 0.997) with the lowest limit of quantification of 0.02 μg/mL for Notoginsenoside Fc, Notoginsenoside ST‐4, and Notoginsenoside Ft1. The intra‐day precision, inter‐day precision, and accuracy of the three analytes were within accepted levels. The degradation kinetics of Notoginsenoside Fc in pH 1 and 3 solutions fits to first‐ and second‐order kinetics, respectively. The degradation of Notoginsenoside Fc is pH‐, temperature‐, and time‐dependent.