Affine holomorphic quantization

We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation, allowing to implement manifest locality without the necessity for metric or causal background structures. The quantization combines the holomorphic version of geometric quantization for state spaces with the Feynman path integral quantization for amplitudes. We also develop an adapted notion of coherent states, discuss vacuum states, and consider observables and their Berezin–Toeplitz quantization. Moreover, we derive a factorization identity for the amplitude in the special case of a linear field theory modified by a source-like term and comment on its use as a generating functional for a generalized S$S$-matrix.     

Convergence of Solutions of General Dispersive Equations Along Curve

In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper.     

Hydrodynamic assist and the dynamic contact angle in the coalescence of liquid drops

^** Email: decentsp{at}for.mat.bham.ac.uk The coalescence of two viscous liquid drops in an inviscid gasor in a vacuum is studied using the interface formation model.In the very early stages of coalescence during the formationof the ‘liquid-bridge’ connecting the two drops,this model predicts a moving contact line and a dynamic contactangle. This paper examines the dynamic evolution of this contactangle, and for small Reynolds number and small Capillary number,relevant particularly in micro-fluidics, a non-linear differentialequation is derived for the contact angle and solved computationally.It is found that the contact angle evolution can only be evaluatedby determining information about the flow away from the contactline. This is a manifestation of so-called hydrodynamic assist,studied experimentally in the context of curtain coating byBlake et al. (1999 Experimental evidence of non-local hydrodynamicinfluence on the dynamic contact angle. Phys. Fluids, 11, 1995–2007).For small Capillary number and small Reynolds number, the free-surfaceevolution is determined for the coalescence of two cylindersof equal radius. Finally, some comments are made on experimentsin coalescence, as well as on issues arising in a computationalsolution of the full model described here.     

Innovative solution of a 2D elastic transmission problem¶

This article is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are, in general, not singular perturbation problems, because of appropriate interface conditions.     

拉氏数值模拟中的人工粘性方法

较好的人工粘性需要满足较小的计算开销、不能去除真实具有的涡运动等条件.提出一种应用于拉氏数值模拟中基于Lew人工粘性,同时增加了限制器的人工粘性方法.可以有效减少数值模拟结果对网格的依赖;采用特征值限制器控制施加的人工粘性大小,通过限制器能够区分激波压缩和等熵压缩;方便应用在二维、三维,结构网格或者非结构网格上.     

ERROR ESTIMATION FOR NUMERICAL METHODS USING THE ULTRA WEAK VARIATIONAL FORMULATION IN MODEL OF NEAR FIELD SCATTERING PROBLEM

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.     

On the blowing up of solutions to quantum hydrodynamic models on bounded domains

The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance. The proof is based on a priori estimates for the energy functional for a new observable constructed with an auxiliary function, and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time. I.M. Gamba is supported by NSF-DMS0507038. M.P. Gualdani acknowledges partial support from the Deutsche Forschungsgemeinschaft, grants JU359/5 and was partially supported under the Feodor Lynen Research fellowship. P. Zhang is partially supported by the NSF of China under Grant 10525101 and 10421101, and the innovation grant from the Chinese Academy of Sciences. Part of the work was done when P. Zhang visited the Department of Mathematics of Texas University at Austin, the author would like to thank the hospitality of the department. Support from the Institute for Computational Engineering and Sciences at the University of Texas at Austin is also gratefully acknowledged.     

Fast analysis of multiple pesticide residues in apple juice using dispersive liquid–liquid microextraction and multidimensional gas chromatography–mass spectrometry

A method for the rapid trace analysis of 24 residual pesticides in apple juice by multidimensional gas chromatography–mass spectrometry (MD-GC/MS) using dispersive liquid–liquid microextraction (DLLME) was developed and optimized. Several parameters of the extraction procedure such as type and volume of extraction solvent, type and volume of dispersive solvent and salt addition were evaluated to achieve the highest yield and to attain the lowest detection limits. The DLLME procedure optimized consists in the formation of a cloudy solution promoted by the fast addition to the sample (5 ml) of a mixture of carbon tetrachloride (extraction solvent, 100 μl) and acetone (dispersive solvent, 400 μl). The tiny droplets formed and dispersed among the aqueous sample solution are further joined and sedimented (85 μl) in the bottom of the conical test tube by centrifugation. Once extracted, all the 24 pesticides were directly injected and separated by a dual GC column system, comprising a short wide-bore DB-5 capillary column with low film thickness connected by a Deans switch system to a second chromatographic narrower column, with identical stationary phase. The instrumental setting used, in combination with carefully optimized operational fast GC and MS parameters, markedly decreased the retention times of the targeted analytes. The total chromatographic run was 8 min. Mean recoveries for apple juice spiked at three concentrations ranged from 60% to 105% and the intra-repeatability ranged from 1% to 21%. The limits of detection of the 24 pesticides ranged from 0.06 to 2.20 μg/L. In 2 of a total of 28 analysed samples were found residues of captan, although at levels below the maximum limit legal established.     

Speciation of very low amounts of arsenic and antimony in waters using dispersive liquid–liquid microextraction and electrothermal atomic absorption spectrometry

A new procedure for the determination of inorganic arsenic (III,V) and antimony (III,V) in water samples by dispersive liquid–liquid micro extraction separation and electrothermal atomic absorption spectrometry (ETAAS) is presented. At pH 1, As(III) and Sb(III) are complexed with ammonium pyrrolidine dithiocarbamate and extracted into the fine droplets formed when mixing carbon tetrachloride (extraction solvent), methanol (disperser solvent) and the sample solution. After extraction, the phases are separated by centrifugation, and As(III) and Sb(III) are determined in the organic phase. As(V) and Sb(V) remain in the aqueous layer. Total inorganic As and Sb are determined after the reduction of the pentavalent forms with sodium thiosulphate. As(V) and Sb(V) are calculated by difference. The detection limits are 0.01 and 0.05 µg L^− 1 for As(III) and Sb(III), respectively, with an enrichment factor of 115. The relative standard deviation is in the 2.9–4.5% range. The procedure has been applied to the speciation of inorganic As and Sb in bottled, tap and sea water samples with satisfactory results.     

Development and validation of a HPLC method for the determination of buprenorphine hydrochloride, naloxone hydrochloride and noroxymorphone in a tablet formulation

A simple isocratic reversed-phase high-performance liquid chromatographic method (RP-HPLC) was developed for the simultaneous determination of buprenorphine hydrochloride, naloxone hydrochloride dihydrate and its major impurity, noroxymorphone, in pharmaceutical tablets. The chromatographic separation was achieved with 10 mmol L⁻¹ potassium phosphate buffer adjusted to pH 6.0 with orthophosphoric acid and acetonitrile (17:83, v/v) as mobile phase, a C-18 column, Perfectsil Target ODS3 (150 mm × 4.6 mm i.d., 5 μm) kept at 35 °C and UV detection at 210 nm. The compounds were eluted isocratically at a flow rate of 1.0 mL min⁻¹. The average retention times for naloxone, noroxymorphone and buprenorphine were 2.4, 3.8 and 8.1 min, respectively. The method was validated according to the ICH guidelines. The validation characteristics included accuracy, precision, linearity, range, specificity, limit of quantitation and robustness. The calibration curves were linear (r > 0.996) over the concentration range 0.22-220 μg mL⁻¹ for buprenorphine hydrochloride and 0.1-100 μg mL⁻¹ for naloxone hydrochloride dihydrate and noroxymorphone. The recoveries for all three compounds were above 96%. No spectral or chromatographic interferences from the tablet excipients were found. This method is rapid and simple, does not require any sample preparation and is suitable for routine quality control analyses.