Singular Solutions of a Boussinesq System for Water Waves

Studied here is the Boussinesq system $$η_t+u_x+(ηu)_x+au_{xxx}-bη_{xxt}=0,$$ $$u_t+η_x+\frac{1}{2}(u²)_x+cη_{xxx}-du_{xxt}=0,$$of partial differential equations. This system has been used in theory and practice as a model for small-amplitude, long-crested water waves. The issue addressed is whether or not the initial-value problem for this system of equations is globally well posed.The investigation proceeds by way of numerical simulations using a computer code based on a a semi-implicit, pseudo-spectral code. It turns out that larger amplitudes or velocities do seem to lead to singularity formation in finite time, indicating that the problem is not globally well posed.     

基于FTIR技术的酸牛奶营养成分快速检测方法研究

酸牛奶作为一种重要的发酵乳制品,伴随着发酵过程,其各种营养成分时刻发生着复杂的变化,因此,建立酸牛奶的快速高效检测技术可以实现对生产过程的实时监控,这也是食品安全监管要达到的重要目标。傅里叶变换红外光谱技术(FTIR)因其快速、高通量、无化学污染、可对掺假成分予以分辨等特点被广泛应用于食品安全领域。以FTIR技术为核心,利用氟化钙薄膜法,将酸牛奶FTIR光谱图与其营养成分(能量值,蛋白质、脂肪、碳水化合物和钠含量)对照,建立了基于最小二乘法(PLS)的定量化预测模型。结果表明,该模型样品校正集的能量值,蛋白质、脂肪、碳水化合物和钠含量的交叉检验R2值分别达到0.938 9,0.926 6,0.918 6,0.941 8和0.977 1;该模型用于预测,其样品验证集的交叉检验R2值分别为0.920 5,0.905 3,0.908 5,0.939 3和0.936 4。由此可见,该模型对酸牛奶各营养指标均具有较好的预测准确性,在时间上具备较好的稳定性。不同于传统的化学检测方法,本研究为实现对酸牛奶品质的快速检测提供了一种较为可行的方法。该方法作为乳制品质量监控技术的一项初步探索,具有较好的应用前景。     

炮体表面瞬态温度分布的散斑干涉测试研究

为了可以实现对炮体表面瞬态温度分布变化的实时监测,同时克服传统瞬态高温测试仪器单点探测以及热惯性大等局限性,设计了基于散斑干涉与光谱频域分析相结合的瞬态温度分布测试系统。系统采用散斑干涉技术将炮体瞬态温度变化引发的微小形变转换成散斑干涉条纹,再由傅氏变换完成干涉条纹形变到光谱分布的函数转换,从而通过光谱分布函数反演任意采样时刻上的温度分布。实验采用ZX-FB1型光纤测温仪测试单点位置上瞬态温度作为标准值,再由555 nm激光器与面阵CCD采集散斑干涉条纹,分别使用图像识别法与傅氏变换法完成干涉条纹与瞬态温度的算法匹配,从而反演瞬态温度。实验结果显示,两种方法均能实现瞬态温度检测,但基于傅氏变换频谱分析的散斑干涉法精度更高,并且可以有效地克服由表面瑕疵、漆面磨损等问题造成的粗大误差。     

热处理竹材的化学成分傅里叶变换红外光谱分析

化学热处理是实现可再生木质生物能源中纤维素高效利用及半纤维素糖化转换的关键步骤。通过预处理过程可以快速去除难溶木质素,实现细胞壁中半纤维素的物理化分离,使得植物细胞壁中化学成分发生变化,从而增加木质纤维素的产出量。以硫酸(H₂SO₄)、稀碱(NaOH)及甘油(glycerol)为预处理介质,采用不同的热处理温度(硫酸(H₂SO₄)、稀碱(NaOH)热处理温度为117和135 ℃;甘油(glycerol)热处理温度为117 ℃)),对竹材处理前后的主要化学组分进行对比分析,并通过傅里叶变换红外光谱进一步证实化学热处理前后竹材化学组分的变化,以获得不同的化学热处理介入下竹材化学成分转换的主要变化规律和机理。结果表明：热化学处理后竹材的纤维素产出量明显增加。纤维素得率及木质素的去除率在不同的处理介质条件下的变化规律为,稀碱(NaOH)处理效果优于稀酸(H₂SO₄)和甘油(glycerol);此外,在相同介质条件下135 ℃热处理效果比117 ℃热处理效果显著。对于不同处理条件的半纤维素的降解程度大小变化结果与此相同。通过红外光谱分析可知,热处理后纤维素环状C-O-C不对称伸缩振动峰出现峰值分解,半纤维素的红外吸收特征峰出现明显陡降变化,木质素苯环特征吸收峰明显减弱,证明纤维素产出量明显增加,半纤维素降解趋势明显,木质素去除效果良好。傅里叶红外变换光谱分析结果与标准测定结果一致。     

Stochastic analysis of groundwater flow in a bounded domain by spectral methods

A saturated flow problem with spatially varying conductivity is studied in a rectangular domain. An expansion of the flow equation with respect to small perturbations of the conductivity is given. Discrete spectra are used to calculate the expected flux across the outflow boundary and its variability. The results obtained are compared with results based on Monte Carlo studies. Another way to deal with heterogeneous soils is to replace the actual conductivity by a smooth, so-called, effective conductivity. A comparison is made between results based on that approach and our results.     

傅里叶变换中一个含参变量广义积分的计算

本文利用含参变量广义积分计算中常用的求导和变量替换等技巧等给出了傅里叶变换中一个重要的含参变量广义积分的计算方法.     

分数阶傅里叶变换结合高峰均比抑制算法对CO-OFDM系统的影响分析

针对相干光正交频分复用系统中出现的高峰值平均功率比问题,提出分数阶傅里叶变换与高峰值平均功率比抑制算法相结合的方法.计算表明:随着分数阶傅里叶变换阶数的减小,信号的峰值平均功率比逐渐降低;与抑制算法结合后可进一步降低系统的峰值平均功率比,并解决抑制算法影响系统性能的问题.从结合的兼容性、抑制高峰值平均功率比效果及改善引入抑制算法后对系统的负面影响三方面进行仿真分析,结果表明:采用选择性映射算法与分数阶傅里叶变换结合后,旋转因子同为4时,峰值平均功率比高于6.6dB的概率较单一选择性映射算法低104;选取高峰值平均功率比抑制情况相近时,结合算法的时间复杂度比单一选择性映射算法降低了8倍;采用限幅算法与分数阶傅里叶变换结合的仿真情况也较单一限幅算法有很大提高,表明该算法结合的兼容性良好.     

Line broadening,shifting and mixing parameters for the ν1 + ν3 band of OCS perturbed by N2 and O2

In this paper, we report measured Rosenkranz N₂- and O₂-broadening, induced pressure-shift and mixing coefficients for OCS in the ν₁ + ν₃ band, using a multi-pressure fitting technique applied to the measured shapes of the lines, including the interference effects caused by the line overlaps. These measurements were made by analysing six laboratory absorption spectra recorded at 0.004 cm^?1 resolution using the Fourier transform spectrometer Bruker IFS125HR located at the Laboratoire Interuniversitaire des Systèmes Atmosphériques, in Créteil. The spectra have been recorded in the 1850–3000 cm^?1 wave number range at 295 K, using a multipass absorption cell with an optical path of 3.249 m. The total sample pressures ranged from 5.97 to 83.28 Torr with OCS volume mixing ratios between 0.001 and 0.013 in nitrogen or oxygen. We have been able to determine the N₂- and O₂-pressure-broadening coefficients of 81 ν₁ + ν₃ transitions with rotational quantum number J up to 50. The measured N₂- and O₂-broadening coefficients range from 0.0815 ± 0.0698 to 0.1169 ± 0.1027 cm^?1 atm^?1 at 295 K, respectively. Most of the measured pressure shifts are positive. The reported N₂- and O₂-induced pressure-shift coefficients vary from about ?0.0103 ± 0.0092 to 0.0097 ± 0.0092 cm^?1 atm^?1, respectively. We have examined the dependence of the measured broadening parameters on the quantum number m (m = ?J for the P branch and m = J + 1 for the R branch) and also developed an empirical expression to describe the broadening coefficients in terms of |m|. On average, this empirical expression reproduces the measured broadening coefficients to within 2%. Using a semi-classical Robert and Bonamy formalism, the theoretical broadening coefficients have been calculated at room temperature and compared with the experimental results. The theoretical results of the broadening coefficients are in very good overall agreement with the experimental data (2%).     

The infrared spectrum of DCCF in the 320–850 cm−1 region: bending states up to υ4+υ5 = 3

Infrared spectra of deuterated monofluoroacetylene, DCCF, have been recorded in the region between 320 and 850 cm^?1 at an effective resolution ranging from 0.0024 to 0.0031 cm^?1. In total, 6650 rotation vibration transitions were assigned to 37 bands involving the bending states with v₄ + v₅ and |l₄+l₅|, respectively, up to 3, allowing the characterisation of the ground state and of 18 vibrationally excited states. The vν₅ bending fundamental has been studied for the first time. In addition, the difference band v₃ ← v₄ has been detected and analysed. All the assigned transitions have been fitted simultaneously by adopting a model Hamiltonian that takes into account the vibration and rotation l?type resonances. Rotational transitions in the ground and in bending excited states reported in the literature have been included in the global analysis. The set of 57 derived spectroscopic parameters reproduces 6130 infrared and 90 microwave and millimetre?wave transitions satisfactorily with root mean square values of 5.3 × 10^?4 cm^?1 and 77 kHz, respectively.