The Cauchy Relations in Linear Elasticity Theory

In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The vanishing of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

Interaction of isotropic turbulence with a normal shock wave

The evolution of incompressible and compressible isotropic 2-d turbulent fields interacting with a normal shock wave up to Mach numbers of 2.4 was investigated by means of direct numerical simulation using an ENO scheme. A comparison of statistics with linear analysis results is presented. Vorticity amplification in the DNS agrees well with the linear theory. Energy spectra are enhanced more in the small scales than in the large scales for incoming incompressible turbulence. The amplification rate for initially compressible turbulence is comparatively small.     

Resonance Vibrations and Dissipative Heating of Thin-Walled Laminated Elements Made of Physically Nonlinear Materials

The dynamic thermomechanical problem for thin-walled laminated elements is formulated based on the geometrically linear theory and Kirchhoff–Love hypotheses. A simplified model of vibrations and dissipative heating of structurally inhomogeneous inelastic bodies under harmonic loading is used. The mechanical properties of materials are described using strain-dependent complex moduli. A nonstationary vibration-heating problem is solved. The dissipative function, derived from the stationary solution, is used to specify internal heat sources. The amplitude–frequency characteristics and spatial distributions of the main field variables are studied for a sandwich beam subjected to forced vibrations     

多层流体的Marangoni对流

介绍微重力环境下矩形液池中多层不相混液体的Marangoni对流及其不稳定性.Marangoni对流流动的形成是由于在该系统施加一个与液体交界面相垂直的外加温度梯度.Marangoni对流的线性不稳定性分析是基于无限延长矩形液池内的两层流体系统.应用数值模拟研究了Marangoni对流的流体动力学和热传输特性,将多层流体的Marangoni对流同两层流体中外加温度梯度与流体交界面平行时引起的热毛细对流的主要特征进行了比较.     

Unsaturated Transport with Linear Kinetic Sorption Under Unsteady Vertical Flow

We consider transport of a solute obeying linear kinetic sorption under unsteady flow conditions. The study relies on the vertical unsaturated flow model developed by Indelman et al. [J. Contam. Hydrol. 32 (1998), 77–97] to account for a cycle of infiltration and redistribution. One of the main features of this type of transport, as compared with the case of a continuous water infiltration, is the finite depth of solute penetration. In the infiltration stage an analytical solution that generalizes the previous results of Lassey [Water Resour. Res. 24 (1988), 343–350] and Severino and Indelman [J. Contam. Hydrol. 70 (2004), 89–115] is derived. This solution accounts for quite general initial solute distributions in both the mobile and immobile concentration. When the redistribution is also considered, two timescales become relevant, namely: (i) the desorption rate k⁻¹, and (ii) the water application time t_ap. In particular, we have assumed that the quantity ε =(k t_ap)⁻¹ can be regarded as a small parameter so that a perturbation analytical solution is obtained. At field-scale the concentration is calculated by means of the column model of Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979), 461–467], i.e. as ensemble average over an infinite series of randomly distributed and uncorrelated soil columns. It is shown that the heterogeneity of hydraulic properties produces an additional spreading of the plume. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying period. The mean solute penetration depth is studied with special emphasis on the impact of the variability of the saturated conductivity upon attaining the maximum solute penetration depth.     

Characterisation and classification of automotive clear coats with Raman spectroscopy and chemometrics for forensic purposes

The clear coats from a collection of automotive paint samples of 139 vehicles, covering a range of Australian and international vehicle manufacturers and sold in Western Australia, were characterised using FT‐Raman spectroscopy. Principal component analysis (PCA) revealed 19 distinct classes that were associated with the vehicles' manufacturer and model, and in the case of Australian manufacturers, the years of manufacture. Linear discriminant analysis based on the PCA groupings gave excellent discrimination between the groups with 96.9% of the calibration set and 97.6% of the validation set being correctly classified. Although the sample set comprised only vehicles available in Australia, the methodology used is universal and hence applicable in any jurisdiction that is willing and able to generate a statistically significant data set and maintain and update it as new vehicles appear on the market. A FT‐Raman spectroscopy‐based database would rapidly provide information regarding vehicle origin and manufacture and hence generate investigative leads for questioned paint samples found at incident sites. Copyright © 2016 John Wiley & Sons, Ltd.     

A consensus successive projections algorithm – multiple linear regression method for analyzing near infrared spectra

The successive projections algorithm (SPA) is widely used to select variables for multiple linear regression (MLR) modeling. However, SPA used only once may not obtain all the useful information of the full spectra, because the number of selected variables cannot exceed the number of calibration samples in the SPA algorithm. Therefore, the SPA-MLR method risks the loss of useful information. To make a full use of the useful information in the spectra, a new method named “consensus SPA-MLR” (C-SPA-MLR) is proposed herein. This method is the combination of consensus strategy and SPA-MLR method. In the C-SPA-MLR method, SPA-MLR is used to construct member models with different subsets of variables, which are selected from the remaining variables iteratively. A consensus prediction is obtained by combining the predictions of the member models. The proposed method is evaluated by analyzing the near infrared (NIR) spectra of corn and diesel. The results of C-SPA-MLR method showed a better prediction performance compared with the SPA-MLR and full-spectra PLS methods. Moreover, these results could serve as a reference for combination the consensus strategy and other variable selection methods when analyzing NIR spectra and other spectroscopic techniques.     

大颗粒磷钼酸铵:制备与结晶动力学(英文)

通过缓慢滴加焦磷酸钾的硝酸溶液到钼酸铵溶液中制得了大颗粒磷钼酸铵(AMP)。研究了AMP的成核速率(G)与晶体生长速率。与晶体生长速率相比成核速率的反应级数更高。最初,大颗粒磷钼酸铵的结晶过程处于相变反应控制的动力学区域,此时溶液的过饱和生成速率比过饱和消除速率高。晶体线生长速率与溶液的过饱和度先增加后降低。在滴加中期,过饱和消除速率增长到与其生成速率相当。在滴加后期,晶体成核速率快速增高,而晶体的线生长速率下降。晶体的成核速率成为过饱和消除的唯一控制步骤。因此,AMP成核大部分是在首先接触到滴加液的局部溶液中完成的。