A compatible and conservative spectral element method on unstructured grids

We derive a formulation of the spectral element method which is compatible on very general unstructured three-dimensional grids. Here compatible means that the method retains discrete analogs of several key properties of the divergence, gradient and curl operators: the divergence and gradient are anti-adjoints (the negative transpose) of each other, the curl is self-adjoint and annihilates the gradient operator, and the divergence annihilates the curl. The adjoint relations hold globally, and at the element level with the inclusion of a natural discrete element boundary flux term.     

Particle Size Analysis: A comparative study of various methods

The particle size distribution of component materials can be important parameter governing the proper function of many industrial products. At present, accurate determination of particle size by currently available methods is difficult for both theoretical and practical reasons. In this paper, some elementary notions regarding particle sizing are reviewed as is the relative performance of commercially available particle sizing instrumentation which could be used for particle size analysis of dry powders. Our results indicate that various particle size instruments yield significantly (even vastly) different particle size distributions for the same material. Without great care on the part of the investigator, the results obtained from any given instrument may not accurately describe the powder in question and thus may cause incorrect technical recommendations. The use of Fraunhofer diffraction instruments on samples containing irregularly shaped small ( < 10 μm) particles of low refractive index requires considerable caution.     

Modal analysis of rib waveguide through finite element and mode matching methods

Two mode solvers based on the finite element and the mode matching methods are compared by way of analyzing rib waveguides. Differences between the normalized propagation constants provided by the two methods are always less than 10^–4 which is at least about one order of magnitude smaller than previously reported values. Results for lossy waveguides and field comparison are also presented.     

A comparative study on pre-smoothing techniques for projection data with poisson noise in computed tomography

A computer simulation was performed to compare pre-smoothing techniques for noisy projection data in reconstructed (computed tomographic) images and to find suitable pre-smoothing techniques for reducing the noise in the reconstruction. Some are applied to Poison (signal-dependent) noise, and the others to signal-independent noise obtained by the Anscombe transformation of signal-dependent noise. Selective for signal-dependent noise is found to produce superior results.     

A comparative study of aqueous DMSO mixtures by computer simulations and integral equation theories

ABSTRACT

Several computer simulation studies of aqueous-dimethylsulfoxide with different force field models, and conducted by different authors, point out to an anomalous depressing of second and third neighbour correlations of the water–water radial distribution functions. This seemingly universal feature can be interpreted as the formation of linear water clusters. We test here the ability of liquid state integral equation theories to reproduce this feature. It is found that the incorporation of the water bridge diagram function is required to reproduce this feature. These theories are generally unable to properly reproduce atom–atom distribution functions. However, the near-ideal Kirkwood–Buff integrals are relatively well reproduced. We compute the X-ray scattering function and compare with available experimental results, with the particular focus to explain why these data do not reproduce the cluster pre-peak observed in the water–water structure factor.     

Sonochemical dosimetry: A comparative study of Weissler,Fricke and terephthalic acid methods

Acoustic cavitation and sonochemical reactions play a significant role in various applications of ultrasound. A number of dosimetry methods are in practice to quantify the amount of radicals generated by acoustic cavitation. In this study, hydroxyl radical (OH) yields measured by Weissler, Fricke and terephthalic acid dosimetry methods have been compared to evaluate the validities of these methods using a 490 kHz high frequency sonochemical reactor. The OH yields obtained after 5 min sonication at 490 kHz from Weissler and Fricke dosimetries were 200 µM and 289 µM, respectively. Whereas, the OH yield was found to be very low (8 µM) when terephthalic acid dosimetry was used under similar experimental conditions. While the results agree with those reported by Iida et al. (Microchem. J., 80 (2005) 159), further mechanistic details and interfering reactions have been discussed in this study. For example, the amount of OH determined by the Weissler and Fricke methods may have some uncertainty due to the formation of HO₂ in the presence of oxygen. In order to account for the major discrepancy observed with the terephthalic acid dosimetry method, high performance liquid chromatography (HPLC) analysis was performed, where two additional products other than 2-hydroxy terephthalic acid were observed. Electrospray ionization mass spectrometry (ESI-MS) analysis showed the formation of 2,5-dihydroxyterephthalic acid as one of the by-products along with other unidentified by-products. Despite the formation of additional products consuming OH, the reason for a very low OH yield obtained by this dosimetry could not be justified, questioning the applicability of this method, which has been used to quantify OH yields generated not only by acoustic cavitation, but also by other processes such as γ-radiolysis. The authors are hoping that this Opinion Paper may initiate further discussion among researchers working in sonochemistry area that could help resolve the uncertainties around using these dosimetry methods.     

Optical dielectric waveguide analysis,based on the modified finite element and integral equation methods

Efficient versions of the finite element and integral equation methods have been developed to analyse the guided (surface) modes of an arbitrary shaped optical fibre. The first approach is based on the replacement of the open waveguide by the screen guide structure with an artificial impedance wall. The integral equation is solved by the adaptive collocation technique. The methods are used to calculate the dispersion characteristics of the elliptical fibre modes and their cut-off frequencies. The results obtained are compared with those calculated by other methods.     

Diffusion in a bistable potential: A comparative study of different methods of solution

The problem of diffusion in a bistable potential is studied by considering the associated nonlinear Langevin equation and its equivalent Fokker-Planck equation. Two numerically exact methods of solution, namely, the Monte Carlo solution of the nonlinear Langevin equation and the solution of the Fokker-Planck equation via the finite difference technique, are considered. The latter method has the advantage that it directly gives the evolution of the probability distribution function. Approximate analyses of the fluctuations using the system size expansion, the Gaussian decoupling procedure, and the scaling approach are also carried out. These investigations are performed on a representative problem for two specific cases: (1) evolution from intrinsically unstable states and (2) evolution from extensive regime. The fluctuations obtained using these approximate methods are compared with those obtained via the numerically exact methods. The study brings out the advantages and limitations of each of the methods considered.     

A comparative study of interface reconstruction methods for multi-material ALE simulations

In this paper we compare the performance of different methods for reconstructing interfaces in multi-material compressible flow simulations. The methods compared are a material-order-dependent Volume-of-Fluid (VOF) method, a material-order-independent VOF method based on power diagram partitioning of cells and the Moment-of-Fluid method (MOF). We demonstrate that the MOF method provides the most accurate tracking of interfaces, followed by the VOF method with the right material ordering. The material-order-independent VOF method performs somewhat worse than the above two while the solutions with VOF using the wrong material order are considerably worse.     

Coupling of finite element and boundary integral methods for electromagnetic scattering in a two-layered medium

Consider a time-harmonic electromagnetic plane wave incident on an inhomogeneity embedded in a two-layered medium. In this paper, a method of coupling of finite element and boundary integral equation methods is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases. The well-posedness of the continuous and discrete problems, as well as optimal error estimates for the coupled variational approximations, are obtained. Numerical results are included to illustrate the accuracy with the optimal convergence property of the proposed method and to show the wave features in a two-layered medium.     

A mixed integral equation of mechanics and a generalized projection method of its solution

A mixed multidimensional integral equation containing integral operators of various types is studied. The case in which the equation has one compact, self-adjoint, and strongly positive operator (with constant limits of integration) and two non-self-adjoint integral Volterra operators (with a variable upper limit of integration) is considered. To solve the equation, an effective projection method allowing one to obtain the result in a form with explicitly distinguished principal singularities is proposed.     

Contrast enhanced maximum intensity projection ultrasound imaging for assessing angiogenesis in murine glioma and breast tumor models: A comparative study

The purpose of this study was to prospectively compare noninvasive, quantitative measures of vascularity obtained from four contrast enhanced ultrasound (US) techniques to four invasive immunohistochemical markers of tumor angiogenesis in a large group of murine xenografts. Glioma (C6) or breast cancer (NMU) cells were implanted in 144 rats. The contrast agent Optison (GE Healthcare, Princeton, NJ) was injected in a tail vein (dose: 0.4 ml/kg). Power Doppler imaging (PDI), pulse-subtraction harmonic imaging (PSHI), flash-echo imaging (FEI), and Microflow imaging (MFI; a technique creating maximum intensity projection images over time) was performed with an Aplio scanner (Toshiba America Medical Systems, Tustin, CA) and a 7.5 MHz linear array. Fractional tumor neovascularity was calculated from digital clips of contrast US, while the relative area stained was calculated from specimens. Results were compared using a factorial, repeated measures ANOVA, linear regression and z-tests. The tortuous morphology of tumor neovessels was visualized better with MFI than with the other US modes. Cell line, implantation method and contrast US imaging technique were significant parameters in the ANOVA model (p < 0.05). The strongest correlation determined by linear regression in the C6 model was between PSHI and percent area stained with CD31 (r = 0.37, p < 0.0001). In the NMU model the strongest correlation was between FEI and COX-2 (r = 0.46, p < 0.0001). There were no statistically significant differences between correlations obtained with the various US methods (p > 0.05). In conclusion, the largest study of contrast US of murine xenografts to date has been conducted and quantitative contrast enhanced US measures of tumor neovascularity in glioma and breast cancer xenograft models appear to provide a noninvasive marker for angiogenesis; although the best method for monitoring angiogenesis was not conclusively established.     

Different methods to calculate heat transfer coefficient in a double-tube heat exchanger: A comparative study

An experimental study performed to compare the results of different methods used in the literature for the calculation of heat transfer coefficient in double-tube heat exchangers. Then, a new fundamental approach was proposed which used the temperature profile and the local heat transfer coefficients. In this method, the heat transfer coefficient has been calculated for the total length of the heat exchanger including developing and fully developed regions. Numerous experimentations have been conducted in a double-tube heat exchanger. A significant difference observed between the results obtained from the suggested approach and those of the previous methods.     

Quantization of constrained systems: A comparative look at three methods

Constrained Hamiltonian systems are investigated using three different methods: Hamilton-Jacobi, Batalin-Fradkin-Tyutin and gauge unfixing methods. The abelian Proca model is analyzed and the involutive Hamiltonian is obtained by the three methods.     

Anharmonic spectra of methanol and silanol: A comparative study

Anharmonic vibrational spectra of methanol and silanol as well as of some of their deuterated isotopomers are analysed using the vibrational self-consistent field approximation corrected by second order perturbation theory (cc-VSCF). Experimental frequencies in the case of methanol and its isotopomers are in general reproduced and anharmonic effects in their vibrational spectra are suitably explained. The similar species containing Si, i.e., silanol, is very unstable. Experimental data about its vibrational spectra are rare in the literature and the only theoretical data available come from the harmonic approach. Thus, to predict further anharmonic effects in its vibrational spectra, we extend our results on methanol to the silanol molecule.     

A comparative study of the influence of different post-treatment methods on the properties of HfO2 single layers

Heat treatment, laser conditioning and ion post-treatment were used, respectively, on HfO₂ single layers deposited by electron beam evaporation (EBE). Optical, structural and laser-induced damage threshold (LIDT) properties of the films had been studied. It was found that all of the post-treatment methods are effective for improving the LIDT, but the mechanism for the improvement differs. Heat treatment in atmosphere was found to be effective for improving film stoichiometry. Laser conditioning was useful to decrease the defects by stress release. While in the ion post-treatment, the defects were removed by ion sputtering and the absorption was reduced at the effect of compression induced by ion bombardment. The most suitable method should be chosen for the required characteristics of the coatings.