Wavenumber Selection Research Articles

Generalized Matching Boundary Conditions Based on Fourier Transform Technique

AbstractThis paper presents a class of generalized matching boundary conditions (GMBCs) for the coupled atomistic/continuum simulation of lattice dynamics. This work is an extension of the MBCs originally proposed by Tang et al. Using the combination of a Fourier transform technique and the generalization of MBCs for arbitrary wavenumbers, a more efficient MBC implementation is developed. After describing the basic methodology, the focus turns to several specific parameterized forms of GMBC. Finally, the proposed approach is validated through several numerical examples, and its robustness is exhibited based upon the capability of wave energy absorption illustrated by the energy history and wave reflection. It is shown that the combination of GMBC expressions and the Fourier transform technique for wavenumber selection enhances both the efficiency and accuracy of the MBCs.

A unified criterion for the centrifugal instabilities of vortices and swirling jets

AbstractSwirling jets and vortices can both be unstable to the centrifugal instability but with a different wavenumber selection: the most unstable perturbations for swirling jets in inviscid fluids have an infinite azimuthal wavenumber, whereas, for vortices, they are axisymmetric but with an infinite axial wavenumber. Accordingly, sufficient condition for instability in inviscid fluids have been derived asymptotically in the limits of large azimuthal wavenumber $m$ for swirling jets (Leibovich and Stewartson, J. Fluid Mech., vol. 126, 1983, pp. 335–356) and large dimensionless axial wavenumber $k$ for vortices (Billant and Gallaire, J. Fluid Mech., vol. 542, 2005, pp. 365–379). In this paper, we derive a unified criterion valid whatever the magnitude of the axial flow by performing an asymptotic analysis for large total wavenumber $ \sqrt{{k}^{2} + {m}^{2} } $. The new criterion recovers the criterion of Billant and Gallaire when the axial flow is small and the Leibovich and Stewartson criterion when the axial flow is finite and its profile sufficiently different from the angular velocity profile. When the latter condition is not satisfied, it is shown that the accuracy of the Leibovich and Stewartson asymptotics is strongly reduced. The unified criterion is validated by comparisons with numerical stability analyses of various classes of swirling jet profiles. In the case of the Batchelor vortex, it provides accurate predictions over a wider range of axial wavenumbers than the Leibovich–Stewartson criterion. The criterion shows also that a whole range of azimuthal wavenumbers are destabilized as soon as a small axial velocity component is present in a centrifugally unstable vortex.

A Hybrid Wavenumber Selection Scheme for Line-By-Line Photon Monte Carlo Simulations in High-Temperature Gases

Recently, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. LBL accuracy, in principle, adds little to the computational load as compared to gray calculations. However, when employing the Monte Carlo method, the original scheme for choosing appropriate emission wavenumbers for statistical photon bundles is numerically expensive. An improved wavelength selection scheme has been applied to hypersonic plasmas for Monte Carlo solvers. However, directly applying this improved scheme to combustion gases may cause significant errors. In this paper, a hybrid scheme for wavenumber selection is proposed, significantly decreasing CPU requirements compared to previous work. The accuracy of the new method is established and its time requirements are compared against the previous method.

A multivariate-based wavenumber selection method for classifying medicines into authentic or counterfeit classes

Attenuated total reflectance (ATR), a sampling technique by Fourier transform infrared (FTIR) spectroscopy, has been adopted as an analytical tool for detecting fraudulent medicines. The spectrum generated by FTIR-ATR typically relies on hundreds of equally spaced wavenumbers which may reduce the performance of techniques tailored to classify samples into classes, i.e., authentic or fraudulent. This paper proposes a novel method for selecting subsets of wavenumbers (variables) that better classify samples into such classes. For that matter, principal components analysis (PCA) is integrated to the k-nearest neighbor (KNN) classification technique. PCA is applied to FTIR-ATR data, and a variable importance index is built on the PCA outputs. An iterative backward variable elimination is started guided by that index; after each variable removal, samples are categorized into authentic or fraudulent classes using KNN, and the classification accuracy is measured. The wavenumber subset compromising high accuracy and reduced percent of retained variables is chosen. When applied to Cialis FTIR-ATR data, the proposed approach retained only average 1.84% of the original variables and increased the classification accuracy average 2.1%, to 0.9897 from 0.9689; as for Viagra data, the method increased average classification accuracy 1.56%, from 0.9135 to 0.9278, using only 7.72% of the original variables.

Compressively excited acoustic wave propagation in a three-dimensional channel bifurcated by an elastic partition

Fluid motion resulting from compression of the exterior walls of a three-dimensional channel that is axially partitioned by a flexible membrane is examined. The axial variation in the acoustic impedance of the partition gives rise to a pressure gradient across the partition and generates an evanescent field at its surface. The effects of these evanescent modes and their impact on spatial wavenumber selectivity are of particular interest. The Green’s function for the pressure is given for the case of low fluid compressibility and channel high aspect ratio. In this limit, it is shown the evanescent modes may be modeled in terms of generalized functions. The complete solution of the pressure field inside the channel will be shown. Implication of the results on the development a MEMS transducer in which the displacement of membrane is used as the method of transduction is presented. [NSF Grant 0841392.]

Nonlinear disturbance growth during sedimentation in dilute fibre suspensions

AbstractDisturbances in a dilute fibre suspension are studied with an Eulerian approach. Based on a linear stability analysis, it is shown that inertia and hydrodynamic diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value, which increases with Reynolds number. Furthermore, the diffusion narrows the range of unstable wavenumbers. Numerical simulations of the full nonlinear evolution in time of a normal-mode perturbation show that the induced flow may either die out or saturate on a finite amplitude. The character of this long-time behaviour is dictated by the wavenumber and the presence or absence, as well as nature, of the translational and rotational diffusivities.

Stability of a Gaussian pancake vortex in a stratified fluid

AbstractVortices in stably stratified fluids generally have a pancake shape with a small vertical thickness compared with their horizontal size. In order to understand what mechanism determines their minimum thickness, the linear stability of an axisymmetric pancake vortex is investigated as a function of its aspect ratio $\alpha $, the horizontal Froude number ${F}_{h} $, the Reynolds number $\mathit{Re}$ and the Schmidt number $\mathit{Sc}$. The vertical vorticity profile of the base state is chosen to be Gaussian in both radial and vertical directions. The vortex is unstable when the aspect ratio is below a critical value, which scales with the Froude number: ${\alpha }_{c} \sim 1. 1{F}_{h} $ for sufficiently large Reynolds numbers. The most unstable perturbation has an azimuthal wavenumber either $m= 0$, $\vert m\vert = 1$ or $\vert m\vert = 2$ depending on the control parameters. We show that the threshold corresponds to the appearance of gravitationally unstable regions in the vortex core due to the thermal wind balance. The Richardson criterion for shear instability based on the vertical shear is never satisfied alone. The dominance of the gravitational instability over the shear instability is shown to hold for a general class of pancake vortices with angular velocity of the form $\tilde {\Omega } (r, z)= \Omega (r)f(z)$ provided that $r\partial \Omega / \partial r\lt 3\Omega $ everywhere. Finally, the growth rate and azimuthal wavenumber selection of the gravitational instability are accounted well by considering an unstably stratified viscous and diffusive layer in solid body rotation with a parabolic density gradient.

Rapid Prediction of Different Wood Species Extractives and Lignin Content Using Near Infrared Spectroscopy

The feasibility of using Fourier transform near infrared spectroscopy (FT-NIR) to rapidly determine the lignin and extractive content of various wood species (including softwoods and hardwoods) was investigated. Partial Least Square regression analyses were performed to describe the relationships between the data sets of wet laboratory chemical data and the FT-NIR spectra. The selection of relevant wavenumbers combined with the appropriate data pre-processing methods produced satisfactory prediction models. The test statistics (R2 , RMSECV, RMSEP, RPD) improved compared with the models over the wave number range 7500 cm−1 to 4000 cm−1. Automatic selection was superior to manual selection. The predicted lignin and extractive content models, using the full cross-validation in the appropriate wave number ranges (in cm−1) of 5450.1 to 4246.7, 6102.1 to 4597.7, 6252.4 to 4246.7, and 6252.4 to 6098.1 using the spectral data preprocessing methods of the straight-line subtraction, minimum–maximum normalization, and first derivative + vector normalization, were established. The high R2 values were 0.9838, 0.9809, and 0.9625, respectively. The low RMSECV values were 0.425%, 0.452%, and 0.185%, respectively. RPD values were 7.86, 7.25, and 5.17, respectively. Predictions were very good, with R2 of 0.9775, 0.9751, and 0.9521; RMSEP of 0.418%, 0.403%, and 0.206%; and RPD of 6.78, 6.7, and 4.57 for the lignin, 1% sodium hydroxide extractive, and ethanol-benzene extractive models, respectively.

Two-Dimensional Finite Difference Forward Modeling for Stable Point Power Field Based on Optimized k Value

The article presents a numerical simulation method for 2D resistivity finite difference forward calculation of point source. On the basis of traditional mixed boundary conditions and decomposition of linear equations, Xu's selection of the wave number k for Fourier inverse transform is using to obtain more accurate numerical results. The results show that this approach simplifies the problem of the numerical simulation for two-dimensional geoelectrical field and effectively control the simulation accurac

Range‐independent background subtraction algorithm for recovery of Raman spectra of biological tissue

An important requirement for the use of Raman spectroscopy for tissue diagnostic applications is an appropriate algorithm that can faithfully retrieve weak tissue Raman signals from the measured raw Raman spectra. Although iterative modified polynomial‐fitting‐based automated algorithms are widely used, these are sensitive to the choice of the fitting range, thereby leading to significantly different Raman spectra for different start and stop wavenumber selection. We report here an algorithm for automated recovery of the weak Raman signal, which is range independent. Given a raw Raman spectrum and the choice of the start and the stop wavenumbers, the algorithm first truncates the spectrum to include the raw data within this wavenumber range, linearly extrapolates the truncated raw spectrum beyond the points of truncation on the two sides by using coefficients of linear least‐square fit, adds two Gaussian peaks of appropriate height and width on the extrapolated linear wings on either side and then iteratively smoothens the data with all these add‐ons such that the smaller of the ordinate values of the smoothed and the starting raw data serve as the input to each successive round of iterative smoothing until the added Gaussian peaks are fully recovered. The algorithm was compared with the modified polynomial‐based algorithms using mathematically simulated Raman spectrum as well as experimentally measured Raman spectra from various biological samples and was found to yield consistently range‐independent and artifact‐free Raman signal with zero baseline. Copyright © 2012 John Wiley & Sons, Ltd.

Grain boundaries in the Swift–Hohenberg equation

We study the existence of grain boundaries in the Swift–Hohenberg equation. The analysis relies on a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, the grain boundaries are found as heteroclinic orbits of a reduced system of ordinary differential equations in normal form. We show persistence of the leading-order approximation using transversality induced by wavenumber selection.

Rapid and nondestructive analysis of pharmaceutical products using near-infrared diffuse reflectance spectroscopy

Near-infrared diffuse reflectance spectroscopy (NIRDRS) was applied to classification and quantification of azithromycin tablets with the aid of chemometric multivariate analysis. Repeatability was investigated by repeated measurements, and the effect of morphology was examined by preparing the tablets in four forms, i.e. tablet product, tablet without coating, powder of tablet without coating, and powder of tablet. Furthermore, baseline elimination by continuous wavelet transform (CWT) and wavenumber selection was discussed for improving the repeatability and accuracy of the method. The results show that the spectra of the samples in the four forms can be measured with an acceptable repeatability, and classification of manufacture sites and quantitative analysis of the active pharmaceutical ingredient (API) can be achieved by principal component analysis (PCA) and partial least squares (PLS) regression, respectively. More importantly, baseline elimination and wavenumber selection can significantly simplify the calculation and improve the results.

High‐throughput analysis of the plasmid bioproduction process in Escherichia coli by FTIR spectroscopy

Monitoring plasmid production systems is a lab intensive task. This article proposes a methodology based on FTIR spectroscopy and the use of chemometrics for the high-throughput analysis of the plasmid bioproduction process in E. coli. For this study, five batch cultures with different initial medium compositions are designed to represent different biomass and plasmid production behavior, with the maximum plasmid and biomass concentrations varying from 11 to 95 mg L(-1) and 6.8 to 12.8 g L(-1), respectively, and the plasmid production per biomass varying from 0.4 to 5.1 mg g(-1). After a short sample processing consisting of centrifugation and dehydration, the FTIR spectra are recorded from the collected cellular biomass using microtiter plates with 96 wells. After spectral pre-processing, the predictive FTIR spectra models are derived by using partial least squares (PLS) regression with the wavenumber selection performed by a Monte-Carlo strategy. Results show that it is possible to improve the PLS models by selecting specific spectral ranges. For the plasmid model, the spectral regions between 590-1,130, 1,670-2,025, and 2,565-3,280 cm(-1) are found to be highly relevant. Whereas for the biomass, the best wavenumber selections are between 900-1,200, 1,500-1,800, and 2,850-3,200 cm(-1). The optimized PLS models show a high coefficient of determination of 0.91 and 0.89 for the plasmid and biomass concentration, respectively. Additional PLS models for the prediction of the carbon sources glucose and glycerol and the by-product acetic acid, based on metabolism-induced correlations between the nutrients and the cellular biomass are also established.

Using near-infrared overtone regions to determine biodiesel content and adulteration of diesel/biodiesel blends with vegetable oils

This work evaluates the use of near-infrared (NIR) overtone regions to determine biodiesel content, as well potential adulteration with vegetable oil, in diesel/biodiesel blends. For this purpose, NIR spectra (12,000–6300cm−1) were obtained using three different optical path lengths: 10mm, 20mm and 50mm. Two strategies of regression with variable selection were evaluated: partial least squares (PLS) with significant regression coefficients selected by Jack-Knife algorithm (PLS/JK) and multiple linear regression (MLR) with wavenumber selection by successive projections algorithm (MLR/SPA). For comparison, the results obtained by using PLS full-spectrum models are also presented. In addition, the performance of models using NIR (1.0mm optical path length, 9000–4000cm−1) and MIR (UATR – universal attenuated total reflectance, 4000–650cm−1) spectral regions was also investigated. The results demonstrated the potential of overtone regions with MLR/SPA regression strategy to determine biodiesel content in diesel/biodiesel blends, considering the possible presence of raw oil as a contaminant. This strategy is simple, fast and uses a fewer number of spectral variables. Considering this, the overtone regions can be useful to develop low cost instruments for quality control of diesel/biodiesel blends, considering the lower cost of optical components for this spectral region.

Compaction-dissolution waves in an upwelling mantle column

SUMMARY Compaction–dissolution waves in porosity and melt pressure form spontaneously in numerical simulations of melt migration in an upwelling, viscously compacting, porous column in a solubilitygradient.Themeltfractionisassumedtobesmallandthesolidcomprisesolivineand orthopyroxene. The solubility of orthopyroxene in the melt is assumed to increase linearly with height and induces a gradient reaction, assumed to be at local equilibrium. Approximations for the vertical, 1-D, steady-state solutions are derived assuming negligible resistance to compaction. The linear stability of the steady-state solutions is characterized by complex eigenvalues and an oscillatory instability with strong wavenumber selection. This instability leads to the formation of checkerboard compaction–dissolution waves observed in the nonlinear numerical simulations. The phase velocity of these waves is larger than the solid velocity but smaller than the melt velocity. The oscillatory instability is realized over a range of parameters and the variation in wave properties is explored. A power-law bulk-viscosity formulation, ξ = η/φ m , is shown to decrease growth rates linearly in the exponent, m. For small perturbations, the growth rates and phase velocities measured from high-resolution numerical simulations are predicted by the linear theory as well as the dominant wavenumber in the non-linear regime. We present a regime diagram for reaction infiltration instabilities in viscouslycompacting porousmediaandshowthatcompaction–dissolutionwaves arefavoured by increasing solid upwelling and small solubility gradients relative to high-porosity channels. The regime diagram suggests that the formation of compaction–dissolution waves is a feasible new physical mechanism for melt transport beneath mid-ocean ridges.

Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

In the present work, four nontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes system: (i) a stage of the influence of the initial conditions (milliseconds); (ii) one-dimensional (1D) self-similar evolution (milliseconds-seconds); (iii) a primary instability of the self-similar solution (seconds); (iv) a nonlinear stage with secondary instabilities. The self-similar character of evolution at moderately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution toward overlimiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest a self-similar growth of the diffusion layer. It also specifies its characteristic length as was first experimentally predicted by Yossifon and Chang [G. Yossifon and H.-C. Chang, Phys. Rev. Lett. 101, 254501 (2008)]. A novel principle for the characteristic wave-number selection from the broadband initial noise is established.

Model Optimization and Wavenumbers Selection for FTIR/ATR Spectroscopy Analysis of Glucose Aqueous Solution

The rapid quantification method of glucose aqueous solution was established by using the Fourier transform infrared spectroscopy (FTIR) and attenuated total reflection (ATR). Model optimization and wavenumbers selection was investigated based on Savitzky-Golay (SG) smoothing. For the whole spectral collecting region 4500-600 cm-1 and the fingerprint region 1600-900 cm-1, Partial least squares (PLS) models without and with SG smoothing were established respectively. The optimal model was on the fingerprint region with SG smoothing of 1st order derivative, 2nd degree polynomial and 73 smoothing points, PLS factor, RMSEP, RP, were 4, 0.331 mmol/L, 0.999 respectively. Based on 19 absorption peaks of the subtracted spectra of glucose aqueous solution for de-ionized water, all possible wavenumber combinations were used to establish discrete multiple linear regression (MLR) models respectively, the optimal wavenumbers combination was 3084, 1034, 991 (cm-1), RMSEP and RP were 0.459 mmol/L, 0.997 respectively. It could provide valuable references for designing spectrophotometer system in special spectrometer and further for glucose analysis of the complex system. To get the stable prediction results, all models and results here were obtained based on the average data on 50 different divisions of calibration set and prediction set.

Convective Instability and Mass Transport of Diffusion Layers in a Hele-Shaw Geometry

We consider experimentally the instability and mass transport of flow in a Hele-Shaw geometry. In an initially stable configuration, a lighter fluid (water) is located over a heavier fluid (propylene glycol). The fluids mix via diffusion with some regions of the resulting mixture being heavier than either pure fluid. Density-driven convection occurs with downward penetrating dense fingers that transport mass much more effectively than diffusion alone. We investigate the initial instability and the quasisteady state. The convective time and velocity scales, finger width, wave number selection, and normalized mass transport are determined for 6000<Ra<90,000. The results have important implications for determining the time scales and rates of dissolution trapping of carbon dioxide in brine aquifers proposed as possible geologic repositories for sequestering carbon dioxide.

Research on Quantitative Prediction of Total Ash in Pollen Typhae by NIRS

Near infrared spectroscopy is used for establishing a rapid and non-destructive analytical method to determine the quantitative of Total Ash in Pollen Typhae, a traditional chinese crude drug. Partial least squares regression (PLSR) was used for building the quantitative prediction model of Pollen Typhae different calibration methods were compared with spectral pretreated methods, wave-number selection and factors of NIRS were discussed in detail. The first derivative and multiplicative scatter correction method was used to predict total ash to correlation coefficients (R), root mean square error of calibration (RMESECV) residual prediction deviation (RPD) and offset obtained by PLSR model were 0.9994, 0.293, 29.4 and 0.013 respectively. The standard deviation was less than 8.2% by the total ash prediction model in the 8 batches of Pollen Typhae from 6% to 27.3%. The predictive result shows the method of this research is rapid, non-destructive and credible, which can be applied to the rapid predict the total ash of Pollen Typhae.

Determination of Lignin Content in Norway Spruce Wood by Fourier Transformed near Infrared Spectroscopy and Partial Least Squares Regression. Part 1: Wavenumber Selection and Evaluation of the Selected Range

Although it might be thought that the determination of lignin content in wood by near infrared (NIR) spectroscopy is well known and has been used for several years, model statistics (mainly errors of prediction) found in the literature recommend further study. It is shown that partial least squares regression (PLS-R) models can be improved, namely the number of PLS vectors and the error of prediction can be substantially decreased by careful selection of the combination of wavenumber range(s) and pre-processing methods and validation of the models. To cover a wide range of the natural variability, the total lignin content of 200 Norway spruce wood samples was determined by wet-laboratory chemical methods. From the same milled samples Fourier transform near infrared (FT-NIR) spectra were recorded using a NIR fibre-optic probe. NIR bands, property weighting spectra and correlation coefficients were used to pre-select convenient wavenumber ranges. PLS regressions were carried out to establish a mathematical correlation between the data sets of wet-laboratory chemical methods and the FT-NIR spectra, leading to a number of “good” models with similar coefficients of determination ( r2)&gt;0.90 and root mean square errors of cross-validation ( RMSECV) below 0.3%. External validation of the models also gave r2&gt;0.90 and root mean square errors of prediction ( RMSEP) below 0.3%. As several models showed similar statistics, a further simple step, called evaluation, was introduced to assist in being able to make a decision about what model should be used. Therefore, in addition, FT-NIR spectra of another 366 wood samples were measured to evaluate the pre-selected combinations of wavenumber ranges and pre-processing methods. With this simple additional step (evaluation) the model with the highest predictability could be selected easily.