Wavenumber Curves Research Articles

DETECTION OF WHITE RICE ADULTERANTS IN LAMPUNG ROBUSTA COFFEE EXTRACT USING FT-IR METHOD BY FINGERPRINT ANALYSIS AND PRINCIPAL COMPONENT ANALYSIS

Lampung Province has 3 areas that produce coffee: West Lampung, Tanggamus, and Waykanan, which can produce 51,484 tons of coffee annually. The high demand for coffee and limited harvest are some factors that cause the addition of adulterants to coffee products such as corn, soybeans, rye, coffee beans, and rice. This study aims to detect rice adulterants in Lampung robusta coffee using the FTIR spectrophotometric method combined with chemometric analysis using the PCA (Principal Component Analysis) method. FTIR spectrophotometric method combined with chemometric analysis using PCA (Principal Component Analysis) method. The PCA method was validated using the cross-validation method. Samples were taken from 3 Lampung coffees on the market. The extraction process was carried out on Lampung coffee and Lampung rice from 3 regions using 96% ethanol. After concentrating, the coffee and rice extracts were measured using FTIR and read in the 4000-650 cm-1 wave number range. Different wave number curves were obtained between coffee and rice. A pre-processing chemometric analysis was performed, which resulted in the classification of Robusta coffee and rice using PC1 and PC2 (50% and 24%). The results of PCA analysis showed that PC1 and PC2 in the three Lampung coffee samples, samples A and C, did not contain adulterants, while sample B was suspected of containing white rice. Keywords: Alduteran, FTIR, Chemometrics, PCA, Lampung Robusta Coffee.

Waveform inversion for wavenumber extraction and waveguide characterization using ultrasonic Lamb waves

Wavenumber dispersion of ultrasonic Lamb waves associating with the thickness and material property of plates plays an important role in waveguide characterization and non-destructive testing. Classical waveguide characterization with wavenumber estimation methods is performed based on a large amount of Lamb wave signals or sensitive to wave mode overlapping and noise. A genetic algorithms-based waveform inversion method is developed for wavenumber extraction of one Lamb wave signal and characterization of plate in this work. The individual chromosome is encoded in real number by the thickness and material properties of the structure. The elastic formula of Lamb waves is solved by the bisection method to further derive the wavenumber curves; then the wave mode signals are generated based on the propagation function, and are linearly combined to form the individual signal. The signal with the minimum residual ratio to the analysis signal is iteratively searched by the genetic algorithm. Finally, the plate properties and wavenumber of Lamb waves are identified with the chromosome of searched individual. Numerical and experimental studies prove the developed waveform inversion method can realize accurate wavenumber extraction of a Lamb wave signal, even though its time–frequency representation has low sparsity, and characterization of plate. The residual ratio between the inversion wavenumber and theory curves is around 1%; and the estimation deviation of material properties of plate is around 6%.

Single-magnon excited states of a Heisenberg spin chain using a quantum computer

Excited states of spin-chains play an important role in condensed matter physics. We present a method of calculating the single magnon excited states of the Heisenberg spin-chain that can be efficiently implemented on a quantum processor for small spin chains. Our method involves finding the stationary points of the energy vs wavenumber curve. We implement our method for 4-site and 8-site Heisenberg Hamiltonians using numerical techniques as well as using an IBM quantum processor. Finally, we give an insight into the circuit complexity and scaling of our proposed method.

Research on 3D finite element simulation model of aluminium beam with lamination defects based on 2D Fourier transform

In order to solve the problems of low detection accuracy and poor modelling effect when building the laminated defect aluminium beam model, a 3D finite element simulation model of laminated defect aluminium beam based on 2D Fourier transform is proposed. The two-dimensional Fourier transform method was used to obtain the full wave field signal and spatial position wave number curve of aluminium beam structure. The three-dimensional point cloud image was generated by MATLAB software, and the solid model of aluminium beam with delamination defect was established. The three-dimensional finite element simulation model of aluminium beam with laminated defects was obtained by introducing it into the worktable. The experimental results show that the accuracy of the method is 98.91%, the average texture number and frame rate are 17.105 ms and 95.507 frames/second, respectively. It has a good effect on the establishment of 3D finite element simulation model of aluminium beam.

MHD instability of the pressure‐driven plane laminar flow in the presence of the uniform coplanar magnetic field: Linear stability analysis

AbstractThe influence of the uniform longitudinal magnetic field on the stability against small disturbances of an electrically conducting Newtonian fluid flow between two parallel horizontal plates is investigated. The sixth‐order system of disturbance equations is solved by the Chebyshev collocation method, and the critical Reynolds number , the critical wave number , and the critical wave speed are computed for a wide range of the magnetic Reynolds number and Alfven number A. Curves of wave number against Reynolds number for neutral stability are presented for different values of the parameters. The onset of instability is also discussed in detail using the growth rate curves for various parameters of the problem. It is observed that the effect of both conductivity of the fluid and the strength of the magnetic field is to decay the onset of instability. A comprehensive study is carried out at the critical state of the fluid using the graph of , , and with respect to for various values of A. The critical values at the onset of instability are also presented for both the Galerkin method and the Chebyshev collocation method.

Dispersion Compensation Method for Lamb Waves Based on Measured Wavenumber

In this study, a delta wavenumber dispersion compensation (∆K-DC) method was developed and applied, not only with the theoretical wavenumber but also with the measured wavenumber. Dispersion compensation can be achieved by the following steps: relative wavenumber measurement, traveling distance estimation, phase compensation, and wave correction. The feasibility of ∆K-DC with the theoretical wavenumber and measured wavenumber was validated with a high-dispersive A0 mode in a 2 mm steel plate experiment. The results showed that phase spectrum measurement was an effective method to construct the wavenumber curve, the propagation distances estimated by SAP2 were very accurate, and the dispersive signals can be compensated perfectly by applying the phase compensation and wave correction methods for each wavepacket. The present results highlight the application of ∆K-DC on dispersion compensation without any material parameters of a waveguide.

A signal domain transform method for spatial resolution improvement of Lamb wave signals with synthetically measured relative wavenumber curves

In practical structural health monitoring with Lamb waves, the signal spatial resolution is usually restricted by not only dispersion but also the space duration of excitation waveforms, that is, the initial spatial resolution for the signals before traveling. As a result, the final resolution and accuracy of damage identification could be badly impaired. To overcome this problem, a signal domain transform method is presented in this article. In signal domain transform, the original dispersive Lamb wave signals are transformed from the time to distance domains, with the time–distance scaling on the excitation waveforms particularly modified. Then, both dispersion compensation and initial spatial resolution enhancement can be actualized to efficiently improve the signal spatial resolution. Considering the practical situation that the structural property parameters could be unavailable to theoretically derive the requisite wavenumber relations, signal domain transform with synthetically measured relative wavenumber curves is further explored. After the frequency domain representation and spatial resolution of Lamb wave signals are basically analyzed, the principle and numerical realization of signal domain transform are investigated. Hereafter, the synthetic measurement of relative wavenumber curves for signal domain transform is discussed and preliminarily validated in an aluminum plate. Finally, signal domain transform is applied for high-resolution imaging of adjacent multiple damages. The efficiency of signal domain transform and signal domain transform–based imaging methods has been well demonstrated by the experimental study on a glass fiber–reinforced composite plate with unknown material parameters.

Solubility and Preferential Solvation of Piroxicam in Neat Solvents and Binary Systems

AbstractThe solubilization and solvatochromic behavior of piroxicam (PRX) were analyzed using UV-vis spectroscopy in neat (protic and aprotic) and binary solvent mixtures. The effects of solvent dipolarity/polarizability and solvent–solute hydrogen bonding interactions on the absorption maxima were evaluated by means of the linear solvation energy relationship concept of Kamlet and Taft. This analysis indicated that both interactions play an important role in the position of the absorption maxima in neat solvents. While, the PRX solubility depends on the solute–solvent specific interactions, polarizability and the cohesive forces of the solvent, manifested mainly by means of the Hildebrand’s solubility parameter. Preferential solvation (PS) was studied in 10 binary mixtures. A non-ideal behavior of the wavenumber curve as the function of analytical mole fraction of co-solvent was detected. Index of preferential solvation, as well as the influence of solvent parameters were calculated. The process of dissolution was analyzed in aqueous binary mixtures of ethanol, ethylene glycol and propylene glycol. They were not spontaneous in all proportions, but when water concentration decreases in the mixtures, the process becomes more spontaneous.

Impact imaging of aircraft composite structure based on a model-independent spatial-wavenumber filter

The spatial-wavenumber filtering technique is an effective approach to distinguish the propagating direction and wave mode of Lamb wave in spatial-wavenumber domain. Therefore, it has been gradually studied for damage evaluation in recent years. But for on-line impact monitoring in practical application, the main problem is how to realize the spatial-wavenumber filtering of impact signal when the wavenumber of high spatial resolution cannot be measured or the accurate wavenumber curve cannot be modeled. In this paper, a new model-independent spatial-wavenumber filter based impact imaging method is proposed. In this method, a 2D cross-shaped array constructed by two linear piezoelectric (PZT) sensor arrays is used to acquire impact signal on-line. The continuous complex Shannon wavelet transform is adopted to extract the frequency narrowband signals from the frequency wideband impact response signals of the PZT sensors. A model-independent spatial-wavenumber filter is designed based on the spatial-wavenumber filtering technique. Based on the designed filter, a wavenumber searching and best match mechanism is proposed to implement the spatial-wavenumber filtering of the frequency narrowband signals without modeling, which can be used to obtain a wavenumber-time image of the impact relative to a linear PZT sensor array. By using the two wavenumber-time images of the 2D cross-shaped array, the impact direction can be estimated without blind angle. The impact distance relative to the 2D cross-shaped array can be calculated by using the difference of time-of-flight between the frequency narrowband signals of two different central frequencies and the corresponding group velocities. The validations performed on a carbon fiber composite laminate plate and an aircraft composite oil tank show a good impact localization accuracy of the model-independent spatial-wavenumber filter based impact imaging method.

Linearly dispersive signal construction of Lamb waves with measured relative wavenumber curves

Dispersion compensation is a vital issue in Lamb wave identification. Except for time reversal process (TRP), the commonly used compensation methods require the priori-knowledge of Lamb wave dispersion characteristics, which is usually derived in theory using the structure material parameters. However, the parameters could be probably unavailable, making the theoretical wavenumber relations hard to be attained. For the practical situation and considering the complexity of absolute wavenumber determination, linearly dispersive signal construction (LDSC) is presented for dispersion compensation of Lamb waves in this paper. LDSC can be performed not only with theoretical wavenumber curves but also with relative wavenumber curves, which can be easily measured without any structure material parameters. Thus, LDSC has high potential in Lamb wave detection for unknown structures. After the basic LDSC principle is fully explored based on the sensing model simplified in frequency domain, the numerical realization for LDSC is discussed. Then, a narrowband spectroscopy method is introduced for relative wavenumber curve measurement, and the applicability of LDSC with the measured relative wavenumber curves is theoretically investigated, which is subsequently validated with an aluminum plate experiment. Finally, associated with the traditional delay-and-sum algorithm, LDSC is used, as a typical application instance, for high spatial resolution Lamb wave imaging. The efficiency of the proposed LDSC and LDSC-based imaging is demonstrated by the experimental study on a glass fiber reinforced composite plate with unknown material parameters.

Rossby wave patterns in zonal and meridional winds

The propagation properties of Rossby waves in zonal and meridional winds are analyzed using the local dispersion relation in its wave number form, the geometry of which plays a crucial role in illuminating radiation patterns and ray trajectories. In the presence of a wind/current, the classical Rossby wave number curve, an offset circle, is distorted by the Doppler shift in frequency and a new branch, consisting of a blocking line with an eastward facing indentation, arises from waves convected with or against the flow. The radiation patterns generated by a time harmonic compact source in the laboratory frame are calculated using the method of stationary phase and are illustrated through a series of figures given by the reciprocal polars to the various types of wave number curves. We believe these results are new. Some of these wave patterns are reminiscent of a “reversed” ship wave pattern in which cusps (caustics) arise from the points of inflection of the wave number curves; whilst others bear a resemblance to the parabolic like curves characteristic of the capillary wave pattern formed around an obstacle in a stream. The Rossby stationary wave in a westerly is similar to the gravity wave pattern in a wind, whereas its counterpart in a meridional wind exhibits caustics, again arising from points of inflection in the wavenumber curve.

UV–Vis spectroscopic study and DFT calculation on the solvent effect of trimethoprim in neat solvents and aqueous mixtures

The solvatochromic behavior of trimethoprim (TMP) was analyzed using UV–Vis spectroscopy and DFT methods in neat and binary aqueous solvent mixtures. The effects of solvent dipolarity/polarizability and solvent–solute hydrogen bonding interactions on the absorption maxima were evaluated by means of the linear solvation energy relationship concept of Kamlet and Taft. This analysis indicated that both interactions play an important role in the position of the absorption maxima in neat solvents. The simulated absorption spectra of TMP and TMP:(solvent)n complexes in ACN and H2O using TD-DFT methods were in agreement with the experimental ones. Binary aqueous mixtures containing as co-solvents DMSO, ACN and EtOH were studied. Preferential solvation was detected as a nonideal behavior of the wavenumber curve respective to the analytical mole fraction of co-solvent in all binary systems. TMP molecules were preferentially solvated by the organic solvent over the whole composition range. Index of preferential solvation, as well as the influence of solvent parameters were calculated as a function of solvent composition.

Construction of multi-dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data

Kernels for non-local elasticity are in general obtained from phonon dispersion relations. However, non-local elastic kernels are in the form of three-dimensional (3D) functions, whereas the dispersion relations are always in the form of one-dimensional (1D) frequency versus wave number curves corresponding to a particular wave direction. In this paper, an approach to build 2D and 3D kernels from 1D phonon dispersion data is presented. Our particular focus is on isotropic media where we show that kernels can be obtained using Fourier–Bessel transform, yielding axisymmetric kernel profiles in reciprocal and real spaces. These kernel functions are designed to satisfy the necessary requirements for stable wave propagation, uniformity of nonlocal stress and stress regularization. The proposed concept is demonstrated by developing some physically meaningful 2D and 3D kernels that will find useful applications in nonlocal mechanics. Relative merits of the kernels obtained via proposed methods are explored by fitting 1D kernels to dispersion data for Argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations. A comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity.

Linear stability analysis of a slightly viscoelastic liquid jet

Gel propellant is one of the non-Newtonian viscoelastic liquids. The study of breakup of a gel propellant jet emanating from an injector has always been a fundamental task for a propulsion system with gel propellants. In this paper, a linear instability analysis method has been used to investigate the breakup of a slightly viscoelastic liquid jet. The disturbance wave growth rate of the axisymmetric mode has been determined by solving the dispersion equation of a slightly viscoelastic liquid jet, which was obtained by combining the linear instability theory and the linear viscoelastic model. Moreover, the maximum growth rate and corresponding dominant wave number have been observed, according to which maximum growth rate curves and dominant wave number curves have been plotted; this theory has been verified in the experiments of other authors. The time constant ratio, zero shear viscosity, liquid jet velocity, surface tension, liquid jet radius, liquid density and the gas density have been tested for their influence on the instability of the viscoelastic liquid jet. The results show that the effect of gas density is the greatest on the breakup of the viscoelastic jet, the jet velocity is affected second and the zero shear viscosity is least affected. However, the effects of other parameters are limited.

Electric-Field-Induced Instabilities in Thin Liquid Trilayers Confined between Patterned Electrodes

Electric-field-induced instabilities of trilayer of immiscible thin films confined between both planar and patterned electrodes have been explored by the linear stability analysis (LSA) and the long-wave nonlinear simulations. The twin liquid–liquid interfaces of a trilayer can undergo either in-phase bending or antiphase squeezing or mixed modes of evolution. The linear and nonlinear analyses together uncover the conditions under which these modes evolve and subsequently form an array of interesting, complex patterns. The study confirms that when the middle layer is of the highest or lowest dielectric permittivity than the other layers the interfaces undergo a squeezing mode of deformation. In other cases, the interfaces evolve in the bending mode, except for the situations where the linear growth coefficient versus wavenumber curves in the LSA show a bimodal behavior and the interfaces evolve in a mixed mode. The LSA also highlights the importance of the ratios of the thermodynamic parameters such as th...

High-pressure Raman spectra of l-histidine hydrochloride monohydrate crystal

Single-crystals of l-histidine hydrochloride monohydrate, C 6H 9N 3O 2·HCl·H 2O, were studied by Raman spectroscopy as a function of pressure in a diamond anvil cell up to 7.5 GPa at room temperature over the spectral range 3450–30 cm −1. The effect of changing pressure on the vibrational spectrum is discussed. From the analysis of results we inferred that the crystal undergoes a reversible structural phase transition between 2.7 and 3.1 GPa. This transition is characterized by the splitting of a band related to torsion of CO 2 −, the disappearance and appearance of modes related with stretching of OH − and deformation of CO 2 −, as well as with bands of low wavenumber which are assigned as lattice modes, and by the discontinuities of the curves of wavenumber versus pressure. Pressure coefficients for all modes observed in this work are also given.

Coupled wavenumbers of structural acoustic waveguides: A unified asymptotic approach

In the literature, the coupled wavenumbers in flexible‐walled acoustic waveguides have been found mainly using numerical methods for a fixed set of parameters. These solutions, although useful, do not continuously track the coupled wavenumbers as the fluid‐loading parameter is varied from small to large values. Such a continuous tracking is possible by applying the asymptotic methods to the coupled dispersion relation. Analytical formulae for the coupled wavenumbers can also be found. In this work, we present a consistent, unified and physically insightful view of structural acoustic coupling in the context of a planar structural‐acoustic waveguide (with two different BCs), the axisymmetric and beam modes of a fluid‐filled circular cylindrical shell and finally a fluid‐filled elliptic cylindrical shell. In all the five cases, we use a single fluid‐structure‐coupling asymptotic parameter (ε). The regular perturbation method is used to solve the coupled dispersion relation for small and large values of ε. The circular and the elliptic cylinders necessitate the use of additional asymptotic parameters. A general trend in all systems is that a given wavenumber branch transits from a rigid‐walled solution to a pressure‐release solution with increasing ε. Also, the wavenumber curves veer where the earlier uncoupled wavenumbers intersected.

Linear stability analysis of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

Temporal and spatiotemporal instabilities of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect have been investigated by a Chebyshev collocation method. Both situations corresponding to the fluid layer heated from below or from above have been studied. When heating is from below and for positive separation factors, the critical thresholds strongly increase when the throughflow is applied, and the boundary curves between absolute and convective instabilities (AI∕CI) increase as well, but more steeply. For large enough positive separation factors, there exist three local minima in the neutral curves Ra(k) (Rayleigh number against wavenumber) for moderate Reynolds numbers (Re), which results in the discontinuity of the critical wavenumber curve and the nonsmoothness of the critical Rayleigh number curve when the Reynolds number is varied. For negative separation factors, there exists a contact point between the critical Rayleigh number curve and the AI∕CI boundary curve at which the fluid system is directly changed from stable to absolutely unstable without crossing the convectively unstable region. This contact point has been characterized and localized for different negative separation factors. When heating is from above, the main observation is that the stationary curve obtained at Re=0 is replaced by two critical curves, one stationary and the other oscillatory, when a throughflow is applied. An energy budget analysis for the binary fluid system is also performed. A better insight into the role played by the solutal buoyancy contribution in the different situations is thus obtained.

Linear stability of ultrathin slipping films with insoluble surfactant

To study the dewetting process of ultrathin slipping films, the stability characteristics of the surfactant-covered ultrathin films with slippage are analyzed with linear theory. A set of nonlinear equations for the film thickness and the concentration of surfactant is derived based on lubrication approximation for Newtonian viscous fluid. Results show slippage can always enhance the development of perturbations, and reduce the number density of holes when rupture occurs. A prominent characteristic of the stability is that two branches of solutions are found in the dispersion relation. This might lead to an inflexion in the growth rate curve of the most unstable modes, and a cusp point in the corresponding wave number curve for infinite slippage, which indicates that the slip has a profound effect on the linear stability of the films. The influences of the Marangoni number M, equilibrium distance lc, and the base concentration of surfactant Γ0 on the linear stability are also discussed for different slip lengths in the present study.

A multimodel method for depth estimation from magnetic data

The local wavenumber and a multimodel wavenumber are complex attributes derived from a complex analytic signal. These quantities have been used to interpret anomalies arising from contacts, thin sheets, and horizontal cylinders. A new multimodel wavenumber can be used for computing depths of 2-D thick dikes and 2-D sloping steps. These two multimodel wavenumbers have been incorporated into a depth-estimation algorithm based on automatic curve matching. This algorithm works on profile data and has three appealing features: (1) the most appropriate of these five models is selected automatically; (2) the automatic curve matching uses a least-squares technique to reject responses that do not conform to the model assumptions; and (3) interference from distant sources can be accounted for as a base-level shift of the multimodel wavenumber curves. Applying the automatic technique to survey data from the Western Canada sedimentary basin yields four thick dikes between 3400 and 4300 m below sensor. These depths are equivalent to 2.2 and 3.1 km below sea level, which is consistent with the basement depths derived from drillhole information. Using these solutions as a starting point in an iterative forward modeling exercise, the measured data were explained with a geologically reasonable model.