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Interference is widely regarded as a foundational attribute of quantum mechanics. However, for a given experimental arrangement, interference can either contribute or not contribute to the outcome depending upon the basis in which it is measured. This observation is both foundational and particularly relevant to coherent control of molecular processes, an approach based upon quantum interference. Here, we address this issue and its relevance to controlling molecular processes via the "coherent control scattering (CCS) matrix," a formalism that allows for an analysis of modifications in an interference structure resulting from a change of basis. This analysis reveals that the change in the interference structure can be attributed to the non-commutativity of the transformation matrix with the CCS matrix and the non-orthogonality of the transformation. Additionally, minimal interference is shown to be associated with the CCS eigenbasis and that the Fourier transform of the eigenvectors of the CCS matrix provides the maximal interference and hence the best coherent control. The change of controllability through a change of basis is illustrated with an example of 85Rb+ 85Rb scattering. In addition, the developed formalism is applied to explain recent experimental results on He + D2 inelastic scattering demonstrating the presence or absence of interference depending on the basis. [ABSTRACT FROM AUTHOR]

A frequency-dependent dielectric constant characterizes the dielectric response of a medium and also represents the time scale of system's collective dynamics. Although it is valuable not only academically but also practically for developing advanced devices, getting the value of a solution at the interface with a solid or electrode surface is challenging both experimentally and computationally. Here, we propose a computational method that imitates the dielectric spectroscopy and AC impedance measurement. It combines a time-dependent voltage applied molecular dynamics simulation with an equivalent circuit representation of a system composed of a solution confined between two identical electrodes. It gives the frequency-dependent dielectric constants of the bulk solution and the interface simultaneously. Unlike the conventional method, it does not require computation of a dipole autocorrelation function and its Fourier transformation. Application of the method on a system of water confined between polarizable Pt electrodes gives the static dielectric constant and the relaxation time of the bulk water in good agreement with previous simulation results and experimental values. In addition, it gives a much smaller static dielectric constant at the interface, consistent with previous observations. The outline of the dielectric dispersion curve of the interface seems similar to that of the bulk, but the relaxation time is several times faster. [ABSTRACT FROM AUTHOR]

A new free-energy functional is proposed for inhomogeneous associating fluids. The general formulation of Wertheim's thermodynamic perturbation theory is considered as the starting point of the derivation. We apply the hypotheses of the statistical associating fluid theory in the classical density functional theory (DFT) framework to obtain a tractable expression of the free-energy functional for inhomogeneous associating fluids. Specific weighted functions are introduced in our framework to describe association interactions for a fluid under confinement. These weighted functions have a mathematical structure similar to the weighted densities of the fundamental-measure theory (i.e., they can be expressed as convolution products) such that they can be efficiently evaluated with Fourier transforms in a 3D space. The resulting free-energy functional can be employed to determine the microscopic structure of inhomogeneous associating fluids of arbitrary 3D geometry. The new model is first compared with Monte Carlo simulations and previous versions of DFT for a planar hard wall system in order to check its consistency in a 1D case. As an example of application in a 3D configuration, we then investigate the extreme confinement of an associating hard-sphere fluid inside an anisotropic open cavity with a shape that mimics a simplified model of zeolite. Both the density distribution and the corresponding molecular bonding profile are given, revealing complementary information to understand the structure of the associating fluid inside the cavity network. The impact of the degree of association on the preferential positions of the molecules inside the cavity is investigated as well as the competition between association and steric effect on adsorption. [ABSTRACT FROM AUTHOR]

The linear double-diffusivity (D-D) model of Aifantis, comprising two coupled Fick-type partial differential equations and a mass exchange term connecting the diffusivities, is a paradigm in modeling mass transport in inhomogeneous media, e.g., fissures or fractures. Uncoupling of these equations led to a higher order partial differential equation that reproduced the non-classical transport terms, analyzed independently through Barenblatt's pseudoparabolic equation and the Cahn–Hilliard spinodal decomposition equation. In the present article, we study transport in a nonlinearly coupled D-D model and determine the regime-switching of the associated diffusive processes using a revised formulation of the celebrated Lux method that combines forward Fourier transform with a Laplace transform followed by an Inverse Fourier transform of the governing reaction–diffusion (R–D) equations. This new formulation has key application possibilities in a wide range of non-equilibrium biological and financial systems by approximating closed-form analytical solutions of nonlinear models. [ABSTRACT FROM AUTHOR]

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data. [ABSTRACT FROM AUTHOR]

A comparison is made between the three principal methods for the analysis of neutron and x-ray diffraction data from noble gas fluids by direct Fourier transform. All three methods (standard Fourier transform, Lorch modification, and Soper–Barney modification) are used to analyze four different sets of diffraction data from noble gas fluids. The results are compared to the findings of a full-scale real-space structure determination, namely, Empirical Potential Structure Refinement. Conclusions are drawn on the relative merits of the three Fourier transform methods, what information can be reliably obtained using each method, and which method is most suitable for the analysis of different kinds of diffraction data. The mathematical validity of the Lorch method is critically analyzed. [ABSTRACT FROM AUTHOR]

The first finite basis set implementation of the real-time time-dependent self-consistent field method in a dynamic (time-dependent) magnetic field using London atomic orbitals (LAOs) is presented. The accuracy of the finite basis approach using LAOs is benchmarked against numerical results from the literature for the hydrogen atom and H2 in the presence of rapidly oscillating magnetic fields. This comparison is used to inform the choice of appropriate basis sets for studies under such conditions. Remarkably, relatively modest compact LAO basis sets are sufficient to obtain accurate results. Analysis of electron dynamics in the hydrogen atom shows that LAO calculations correctly capture the time evolution of orbital occupations. The Fourier transformation of the autocorrelation function yields a power spectrum exhibiting harmonics associated with coherent emission, which closely matches the literature and further confirms the accuracy of this approach. The dynamical response of the electron density in H2 for a magnetic field parallel to the internuclear axis shows similar behavior to benchmark studies. The flexibility of this implementation is then demonstrated by considering how the dynamical response changes as a function of the orientation of the molecule relative to the applied field. At non-parallel orientations, the symmetry of the system is lowered and numerical benchmark data, which exploit cylindrical symmetry, are no-longer readily available. The present study demonstrates the utility of LAO-based calculations for extreme dynamic magnetic fields, providing a stress-test on the choice of basis. Future applications of this approach for less extreme dynamic magnetic fields are briefly discussed. [ABSTRACT FROM AUTHOR]

Non-impact effects in the absorption spectra of HCl in various collision-partners are investigated both experimentally and theoretically. Fourier transform spectra of HCl broadened by CO2, air, and He have been recorded in the 2-0 band region at room temperature and for a wide pressure range, from 1 to up to 11.5 bars. Comparisons between measurements and calculations using Voigt profiles show strong super-Lorentzian absorptions in the troughs between successive lines in the P and R branches for HCl in CO2. A weaker effect is observed for HCl in air, while for HCl in He, Lorentzian wings are in very good agreement with measurements. In addition, the line intensities retrieved by fitting the Voigt profile on the measured spectra decrease with the density of the perturber. This perturber-density dependence decreases with the rotational quantum number. For HCl in CO2, the decrease in the retrieved line intensity can reach 2.5% per amagat for the first rotational quantum numbers. This number is about 0.8% per amagat for HCl in air, while for HCl in He, no density dependence of the retrieved line intensity is observed. Requantized classical molecular dynamics simulations have been performed for HCl–CO2 and HCl–He in order to simulate the absorption spectra for various perturber-density conditions. The density dependence of the intensities retrieved from the simulated spectra and the predicted super-Lorentzian behavior in the troughs between lines are in good agreement with experimental determinations for both HCl–CO2 and HCl–He. Our analysis shows that these effects are due to incomplete or ongoing collisions, which govern the dipole auto-correlation function at very short times. The effects of these ongoing collisions strongly depend on the details of the intermolecular potential: they are negligible for HCl–He but significant for HCl–CO2 for which a line-shape model beyond the impact approximation will be needed to correctly model the absorption spectra from the center to the far wings. [ABSTRACT FROM AUTHOR]

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used. [ABSTRACT FROM AUTHOR]

A novel quinoxaline-based phthalonitrile monomer, namely, 4,4′-(((quinoxaline-2,3-diylbis (oxy))bis (3,1-phenylene))bis (oxy))di-phthalonitrile (QDOP), was successfully synthesized by nucleophilic substitution reaction, which exhibits a low melting point (85°C) and a wide processing window (150°C). The QDOP monomer was cured with 4-aminophenoxy phthalonitrile (APPH) as catalyst by different temperature programs, and the curing process and kinetics were discussed in detail by non-isothermal differential scanning calorimetric (DSC). The QDOP polymer mainly forms triazine, isoindoline and phthalocyanine structure, as revealed by Fourier transform infrared (FTIR) spectroscopy, and its properties improved with the increase of post-curing temperature and curing time. After post-curing at 380°C, the polymer exhibited high storage modulus (3731 MPa), high glass-transition temperature (>400°C), and outstanding thermal stability and thermal oxidation stability. [ABSTRACT FROM AUTHOR]

Glass-nanocomposites (GNCs) samples of composition [(100−x) Li2B4O7–xPbTiO3] with x = 5, 10, 15 and 20 mol% were prepared by melt quenching method. The two phases of the GNCs samples, a glassy phase and PbTiO3 nanoparticles/clusters phase, can be seen in the energy dispersive X-ray spectra and scanning electron microscopic micrographs. Fourier transformation infrared spectra of the GNCs samples exhibited bands due to triangular with NBO's and tetrahedral borate groups. Additionally, the Ti4+ ions exist in both TiO4 and TiO6 structural units while the Ti3+ ions exist in TiO6 structural units. The electron spin resonance (ESR) spectra of the GNCs samples exhibit two ESR signals, broad and narrow, corresponding to the Ti3+ (3d1) ions in both tetragonal deformed octahedral and in the other structural configuration, respectively. The optical transmission spectra of the GNCs samples exhibited three transmission bands, 3Γ5 → 2Γ3, 2B2g → 2B1g and 2B2g → 2A1g transitions, in the visible region. The variation in optical band gap (Eopt) with increasing PbTiO3 content were due to the conversion between BO3 with NBOs and BO4 units as well as the reduction of Ti4+ to Ti3+ ions in the GNCs matrix. These results demonstrate that the present GNCs may be used for practical applications such as optical devices. [ABSTRACT FROM AUTHOR]

• Dynamic loaded tooth contact analysis (DLTCA) for computing entrainment speed. • Accurate solution to elastohydrodynamic lubrication (EHL) governing equation. • Discrete convolution and fast Fourier transformation (DC-FFT) for flank elastic deformation. • A separation flow method for iteration of EHL governing equation. • Accurate entrainment effect-based EHL forecasting model for hypoid gears. In full consideration of time-varying meshing performance and oil film characteristics, entrainment effect on elastohydrodynamic lubrication (EHL) is developed for establishing accurate forecasting model of the complex hypoid gears. Firstly, dynamic loaded tooth contact analysis (DLTCA) is employed to determine the meshing interface kinematics, load distribution and entrainment speed under dynamic load condition. Then, entrainment speed is introduced into the EHL governing equation and accurate forecasting model is established. With accurate discretization of EHL governing equation, discrete convolution and fast Fourier transformation (DC-FFT) method is employed to compute the flank elastic deformation. Finally, a hypoid gear set in automotive industrial application is exercised to verify entrainment effect on EHL assessment in the proposed model. [ABSTRACT FROM AUTHOR]

In the industrial application of bacterial cellulose (BC), the yield becomes a crucial factor because it drives the selling price of BC. A Box–Behnken experimental design with three components and three levels was employed to create seventeen samples. A response surface method was then used to optimize the BC yield from the most relevant parameters, including incubation temperature, medium shaking intensity, and nitrogen supply pH. Fourier transform infrared (FTIR) analysis proved that BC was pure. By analyzing BC morphology using scanning electron microscopy (SEM), rod-like microfibrils with an average diameter of 6.5 were revealed. X-ray diffraction (XRD) tested the crystalline size and crystallinity and found 4.7 nm and 69%, respectively. Thermal transition and stability were assessed using a differential scanning calorimeter (DSC) and a thermogravimetric analyzer (TGA). For the manufacture of BC composite hydrogel, a chemical test method was used to determine the solubility of BC. This study aimed to identify the ideal circumstances for using leftover sweet lime pulp for biomedical applications to produce reasonably priced and effective BC. At 28.87 °C, 125.91 rpm shaking frequency, and 5.65 pH, a sweet lime pulp waste medium produced the highest yield of BC, three times greater than the yield in a Hestrin–Schramm medium under static circumstances. [ABSTRACT FROM AUTHOR]

This work is carried out using the generalized thermoelastic model to study the variation of temperature, the stresses, and displacement components in a two-dimensional orthotropic elastic material. The Fourier–Laplace integral transforms to get the analytical solution of the problem, the basic formulations of the two-dimensional problem are expressed as matrix-vector forms, which are then solved by the eigenvalue technique. Numerical techniques are used for the inverse process of the Laplace and Fourier transform. The results of all the variables considered are implemented and represented graphically. The outcomes of the current model are compared with those of the existent model of thermoelasticity. [ABSTRACT FROM AUTHOR]

The antiplane deformation of a two layered model consisting of a homogeneous, elastically isotropic (HEI) stratum of finite thickness lying on a HEI substratum occurring from a buried inclined strike-slip fault (ISF) situated in the stratum has been studied. The stratum is in welded contact with the substratum having different rigidity. The integral expressions for the deformation field occurring from a long strike-slip line dislocation for the antiplane strain case have been obtained using Fourier transform approach. The integrals have been solved analytically by expanding the denominator into a finite sum of exponential terms (FSET) using least square method. Further, the deformation is obtained for a long buried ISF of finite width via integrating over the width of line dislocation. The variation of the displacement has been computed graphically with respect to the epicentral distance as well as with depth. [ABSTRACT FROM AUTHOR]

In this article, the nonclassical transient heat propagation process in a cracked strip is investigated by Guyer–Krumhansl (G–K) model, which incorporates both the time lagging behavior and the spatially nonlocal effect. The impulsive thermal loading as well as cyclic loading exerted on the top bounding surface are examined to explore the non-Fourier thermal characteristics. By means of the Laplace transform and Fourier transform, the governing partial differential equations subjected to mixed boundary conditions are converted to a group of singular integral equations. With the aid of numerical Laplace inversion, the transient temperatures are calculated to make comparisons of thermal responses determined by Fourier's law, Cattaneo–Vernotte (C–V) equation, and G–K model. The numerical results display the specific thermal behaviors of G–K model in the cracked medium and demonstrate the G–K model's capabilities in eliminating the unrealistic phenomena accompanied by C–V equation. Our research would contribute to achieving a better understanding of the transient heat conduction in small-sized systems or composites at the macroscopic scale. [ABSTRACT FROM AUTHOR]

The behavior of axisymmetric cylinders under various surface loading has remained the topic of research for many years. Most of the solutions presented in the literature are load-specific. Therefore a general solution is sought to satisfy any boundary conditions prescribed on any surface. This paper presents a general solution to satisfy a wide combination of boundary conditions prescribed on the curved as well as on the flat ends of a cylinder. A hollow cylinder was considered, composed of transversely isotropic material. The formulation is based on the variational principle, resulting in a set of coupled governing equations and associated boundary conditions. The solutions to the coupled governing partial differential equations are obtained by systematically decoupling them, followed by the method of separation of variables and the Frobenius method. All the boundary conditions are satisfied by making use of either the Fourier or the Fourier–Bessel transformation. The solutions for various test cases were validated by comparing them against three-dimensional solutions obtained using finite-element analysis. The solution for the solid cylinder was obtained by considering the limiting case of the internal radius approaching Zero. [ABSTRACT FROM AUTHOR]

The windowed coupled fractional Fourier transform was recently proposed in the literature. It may be considered as a generalized version of the windowed fractional Fourier transform. In this study, we first present various basic properties of the windowed coupled fractional Fourier transform including linearity, shifting, modulation, parity, orthogonality relation, and inversion formula. Further, the close relation of the windowed coupled fractional Fourier transform with the two‐dimensional Fourier transform and the windowed fractional Fourier transform is studied. By combining the properties and relation, we derive several versions of the uncertainty inequalities related to the windowed coupled fractional Fourier transform. [ABSTRACT FROM AUTHOR]

Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform (GFT). Singular values, commonly employed in feature extraction and fault diagnosis, effectively encapsulate various fault states of mechanical equipment. However, prior methods neglect the inter-relationships among singular values, resulting in the loss of subtle fault information concealed within. To precisely and effectively extract subtle fault information from gear vibration signals, this study incorporates graph signal processing (GSP) technology. Following SVD of the original vibration signal, the method constructs a graph signal using singular values as inputs, enabling the capture of topological relationships among these values and the extraction of concealed fault information. Subsequently, the graph signal undergoes a transformation via GFT, facilitating the extraction of fault features from the graph spectral domain. Ultimately, by assessing the Mahalanobis distance between training and testing samples, distinct defect states are discerned and diagnosed. Experimental results on bearing and gear faults demonstrate that the proposed method exhibits enhanced robustness to noise, enabling accurate and effective diagnosis of gearbox faults in environments with substantial noise. [ABSTRACT FROM AUTHOR]

State-of-the-art smart cities have been calling for economic but efficient energy management over a large-scale network, especially for the electric power system. It is a critical issue to monitor, analyze, and control electric loads of all users in the system. In this study, a non-intrusive load monitoring method was designed for smart power management using computer vision techniques popular in artificial intelligence. First of all, one-dimensional current signals are mapped onto two-dimensional color feature images using signal transforms (including the wavelet transform and discrete Fourier transform) and Gramian Angular Field (GAF) methods. Second, a deep neural network with multi-scale feature extraction and attention mechanism is proposed to recognize all electrical loads from the color feature images. Third, a cloud-based approach was designed for the non-intrusive monitoring of all users, thereby saving energy costs during power system control. Experimental results on both public and private datasets demonstrate that the method achieves superior performances compared to its peers, and thus supports efficient energy management over a large-scale Internet of Things network. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of weak maneuvering target detection in the space-based bistatic radar system through long-time coherent integration (LTCI). The space-based bistatic radar is vulnerable to the high-order range migration (RM) and Doppler frequency migration (DFM), since the target, the receiver and the transmitter all can play fast movement independently. To correct high- order RM and DFM, this usually involves joint high-dimensional parameter searching, incurring a large computational burden. In our previous work, a dual-scale (DS) decomposition of motion parameters was proposed, in which the optimal GRFT is conditionally decoupled into two cascade procedures called the modified generalized inverse Fourier transform (GIFT) and generalized Fourier transform (GFT), resulting in the DS-GRFT detector. However, even if the DS-GRFT detector preserves the superior performance and dramatically decreases the complexity, high-dimensional searching is still required. In this paper, by analyzing the structure of the DS-GRFT detector, we further designed a conditioned cubic phase function (CCPF) tailored to the range–slow-time signal after GIFT, breaking the joint high-dimensional searching into independent one-dimensional searching. Then, by connecting the proposed CCPF with the GIFT, we achieved a new LTCI detector called the DS-GIFT-CCPF detector, which obtained a significant computational cost reduction with acceptable performance loss, as demonstrated in numerical experiments. [ABSTRACT FROM AUTHOR]

In this study, the plane continuous and discontinuous contact problems between a graded piezoelectric layer and a homogeneous piezoelectric half plane are considered. The layer is pressed by a rigid conducting flat punch with an electrical load. The problem is converted using Fourier integral transform into a singular integral equation. This equation is then solved numerically by applying the Gauss-Chebychev integration formula. The primary objective of this article is to investigate the effect of varying several parameters including the contact length, the mechanical and electrical loads, and the graded layer non-homogeneity parameter on the contact stresses and on the normal electric displacement. [ABSTRACT FROM AUTHOR]

Fourier transform points out that a certain function that meets certain conditions can be decomposed into a linear combination of trigonometric functions (sine or cosine functions). The functions of high-order cumulant include suppressing the Gaussian noise, eliminating independent signal components, and identifying the phase coupling phenomenon of the signal. To prove this hypothesis, this study constructs a cosine signal with the phase coupling phenomenon based on Fourier transform theory which substitutes it into the third-order cumulant expression and performs detailed reasoning. The constructed signal is extended to the complex signal domain and the same conclusion is obtained. The number of coupled signals is expanded from three to a higher value. The results of the study give definite mathematical and physical meaning to the bispectral peaks. The collected mechanical vibration signals are given to demonstrate this conclusion. The demonstrated characteristics of high-order cumulants have made them widely used in many fields. [ABSTRACT FROM AUTHOR]

• The accuracy of MODIS IR PWV is poor. • The GPS station and MODIS pixel points do not coincide completely in point position. • The problems of spatial interpolation and calibration model are considered in MODIS calibration process. • Compared with the original MODIS IR PWV, the accuracy of the new model is greatly improved in all aspects. • MODIS IR PWV of the new model is in good agreement with GPS PWV. The monitoring of precipitable water vapor (PWV) is of significant importance for meteorological research and rainstorm prediction. The moderate resolution imaging spectroradiometer (MODIS) is one of the most widely used remote sensing PWV instruments aboard the Terra and Aqua satellites. The main objective of this study is to develop a fused inverse distance weighting and the Fourier transform model (FIDWFT) to calibrate MODIS Infrared (IR) PWV. In this research, one year of ground observation data from 17 GPS stations were utilized to evaluate the accuracy of MODIS IR PWV in Hong Kong. Initially, the PWV obtained by one radiosonde was used to verify the GPS PWV. Comparison between GPS and radiosonde showed good agreement with an R-squared of 0.97. After the estimation of GPS PWV in the study area was evaluated, MODIS IR products in the study area were extracted for evaluation. The comparison between MODIS and GPS showed that the R-squared is 0.81 and the mean bias (MB) is −1.60 mm. Considering the spatial interpolation and calibration problems of MODIS products, new model used an inverse distance weighting method to make MODIS IR PWV and GPS PWV completely coincide in space, and fifteen MODIS pixel points were selected for interpolation. Then the MODIS IR PWV was calibrated by GPS PWV using Fourier transform model. Results showed that compared with the MODIS IR PWV before calibration, the R-squared increases from 0.81 to 0.94, the root mean square error decreases from 8.72 mm to 4.98 mm, and the MB decreases from −1.60 mm to −0.83 mm. Therefore, the method is feasible to estimate MODIS IR water vapor, and it achieves better results. [ABSTRACT FROM AUTHOR]

We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals. [ABSTRACT FROM AUTHOR]

Background Atopic dermatitis (AD) is characterized by skin barrier defects that are often measured by biophysical tools that observe the functional properties of the stratum corneum (SC). Objectives To employ in vivo infrared spectroscopy alongside biophysical measurements to analyse changes in the chemical composition of the SC in relation to AD severity. Methods We conducted an observational cross-sectional cohort study where attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy measurements were collected on the forearm alongside surface pH, capacitance, erythema and transepidermal water loss (TEWL), combined with tape stripping, in a cohort of 75 participants (55 patients with AD stratified by phenotypic severity and 20 healthy controls). Common FLG variant alleles were genotyped. Results Reduced hydration, elevated TEWL and redness were all associated with greater AD severity. Spectral analysis showed a reduction in 1465 cm–1 (full width half maximum) and 1340 cm–1 peak areas, indicative of less orthorhombic lipid ordering and reduced carboxylate functional groups, which correlated with clinical severity (lipid structure r = –0.59, carboxylate peak area r = –0.50). Conclusions ATR-FTIR spectroscopy is a suitable tool for the characterization of structural skin barrier defects in AD and has potential as a clinical tool for directing individual treatment based on chemical structural deficiencies. [ABSTRACT FROM AUTHOR]

BACKGROUND: Carboxymethylpachymaran (CMP) is created by carboxymethylating pachyman (PM), which increases its water solubility and enhances a number of biological activities. Traditional polysaccharides modified by carboxymethylation employ strong chemical techniques. Carboxymethylcellulose (CMC) has been used previously for liquid fermentation to carboxymethyl modify bacterial polysaccharides. This theory can be applied to fungal polysaccharides because Poria cocos has the ability to naturally utilize cellulose. RESULTS: CMC with different degrees of substitution (DS) (0.7, 0.9 and 1.2) were added to P. cocos fermentation medium, and CMPs with different DS (0.38, 0.56 and 0.78, respectively) were prepared by liquid fermentation. The physical and chemical properties and biological activities of the CMPs were determined. Their structures were confirmed by Fourier transform infrared (FTIR) spectroscopy and monosaccharide composition. With the increase of DS, the viscosity and viscosity‐average molecular weight of CMPs decreased, whereas polysaccharide content and water solubility increased, although the triple helix structure was not affected. The results of bioactivity assay showed that the higher the DS of CMPs, the higher the 2,2‐diphenyl‐1‐picrylhydrazyl radical scavenging ability, and the stronger the bacterial inhibition ability. CONCLUSION: The present study has developed a method for producing CMPs by P. cocos liquid fermentation. The results of the study confirm that enhancing the DS of CMP could effectively enhance its potential biological activity. The findings provide safe and reliable raw materials for creating CMP‐related foods and encourage CMP application in the functional food industry. © 2024 Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

Using the data from weather observation stations, an assessment of statistical significance of the first harmonic amplitude of the long-term average daily precipitation series in Russia in 1961‒2020 and their changes in 1991‒2020 compared to 1961‒1990 is made. It is shown that at most stations the first harmonic has a reliable value different from the noise, except for eleven stations in the southern regions of the European part of Russia. It is revealed that on average there is a significant decrease in the first harmonic amplitudes of the daily precipitation series across Russia. An analysis of the spatial distribution of the studied quantities is performed and the presence of large areas with their homogeneous character is demonstrated. [ABSTRACT FROM AUTHOR]

This study achieves the successful immobilization of simulated alpha- and beta-emitting radionuclides (Nd3+ and Sr2+, respectively) by incorporating them into a glass matrix through Nd2O3/SrSO4 (Nd/Sr). Varying mixture concentrations (5–30 wt% with mass ratios Nd:Sr varied from 10:1 to 1:10) in simulated radioactive soils were subjected to microwave sintering at 1500 °C for 0.5 h. Comprehensive assessments, including X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectra, scanning electron microscopy (SEM), and energy dispersive X-ray spectrometry (EDS), confirm the vitrification process's efficacy. The vitrified sample exhibits an amorphous structure, smooth surface, and homogeneously distributed elements, highlighting microwave sintering as a promising method for the effective disposal of radioactive-contaminated soil. [ABSTRACT FROM AUTHOR]

The influence of apparent slip on oscillatory shear measurements of a viscoplastic microgel [0.6 wt. % of poly(acrylic acid)] is analyzed by Couette and parallel-plate rheometry and particle image velocimetry (Rheo-PIV). We first provide direct evidence of a critical shear stress for the onset of slip of the microgel under oscillatory (σos) and nonoscillatory measurements (σs). Afterward, we describe the effect of slip on oscillatory measurements via waveforms, Bowditch–Lissajous curves, Fourier transform (FT) rheology, PIV, and as a sequence of physical processes (SPP). The effect of slip is mainly observed at low oscillating frequencies. For amplitudes of the oscillating stresses σ0 ≤ σos, the microgel exhibits linear viscoelastic behavior with in-phase strain response. For σos< σ0 ≤ yield stress (σy), slip introduces a phase shift in the strain response with a forward-tilted waveform and "mango" shape Bowditch–Lissajous curves. Meanwhile, FT rheology shows negligible even harmonics. The strain measured by the rheometer does not match the true strain determined by PIV in the presence of slip, resulting in waveforms that depend on how the displacement distribution is interpreted. This result indicates a break in the symmetry of the flow, that is, the microgel response no longer follows the imposed oscillation, which makes any attempt to correct oscillatory data for slip complex. This behavior arises from recoil of the slipping microgel after reaching its maximum displacement in a cycle. Finally, we provide an overall picture of the kinematics of the process of yielding in the presence of slip as an SPP. [ABSTRACT FROM AUTHOR]

We theoretically investigate the propagation properties of a Laguerre higher order cosh Gaussian beam (LHOchGB) in a fractional Fourier transform (FRFT) optical system. Based on the Collins formula and the expansion of the hard aperture function into a finite sum of Gaussian functions, we derive analytical expressions for a LHOchGB propagating through apertured and unapertured FRFT systems. The analysis of the evolution of the intensity distribution at the output plane has shown from the obtained expressions, using illustrative numerical examples. The results show that the intensity distribution of the considered beam propagating in FRFT is significantly influenced by the source beam parameters and the parameters of the FRFT system. It is possible to demonstrate the potential benefits of the results obtained for applications in laser beam shaping, optical trapping, and micro-particle manipulation. [ABSTRACT FROM AUTHOR]

In this study, an effect that we will call entanglement closed loop (ECL) and that results from the implementation of entangled states through quantum Fourier transform (QFT) blocks, is presented. The dual-channel Bell test can be implemented using two linear polarizers (LP) or two half-wave plates (HWP). ECL allows us to verify that the arbitrary relocation of both the LPs and the HWPs is indifferent when it comes to reproducing the results of quantum mechanics. Implementations of two conspicuous relocations of the LPs on an optical table experimentally prove the existence of the entanglement closed loop. Finally, a new interpretation of quantum mechanics based on ECL, which explains the operation of a new family of quantum communications protocols, is presented. [ABSTRACT FROM AUTHOR]

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit δ (f ; Ω) which measures by how much the STFT of a function f ∈ L 2 (R) fails to be optimally concentrated on an arbitrary set Ω ⊂ R 2 of positive, finite measure. We then show that an optimal power of the deficit δ (f ; Ω) controls both the L 2 -distance of f to an appropriate class of Gaussians and the distance of Ω to a ball, through the Fraenkel asymmetry of Ω . Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context. [ABSTRACT FROM AUTHOR]

The aim of this work is to quantitatively assess the wavefront phase of keratoconic eyes measured by the ocular aberrometer t·eyede (based on WaveFront Phase Imaging Sensor), characterized by a lateral resolution of 8.6 µm without requiring any optical element to sample the wavefront information. We evaluated the parameters: root mean square error, Peak-to-Valley, and amplitude of the predominant frequency (Fourier Transform analysis) of a section of the High-Pass filter map in keratoconic and healthy cohorts. Furthermore, we have analyzed keratoconic eyes that presented dark–light bands in this map to assess their period and orientation with the Fourier Transform. There are significant statistical differences (p value < 0.001) between healthy and keratoconic eyes in the three parameters, demonstrating a tendency to increase with the severity of the disease. Otherwise, the quantification of the bands reveals that the width is independent of eye laterality and keratoconic stage as orientation, which tends to be oblique. In conclusion, the quantitative results obtained with t·eyede could help to diagnose and monitor the progression of keratoconus. [ABSTRACT FROM AUTHOR]

In this study, the two-dimensional dynamic contact problem between a rigid flat punch and a viscoelastic orthotropic layer is investigated. The motivation of the study is to provide a better understanding of the vertical vibration of the two-parameter Winkler–Pasternak foundation, which has not yet been investigated. For the contact problem, the mixed boundary conditions on the top and bottom surfaces are transformed into linear equations using the Fourier transform technique and Helmholtz functions. Based on the Gauss–Chebyshev integration formula, the singular integral equation is obtained and solved numerically. As a result of the solutions, the effects of various parameters on the contact stresses are analyzed and examples are given. It was found that the Winkler foundation modulus does not affect the dynamic contact stress, while the Pasternak foundation modulus significantly affects the contact stress. [ABSTRACT FROM AUTHOR]

Information on boll distribution within a cotton plant is critical to evaluate the adaptation and response of cotton plants to environmental and biotic stress in cotton production. Cotton researchers have applied available conventional fiber measurements, such as the high volume instrument (HVI) and advanced fiber information system (AFIS), to map the location and the timing of boll development and distribution within plants and further to determine within-plant variability of cotton fiber properties. Both HVI and AFIS require numerous cotton bolls combined for the measurement. As an alternative approach, attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy was proposed to measure fiber maturity (MIR) and crystallinity (CIIR) of a sample as little as 0.5 mg lint. Extending fiber maturity and crystallinity measurement into a single boll for node-by-node mapping, FT-IR method might be advantageous due to less sampling amount compared with HVI and AFIS methods. Results showed that FT-IR technique enabled the evaluation of fiber MIR and CIIR at a boll level, which resulted in average MIR and CIIR values highly correlated with HVI micronaire (MIC) and AFIS maturity ratio (M). Hence, FT-IR technique possesses a good potential for a rapid and non-destructive node-by-node mapping of cotton boll maturity and crystallinity distribution. [ABSTRACT FROM AUTHOR]

Spectrally resolved interferometry utilizing a femtosecond laser is widely employed for absolute distance measurement. However, deviations in the output time pulse of the conventional algorithm through inverse Fourier transform are inevitable. Herein, an improved data processing algorithm employing a time-shifting parameter is proposed to improve the accuracy of spectrally resolved interferometry. The principle of the proposed time-shifting algorithm is analyzed theoretically after clarifying the deviation source of the conventional algorithm. Simulation and experimental work were conducted to indicate the improvement in the accuracy of the output absolute distance. The results demonstrated that the proposed algorithm could reduce the deviation of output distances towards the reference values, reaching 0.58 μm by half compared to the conventional algorithm. Furthermore, the measurement uncertainty was evaluated using the Guide to the Expression of Uncertainty in Measurement (GUM), resulting in an expanded uncertainty of 0.71 μm with a 95% confidence. [ABSTRACT FROM AUTHOR]

This study presents a new approach to determining the preload force of bolted joints. The concept involves measuring the torsional angle without contact. For this purpose, we present a circular magnetic sensor array integrated into the torque wrench. The torsional angle in bolted joints depends on the dimensions of the screw and the materials used and is typically less than four degrees. For this reason, one requirement is a high angular resolution so that a continuous recording of the torsion angle is feasible during the assembly process. This can be achieved using the circular sensor array and adapted signal processing methods. Two signal processing approaches are utilized. First, the direct method uses the discrete Fourier transformation to calculate the rotation angle from the signal phase. This approach is robust to signal distortion and does not depend on signal amplitude. Second, the method with a learning phase employs Gaussian process regression to minimize the angle error. In an experiment, both approaches were applied within a test bench and showed promising results. The direct method demonstrated a very good angular resolution without training and calibration. For mobile and less-complex applications where a reference system is unavailable, the direct method is preferable. However, in complex measurement systems where reference systems can be utilized initially, significant enhancements to an excellent resolution can be achieved through prior training. [ABSTRACT FROM AUTHOR]

• Size-dependent near-surface response of FG elastic layer is investigated. • Size effects induced by material microstructures are modeled by couple stress elasticity theory. • Solution of surface loaded layer is derived in closed-form via Fourier transform method. • Efficient numerical scheme is implemented for layer under frictionless contacts. • Effects of length scale and model's parameters on contact response are highlighted. This paper focuses on a theoretical examination of the mechanical behavior of elastic layers made of functionally graded (FG) materials. It particularly highlights the impact of material microstructures by utilizing the couple stress theory to introduce FG characteristics of the coating material across the thickness direction, along with size effects. The study distinctively addresses both surface loading and contact problems, employing various indenter shapes and eccentric indentation forces. The Fourier transform is utilized to solve for displacements and stress fields resulting from surface tractions. The method for approximating the pressure distribution under the indenter is based on a collocation method with a simple discretization of the contact pressure. Brent's method is applied to determine the unknown contact region when using indenters with non-sharp edges. The results demonstrate that the shear modulus ratio and the intrinsic material length scale significantly influence the pressure intensity, highlighting a substantial dependence on the mechanical properties of materials under indentation force. The research also shows that the effect of the length scale and shear modulus ratio affects the limit eccentricity and tilt angle. The results highlight the necessity of considering both the size effect and material gradation when analyzing FG materials under mechanical stress. [ABSTRACT FROM AUTHOR]

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion. [ABSTRACT FROM AUTHOR]

This paper proposes a digital morphological filtering method based on a novel structuring element (SE) formulated using fractional Fourier transform (FrFT) and cross-convolution of window functions. The highlighting feature of this newly formulated filter is its flexibility in adding an adaptive nature to classical morphological filtering. Until now, every method listed in the literature makes a convenient assumption that noises corrupting ECG signal are Gaussian and model the filter around this assumption. Addressing this shortcoming, the first-of-its-kind filter adopts the α -stable distribution model (of which Gaussian distribution is a special case) of noise to better replicate the real-time noises interfering with ECG signals. The designed filter can suppress the noise and adapt to the changes in ECG signal morphology for better reconstruction. The proposed filter is tested on MIT-BIH Arrhythmia Database. The simulation results show improved performance in several quantitative metrics, demonstrating the superiority of our suggested method over the currently used state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

The cognition radar utilizes the dynamic waveform configuration to adapt to the environment to improve tracking performance. A novel tracking algorithm based on waveform selection is proposed to address the maneuvering aircraft tracking problem in clutter. Based on the modified current statistical (MCS) model, the modified probabilistic data association filter (MPDAF) is integrated with the square-root cubature Kalman filter (SCKF) to deal with the nonlinear measurement and the clutter. Additionally, the waveform library is established by applying the fractional Fourier transform (FRFT) to a base waveform, and a direct method is proposed to select the optimal waveform to minimize the posterior state error covariance matrix. The simulation results showed that, compared with the filters with the fixed waveform as well as the state-of-the-art algorithms, the proposed algorithm achieved higher estimation precision and lower track loss percentage while maintaining a low computational burden. [ABSTRACT FROM AUTHOR]

Titania is a functional oxide used as a catalyst and photocatalyst, which has various applications. Modifying the surface morphology and creating micro patterns on titania can significantly enhance its catalytic efficiency and utility in semiconductor devices. This study focuses on the fabrication of submicron patterns on titania using thermal nanoimprinting. The process involves the preparation of a high-viscosity sol consisting of 2-butoxyethanol, titanium butoxide, ethylene glycol, and water, followed by drying on a substrate to obtain a printable titania gel. We investigated the structural characteristics of this printable titania gel using Fourier transform infrared thermal analysis and high-energy X-ray diffraction. These structural analyses shed light on the critical factors affecting the growth of the Ti–O network within the gel and the effect of the organic content of the gel on its properties. [ABSTRACT FROM AUTHOR]

In this study, 2 flexible and pre-organized tetraamide compounds derived from N-6-[(4- pyridylmethylamino)carbonyl]-pyridine-2-carboxylic acid methyl ester namely 1,2-bis[N,N'-6-(4- pyridylmethylamido)pyridyl-2-carboxyamido]pentane (L1) and 1,2-bis[N,N'-6-(4- pyridylmethylamido)pyridyl-2-carboxyamido]hexane (L2) have been successfully synthesized when reacted with diamines in 1:2 ratio. These new compounds were built from combination of 3 main components, as a trend requires for anion receptor which are (i) 2,6-pyridine dicarboxamide moieties as targeted anion binding host, (ii) amino methyl pyridine pendants arms as the flexible moieties and (iii) pentyl (-C5H10-) and hexyl (-C6H12-) unit as the spacer. Compounds L1-L2 were fully characterized by using elemental analyzer, Fourier transform infrared (FTIR) spectroscopy, gas chromatography-mass spectroscopy (GC-MS), ¹H, 2D NOESY and 13C Nuclear Magnetic Resonance (NMR) spectroscopies, and Ultraviolet-visible (UV-Vis) spectroscopies. In this study, anion titration methods were used to identify the affinity towards selected anions. The results showed that L1 (having a pentyl spacer) had the highest affinity towards phosphate anions as compared to L2, where the red shift changes were observed in the UV-vis spectrum at the amide region. [ABSTRACT FROM AUTHOR]

The thermoreflectance method, which can measure thermal diffusivity in the cross-plane direction of thin films, mainly has two possible configurations; rear-heat front-detect (RF) and front-heat front-detect (FF) configuration. FF configuration is applicable to a wide variety of thin films including thin films deposited on opaque substrates, but this configuration has some problems in determination of the thermal diffusivity. One of the main problems is the effect of the penetration of pump beam and probe beam in thin film, which affects the initial temperature distribution near the sample's surface after pulse heating. Several studies have tried to analyze the effect but there have been no practical analytical solutions which can solve this problem in FF configuration. In this paper, we propose a new analytical solution which considers the penetration of pump beam and probe beam into thin film, and by applying Fourier expansion analysis which we developed in a previous study to thermoreflectance signals, we have determined the thermal diffusivity of thin film in the thermoreflectance method under FF configuration. We measured platinum thin films with different thickness under both FF and RF configuration and obtained consistent thermal diffusivity values from both configurations. [ABSTRACT FROM AUTHOR]

In order to solve the problem of untimely monitoring of tool wear status during laser-ultrasonic compound cutting (LUCC), which leads to the reduction of process accuracy and product quality damage, a method of tool wear status monitoring based on acoustic emission (AE) and deep learning is proposed in this paper. The AE signal is collected and analyzed in the frequency and time-frequency domains by using Fourier transform (FT) and wavelet packet decomposition (WPD), it is found that the AE signal energy is mainly concentrated in the 1st, 2nd, 3rd, and 4th frequency bands, and the energy of each frequency band in the signal increases gradually when the tool wear degree increases, however, the percentage of energy of each frequency band in the total energy shows different change trend. According to the amount of flank wear of the tool, the tool wear degree is divided into four tool wear states. The SVM model and BP neural network model were established based on MATLAB software to realize the tool wear state monitoring. The results show that the tool wear monitoring based on BP neural network is better than that of SVM for tool wear status monitoring. The model identification correct rate reaches 99 %, which is more suitable for the tool wear state monitoring designed in this paper. [ABSTRACT FROM AUTHOR]