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In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlap, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these types of relaxations are widely used. [ABSTRACT FROM AUTHOR]

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made. [ABSTRACT FROM AUTHOR]

This work presents a post-data analysis procedure, namely, proper orthogonal decomposition (POD)–dynamic mode decomposition (DMD)–discrete Fourier transform analysis, for evaluating the dominant features of the flow fields from both energetic and dynamic perspectives. The large-eddy simulation (LES) was first employed to reproduce the flow field surrounding three types of building layouts. Subsequently, both POD and DMD were conducted according to LES simulation results. The extracted modes were classified into three types based on the POD and DMD: Type-1 mode: energetically and dynamically significant mode, Type-2 mode: energetically significant and dynamically insignificant mode, and Type-3 mode: energetically insignificant and dynamically significant mode. The findings indicate that Type-1 mode governs the primary velocity field and the predominant vortex patterns observed at the rear of the building arrays, as the reduction of inter-building widths leads to a shorter flow separation region. Type-2 mode is characterized by the presence of small-scale vortices and the high turbulent kinetic energy region, which periodically triggers pollutant increase in the vicinity of structures. Type-3 mode demonstrates a minimal energetic influence on the flow field; nevertheless, it significantly contributes to the consistent build-up of pollutants within the far-wake region. The present study also investigates the predominant coherent structures of flow fields concerning various building layouts and highlights the influence of passage widths on the efficiency of pollutant removal. This comprehensive analysis enables a systematic exploration of flow patterns within various building layouts, offering potential solutions for pollutant dispersion challenges in metropolitan areas. [ABSTRACT FROM AUTHOR]

We study the homogeneously precessing domain (HPD) in superfluid 3 He-B in a regular continuous-wave nuclear magnetic resonance (CW NMR) experiment. Using Fourier analysis of CW NMR time traces, we identify several oscillation modes with frequency monotonically increasing with the frequency shift of the HPD. Some of these modes are localized near the cell walls, while others are localized in bulk liquid and can be interpreted as oscillations of ϑ -solitons. We also observe chaotic motion of the HPD in a certain range of temperatures and frequency shifts. [ABSTRACT FROM AUTHOR]

Among unmanned surface vehicle (USV) components, underwater thrusters are pivotal in their mission execution integrity. Yet, these thrusters directly interact with marine environments, making them perpetually susceptible to malfunctions. To diagnose thruster faults, a non-invasive and cost-effective vibration-based methodology that does not require altering existing systems is employed. However, the vibration data collected within the hull is influenced by propeller-fluid interactions, hull damping, and structural resonant frequencies, resulting in noise and unpredictability. Furthermore, to differentiate faults not only at fixed rotational speeds but also over the entire range of a thruster's rotational speeds, traditional frequency analysis based on the Fourier transform cannot be utilized. Hence, Continuous Wavelet Transform (CWT), known for attributions encapsulating physical characteristics in both time-frequency domain nuances, was applied to address these complications and transform vibration data into a scalogram. CWT results are diagnosed using a Vision Transformer (ViT) classifier known for its global context awareness in image processing. The effectiveness of this diagnosis approach was verified through experiments using a USV designed for field experiments. Seven cases with different fault types and severity were diagnosed and yielded average accuracy of 0.9855 and 0.9908 at different vibration points, respectively. [ABSTRACT FROM AUTHOR]

A three-phase multilevel inverter (MLI), synthesized with 31 levels in regard to its output voltage, is used to provide the AC supply to a three-phase, squirrel cage induction motor. The gating angles required for the 30 power switches on the MLI are optimized using both the genetic algorithm (GA) and the grey wolf optimizer (GWO), in which the optimal angles are determined through solving the trigonometric equations taken from Fourier analysis to target the minimum total harmonic distortion (THD) at the MLI output. A simulation model and an experimental prototype are developed for performance analysis and validation. The results demonstrate that the MLI is effectively able to produce 31 levels of three-phase AC output voltage, with the THD not exceeding 5% when loaded with a resistive load and a three-phase induction motor. The voltage and current are measured and recorded for different loads and operating conditions, including the amount of energy consumed by the load. The results of the frequency analysis demonstrate that most of the triple harmonics, which can harm the efficiency of the inverter, are cancelled. [ABSTRACT FROM AUTHOR]

The warp is a well-known undulation of the Milky Way disc. Its structure has been widely studied, but only since Gaia DR2 has it been possible to reveal its kinematic signature beyond the solar neighbourhood. In this work, we present an analysis of the warp traced by Classical Cepheids by means of a Fourier decomposition of their height (Z) and, for the first time, of their vertical velocity (Vz). We find a clear but complex signal that in both variables reveals an asymmetrical warp. In Z , we find the warp to be almost symmetric in amplitude at the disc's outskirts, with the two extremes never being diametrically opposed at any radius and the line of nodes presenting a twist in the direction of stellar rotation for R > 11 kpc. For Vz , in addition to the usual m  = 1 mode, an m  = 2 mode is needed to represent the kinematic signal of the warp, reflecting its azimuthal asymmetry. The line of maximum vertical velocity is similarly twisted as the line of nodes and trails behind by ≈25°. We develop a new formalism to derive the pattern speed and change in amplitude with time |$\dot{A}$| of each Fourier mode at each radius, via a joint analysis of the Fourier decomposition in Z and Vz. By applying it to the Cepheids we find, for the m  = 1 mode, a constant pattern speed in the direction of stellar rotation of 9.2 ± 3.1 km s−1 kpc−1, a negligible |$\dot{A}$| up to R ≈ 14 kpc and a slight increase at larger radii, in agreement with previous works. [ABSTRACT FROM AUTHOR]

Continuing our earlier work in Nam et al. (One-step replica symmetry breaking of random regular NAE-SAT I, arXiv:2011.14270, 2020), we study the random regular k-nae-sat model in the condensation regime. In Nam et al. (2020), the (1rsb) properties of the model were established with positive probability. In this paper, we improve the result to probability arbitrarily close to one. To do so, we introduce a new framework which is the synthesis of two approaches: the small subgraph conditioning and a variance decomposition technique using Doob martingales and discrete Fourier analysis. The main challenge is a delicate integration of the two methods to overcome the difficulty arising from applying the moment method to an unbounded state space. [ABSTRACT FROM AUTHOR]

For site characterization, the elliptic particle motion of Rayleigh waves and its frequency dependence is a well-known property that aroused less interest than the frequency dependence of the phase velocity. More than 50 yr ago, ellipticity was already recognized as providing information independent from phase velocity, despite the difficulties inherent to its accurate and precise measurement. Several techniques were developed during the last two decades to extract the ellipticity curve from ambient vibration recordings, with a single three-component (3C) station, with pairs of 3C stations and more recently with 3C arrays. The latter has the advantage over the other approaches that the sign of the ellipticity can be retrieved. Moreover, higher order mode separation is possible under certain conditions. Nevertheless, Rayleigh Three-component BeamForming (RTBF) proposed by Wathelet et al. encounters difficulties in the presence of significant levels of incoherent noise when the true ellipticity is vanishing or when it has a high absolute value. In this work, the analytical expressions of the beam power for a single source wavefield are revised under more realistic assumptions for the incoherent noise azimuthal distribution. The proposed model also includes an asymmetric distribution of the incoherent noise between vertical and horizontal components, which was not the case in the original publication. Switching from ellipticity to angular ellipticity drastically simplifies the formalism. Moreover, it naturally leads to a new steering matrix (all-component ellipticity steering) which solves the limitation around zero and infinity observed for RTBF. Interestingly, the accuracy of the ellipticity is no longer influenced by the absolute level of incoherent noise but by the difference between the incoherent noise ratio on vertical and horizontal components. A method based on the second derivative of the beam power versus the radial wavenumber is finally proposed to experimentally measure the noise ratio difference, which allows experimental values to be corrected. The methodology is compared with classical vertical beamforming and RTBF for a synthetic case and three experimental data sets. [ABSTRACT FROM AUTHOR]

We study the singularity formation of a quasi-exact 1D model proposed by Hou and Li (2008 Commun. Pure Appl. Math. 61 661–97). This model is based on an approximation of the axisymmetric Navier–Stokes equations in the r direction. The solution of the 1D model can be used to construct an exact solution of the original 3D Euler and Navier–Stokes equations if the initial angular velocity, angular vorticity, and angular stream function are linear in r. This model shares many intrinsic properties similar to those of the 3D Euler and Navier–Stokes equations. It captures the competition between advection and vortex stretching as in the 1D De Gregorio (De Gregorio 1990 J. Stat. Phys. 59 1251–63; De Gregorio 1996 Math. Methods Appl. Sci. 19 1233–55) model. We show that the inviscid model with weakened advection and smooth initial data or the original 1D model with Hölder continuous data develops a self-similar blowup. We also show that the viscous model with weakened advection and smooth initial data develops a finite time blowup. To obtain sharp estimates for the nonlocal terms, we perform an exact computation for the low-frequency Fourier modes and extract damping in leading order estimates for the high-frequency modes using singularly weighted norms in the energy estimates. The analysis for the viscous case is more subtle since the viscous terms produce some instability if we just use singular weights. We establish the blowup analysis for the viscous model by carefully designing an energy norm that combines a singularly weighted energy norm and a sum of high-order Sobolev norms. [ABSTRACT FROM AUTHOR]

Here, we show how to extend the possibilities of the conventional F-analysis and adapt it for quantitative description of multi-periodic signals recorded from different complex systems. The basic idea lies in filtration property of the Dirichlet function that allows finding the leading frequencies (having the predominant amplitudes) and the shortcut frequency band allows to fit the initial random signal with high accuracy (with the value of the relative error less than 5%). This modification defined as NOCFASS-approach (Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals) can be applied to a wide class of different signals having multi-periodic structure. We want to underline here that the shortcut frequency dispersion has linear dependence Ωk = c:k+d that differs from the conventional dispersion accepted in the conventional Fourier transformation ω(k) = 2πk/T. (T is a period of the initial signal). With the help of integration procedure one can extract a low-frequency trend from trendless sequences that allows to applying the NOCFASS approach for calculation of the desired amplitude-frequency response (AFR) from different noisy random sequences. In order to underline the multi-periodic structure of random signals under analysis we consider two nontrivial examples. (a) The peculiarities of the AFR associated with Weierstrass-Mandelbrot function. (b) The random behavior of the voltammograms (VAGs) background measured for an electrochemical cell with one active electrode. We do suppose that the proposed NOCFASS-approach having new attractive properties as the simplicity of realization, agility to the problem formulated will find a wide propagation in the modern signal processing area. [ABSTRACT FROM AUTHOR]

In part I of the article, we demonstrated that a variant of the dynamic mode decomposition (DMD) algorithm based on variable projection optimization, called optimized DMD (OPT-DMD), enables a robust identification of the dominant spatiotemporally coherent modes underlying the data across various test cases representing different physical parameters in an E × B simulation configuration. We emphasized that the OPT-DMD significantly improves the analysis of complex plasma processes, revealing information that cannot be derived using conventionally employed analyses such as the fast Fourier transform. As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case. The predictive capacity of the OPT-DMD ROM is assessed primarily in terms of short-term dynamics forecast or, in other words, for large ratios of training-to-test data. However, the utility of the ROM for long-term dynamics forecasting is also presented for an example case in the radial-azimuthal configuration. The model's predictive performance is heterogeneous across various test cases. Nonetheless, a remarkable predictiveness is observed in the test cases that do not exhibit highly transient behaviors. Moreover, in all investigated cases, the error between the ground-truth and the reconstructed data from the OPT-DMD ROM remains bounded over time within both the training and the test window. As a result, despite its limitation in terms of generalized applicability to all plasma conditions, the OPT-DMD is proven as a reliable method to develop low computational cost and highly predictive data-driven ROMs in systems with a quasi-periodic global evolution of the plasma state. [ABSTRACT FROM AUTHOR]

This article, titled "Approximation of Periodic Functions of High Generalized Smoothness by Fourier Sums," discusses the conditions under which Fourier sums provide the best approximation for periodic functions with high generalized smoothness. The article presents necessary and sufficient conditions for the generator of a generalized derivative, and explores the cases where the best order of approximation is not achieved by partial Fourier sums or de la Vallée-Poussin means. The article also introduces Theorem 1, which provides a criterion for determining when Fourier sums provide the best approximation. The authors conclude that the quality of approximation by partial Fourier sums depends on the scale of generators and the behavior of the function and its derivative. The article was published in Mathematical Notes in 2024 and was written by N. V. Laktionova and K. V. Runovskii. [Extracted from the article]

This work is conducted to improve the electrochemical performance of PANI with the incorporation of spinel‐type transition metal oxide, that is, 1 wt.% of nickel ferrite (NiFe2O4) (NF). The addition of NiFe2O4 into the PANI matrix is accomplished via in situ oxidative polymerization approach at a very low temperature (0‐5°C). It is observed that the various valence states of NiFe2O4 in the electrolytic ions considerably increase due to formation of a well‐interconnected conducting network with PANI. The requisite interaction of PANI/NiFe2O4 is verified by Raman analysis and Fourier Transform Infrared Spectroscopy (FTIR). PANI1:1/NF1 ratio of the composite facilitates strong conducting route improving delocalization of the electrons in the polymeric chain resulting in extra stability of the system. It is observed that NF nanoparticles fills the gaps in the polymeric matrix rendering to attain highest specific capacitance of 758 F g−1 of the PANI 1:1/NF1 electrode cell as compared to bare PANI1:1 (677 F g−1), PANI1:2 (500 F g−1), NF (253 F g−1) and other PANI1:2/NF2 (686 F g−1) samples at 10mV/s. The PANI1:1 device also shows energy density ~ 54 W kg−1 at 0.3 mA/cm2 with corresponding power density at ~1705 W kg−1, and the cyclic stability ~97% after 10,000 GCD cycles. The said device also exhibits a lower charge transfer resistance (Rct) 0.35 Ω as compared to other fabricated devices. NiFe2O4 acts as a 'superhighway' for charge transportation between PANI, which is beneficial for supercapacitors. [ABSTRACT FROM AUTHOR]

In the present study, poly(N‐Isopropylacrylacrylamide‐co‐N‐tertiarybutylacrylamide‐co‐hydroxyethylcrylamide) (NIPAM‐co‐NTBA‐co‐HEAAm) hydrogels are prepared with variation of molar ratio of hydrophilic HEAAm and hydrophobic NTBA. The prepared hydrogels are characterized with elemental analysis and Fourier transform infrared (FTIR) spectroscopy. The thermodynamics of swelling properties of poly(NIPAM‐co‐NTBA‐co‐HEAAm) hydrogels have also been discussed. The experimental C/N ratios are comparable with the theoretical value. The enthalpy change of mixing ∆Hmix, entropy change of mixing ∆Smix, free energy change of mixing ∆Gmix are determined for swelling of hydrogels at 25 °C. The value of total free energy of hydrogel swelling is found to be negative which confirms the lower critical solution temperature (LCST) exhibited in all hydrogels and the volume change transition shows the thermoresponsive behavior. The values of ∆Smix increase and ∆Gmix decrease with increasing amount of hydrophobic NTBA content in the hydrogels. The values of free energy change of elasticity (∆Gel) are found to be increased with increasing the hydrophobic NTBA content followed by decrease in swelling percentage. Also, the transition temperature of the hydrogel is found to be decreased with increasing the hydrophobic NTBA. [ABSTRACT FROM AUTHOR]

Background Efficient infection control during carbapenem-resistant Enterobacterales outbreaks demands rapid and simple techniques for outbreak investigations. WGS, the current gold standard for outbreak identification, is expensive, time-consuming and requires a high level of expertise. Fourier-transform infrared (FTIR) spectroscopy (IR Biotyper) is a rapid typing method based on infrared radiation applied to samples, which provides a highly specific absorption spectrum. Objectives To investigate an outbreak of OXA-48-producing Escherichia coli in real-time using FTIR and subsequently compare the results with WGS. Methods Twenty-one isolates were collected during a nosocomial outbreak, and identification and antibiotic susceptibilities were confirmed by VITEK®2. FTIR was conducted for all isolates, and nine representative isolates were sequenced. Results FTIR was able to correctly determine the clonal relatedness of the isolates and to identify the outbreak cluster, as confirmed by WGS. By WGS, isolates in the main FTIR cluster belonged to the same MLST type and core-genome MLST type, and they harboured similar plasmids and resistance genes, whereas the singletons external to the FTIR cluster had different genetic content. Conclusions FTIR can operate as a rapid, efficient and reliable first-line tool for outbreak investigations during a real-time ongoing E. coli outbreak, which can contribute to limiting the spread of pathogens. [ABSTRACT FROM AUTHOR]

In the present paper, the unique solvability of the direct and inverse source problems for the pseudo-parabolic equation involving the bi-ordinal Hilfer fractional derivative and 2D Landau Hamiltonian operator is considered. Applying the Fourier analysis for the operator Landau Hamiltonian, the theorems of uniqueness and existence of solutions to direct and inverse source problems are proved. In the investigation of the inverse source problem, we have used the value of unknown function at the final time in order to find the right-hand side of the equation. It is also presented the stability result of the inverse problem. [ABSTRACT FROM AUTHOR]

In this study, beach cusp characteristics were explored using 15 months of 3D lidar scans collected hourly at the Field Research Facility in Duck, NC. Fourier analyses were performed on lidar‐derived beach elevation contours to generate spatial cusp spectra. Active cusp events were identified on the basis of the location and magnitude of each spectrum's peak and used to evaluate conditions during cusp formation and evolution. Cusps primarily developed during times with normally‐incident, long period, low energy wave conditions with low frequency spread, and reflective beach conditions. The upper and lower beaches often exhibited different behavior and morphologies, with persistent upper‐beach cusps lasting days to months and dynamic lower‐beach cusps evolving over individual tidal cycles. At times, beaches exhibiting multiple cusp systems reverted to a single cusp system extending over the entire beach when the high‐tide waterline reached the upper‐beach cusps, with the location and spacing of the resulting lower‐beach cusps controlled by the upper‐beach cusps. These observations are consistent with a "morphological coupling" hypothesis proposing that hydrodynamic‐morphodynamic feedbacks between the swash and upper‐beach cusps can result in the formation of lower‐beach cusps with a related wavelength as the tide falls. However, there were also times when the high‐tide waterline reached the upper‐beach cusps that did not result in a unified beach state. These results suggest that while morphological coupling is often an important factor in controlling the development of new lower‐beach cusps, this coupling cannot initiate cusp formation in hydrodynamic conditions outside those favorable for cusp activity. Plain Language Summary: Beach cusps, rhythmic topographic features that form near the waterline, are frequently observed on beaches around the world. Although beach cusps are common, collecting a high resolution, long‐duration observations of cusps and the associated environmental conditions is difficult, leaving open questions regarding the dynamics of cusp events and the range of conditions in which cusps form. Here, hourly lidar scans were used to analyze the characteristics of beach cusp events using approximately 15 months of data collected over 20 months. Cusps formed primarily during times with small waves approaching from directly offshore with long, consistent wave periods. Cusp fields with different physical characteristics were often observed on the upper and lower portions of the beach, with cusps on the upper beach generally lasting days to months, and cusps on the lower beach evolving on the scales of individual tidal cycles. Times when the high tide reached the upper‐beach cusp system often resulted in the unification of the two systems. However, this unification did not occur every time the high tide reached the upper cusps, suggesting that the presence of upper cusps alone is not sufficient to induce cusp growth on the lower beach in conditions that are not conducive to cusp activity. Key Points: The characteristics of beach cusp formation and evolution were analyzed using an hourly terrestrial lidar data set collected over 15 monthsBeach cusps primarily formed during times with normally‐incident, long period, low energy wave conditions with low frequency spreadDifferent morphologies were often seen on the upper and lower beaches, with upper‐beach cusps generally lasting longer than lower‐beach cusps [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical computation method for a one-dimensional self diffusion plant water model with homogeneous Neumann boundary conditions. First, a high accuracy compact difference scheme for the diffusive plant water model in an arid flat environment is constructed using the finite difference method. The fourth order compact difference scheme is used for the spatial derivative term, and the Taylor series expansion and residual correction function are used to discretize the time term. We obtain a difference scheme with second-order accuracy in time and fourth-order accuracy in space. Second, the Fourier analysis method is used to prove that the above format is unconditionally stable. Then, the numerical examples provided the convergence and accuracy of the difference scheme. Finally, numerical simulations are conducted near the Turing Hopf bifurcation point of the model to obtain the spatial distribution maps of vegetation and water under small disturbances of different parameters. In this paper, the evolution law of vegetation quantity and water density at any time is observed. Revealing the impact of small changes in parameters on the spatiotemporal dynamics of plant water models will provide a basis for understanding whether ecosystems are fragile. [ABSTRACT FROM AUTHOR]

The use of tuned liquid dampers (TLDs) as an alternative to reduce the response of flexible structures with a low amount of structural damping is a viable option. The correct characterization of the dynamic properties of the TLD plays an important role in the performance of the TLD-main structure system. This work presents the results of an experimental study to evaluate the dynamic properties of a scaled rectangular TLD using high-speed videos. For the experimental investigation, a scaled rectangular TLD is subjected to lateral displacement of the sinusoidal type with amplitudes that range from 5 to 40 mm and frequency equal to 0.625 Hz. The dynamic properties of the TLD system are identified with the use of high-speed videos with a duration of 28.96 s and recorded at 500 frames per second (fps). The recorded videos are analyzed with the software Tracker to extract time histories of wave elevation at predefined locations. The frequency and damping of the TLD system are identified from the time histories of wave elevation through Fourier analysis and free-vibration decay. The findings of this study revealed that the identified dynamic properties of the TLD by using high-speed videos presented small differences with respect to the target values, with errors that range from 0.93 to 2.9% for frequency and from 1.6 to 8.8% for damping, indicating that the use of high-speed videos can be an alternative to evaluate the dynamic properties of TLD systems. [ABSTRACT FROM AUTHOR]

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The recent discovery of barred spiral galaxies in the early Universe (z > 2) poses questions of how these structures form and how they influence galaxy evolution in the early Universe. In this study, we investigate the morphology and kinematics of the far-infrared (FIR) continuum and [C  ii ] emission in BRI1335-0417 at z ≈ 4.4 from ALMA observations. The variations in position angle and ellipticity of the isophotes show the characteristic signature of a barred galaxy. The bar, |$3.3^{+0.2}_{-0.2}$| kpc long in radius and bridging the previously identified two-armed spiral, is evident in both [C  ii ] and FIR images, driving the galaxy's rapid evolution by channelling gas towards the nucleus. Fourier analysis of the [C  ii ] velocity field reveals an unambiguous kinematic m  = 2 mode with a line-of-sight velocity amplitude of up to ∼30–40 km s−1; a plausible explanation is the disc's vertical bending mode triggered by external perturbation, which presumably induced the high star formation rate and the bar/spiral structure. The bar identified in [C  ii ] and FIR images of the gas-rich disc galaxy (≳ 70 per cent of the total mass within radius R ≈ 2.2 disc scale lengths) suggests a new perspective of early bar formation in high redshift gas-rich galaxies – a gravitationally unstable gas-rich disc creating a star-forming gaseous bar, rather than a stellar bar emerging from a pre-existing stellar disc. This may explain the prevalent bar-like structures seen in FIR images of high-redshift submillimeter galaxies. [ABSTRACT FROM AUTHOR]

Several methods have been proposed to characterize the complex interactions in turbulent wakes, especially for flows with strong cyclic dynamics. This paper introduces the concept of Fourier-averaged Navier-Stokes (FANS) equations as a framework to obtain direct insights into the dynamics of complex coherent wake interactions. The method simplifies the interpretations of flow physics by identifying terms contributing to momentum transport at different time scales. The method also allows for direct interpretation of nonlinear interactions of the terms in the Navier-Stokes equations. By analysing well-known cases, the characteristics of FANS are evaluated. Particularly, we focus on physical interpretation of the terms as they relate to the interactions between modes at different time scales. Through comparison with established physics and other methods, FANS is shown to provide insight into the transfer of momentum between modes by extracting information about the contributing pressure, convective and diffusive forces. The FANS equations provide a simply calculated and more directly interpretable set of equations to analyse flow physics by leveraging momentum conservation principles and Fourier analysis. By representing the velocity as a Fourier series in time, for example, the triadic model interactions are apparent from the governing equations. The method is shown to be applicable to flows with complex cyclic waveforms, including broadband spectral energy distributions. [ABSTRACT FROM AUTHOR]

This is a continuation of our previous study on the shape parameter contained in the shifted surface spline. We insist that the data points be purely scattered without meshes and the domain can be of any shape when conducting function interpolation by shifted surface splines. We also endeavor to make our approach easily accessible for scientists, not only mathematicians. However, the space of interpolated functions is smaller than that used before, leading to sharper function approximation. This function space has particular significance in numerical partial differential equations, especially for equations whose solutions lie in Sobolev space. Although the Fourier transform is deeply involved, scientists without a background in Fourier analysis can easily understand and use our approach. [ABSTRACT FROM AUTHOR]

Astaxanthin (AST)-encapsulated nanoparticles were fabricated using glycol chitosan (Chito) through electrostatic interaction (abbreviated as ChitoAST) to solve the aqueous solubility of astaxanthin and improve its biological activity. AST was dissolved in organic solvents and then mixed with chitosan solution, followed by a dialysis procedure. All formulations of ChitoAST nanoparticles showed small diameters (less than 400 nm) with monomodal distributions. Analysis with Fourier transform infrared (FT-IR) spectroscopy confirmed the specific peaks of AST and Chito. Furthermore, ChitoAST nanoparticles were formed through electrostatic interactions between Chito and AST. In addition, ChitoAST nanoparticles showed superior antioxidant activity, as good as AST itself; the half maximal radical scavenging concentrations (RC50) of AST and ChitoAST nanoparticles were 11.8 and 29.3 µg/mL, respectively. In vitro, AST and ChitoAST nanoparticles at 10 and 20 µg/mL properly inhibited the production of intracellular reactive oxygen species (ROSs), nitric oxide (NO), and inducible nitric oxide synthase (iNOS). ChitoAST nanoparticles had no significant cytotoxicity against RAW264.7 cells or B16F10 melanoma cells, whereas AST and ChitoAST nanoparticles inhibited the growth of cancer cells. Furthermore, AST itself and ChitoAST nanoparticles (20 µg/mL) efficiently inhibited the migration of cancer cells in a wound healing assay. An in vivo study using mice and a pulmonary metastasis model showed that ChitoAST nanoparticles were efficiently delivered to a lung with B16F10 cell metastasis; i.e., fluorescence intensity in the lung was significantly higher than in other organs. We suggest that ChitoAST nanoparticles are promising candidates for antioxidative and anticancer therapies of B16F10 cells. [ABSTRACT FROM AUTHOR]

It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that the converse holds, and approximate the inverse of the linear elasticity operator with a convex linear combination of parameter-free operators. In such a way, we construct a uniform preconditioner for linear elasticity for all values of the Lamé parameter λ ∈ [ 0 , ∞). Numerical results confirm that by using inf-sup stable finite-element spaces for the solution of Stokes' equations, the proposed preconditioner is robust in λ. [ABSTRACT FROM AUTHOR]

In this work, we present a binary assembly model that can predict the co-assembly structure and spatial frequency spectra of monodispersed nanoparticles with two different particle sizes. The approach relies on an iterative algorithm based on geometric constraints, which can simulate the assembly patterns of particles with two distinct diameters, size distributions, and at various mixture ratios on a planar surface. The two-dimensional spatial-frequency spectra of the modeled assembles can be analyzed using fast Fourier transform analysis to examine their frequency content. The simulated co-assembly structures and spectra are compared with assembled nanoparticles fabricated using transfer coating method are in qualitative agreement with the experimental results. The co-assembly model can also be used to predict the peak spatial frequency and the full-width at half-maximum bandwidth, which can lead to the design of the structure spectra by selection of different monodispersed particles. This work can find applications in fabrication of non-periodic nanostructures for functional surfaces, light extraction structures, and broadband nanophotonics. [ABSTRACT FROM AUTHOR]

Type 2 diabetes mellitus (T2DM) is characterized by several complications, such as retinopathy, renal failure, cardiovascular disease, and diabetic neuropathy. Among these, neuropathy is the most severe complication, due to the challenging nature of its early detection. The linear Hearth Rate Variability (HRV) analysis is the most common diagnosis technique for diabetic neuropathy, and it is characterized by the determination of the sympathetic–parasympathetic balance on the peripheral nerves through a linear analysis of the tachogram obtained using photoplethysmography. We aimed to perform a multifractal analysis to identify autonomic neuropathy, which was not yet manifest and not detectable with the linear HRV analysis. We enrolled 10 healthy controls, 10 T2DM-diagnosed patients with not-full-blown neuropathy, and 10 T2DM diagnosed patients with full-blown neuropathy. The tachograms for the HRV analysis were obtained using finger photoplethysmography and a linear and/or multifractal analysis was performed. Our preliminary results showed that the linear analysis could effectively differentiate between healthy patients and T2DM patients with full-blown neuropathy; nevertheless, no differences were revealed comparing the full-blown to not-full-blown neuropathic diabetic patients. Conversely, the multifractal HRV analysis was effective for discriminating between full-blown and not-full-blown neuropathic T2DM patients. The multifractal analysis can represent a powerful strategy to determine neuropathic onset, even without clinical diagnostic evidence. [ABSTRACT FROM AUTHOR]

In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert-Montgomery-Vaughan inequality. [ABSTRACT FROM AUTHOR]

Introduction: Oscillations are frequently observed on plasma dilution curves during intravenous fluid therapy. This study aimed to examine how common these oscillations are and what they represent. Methods: Fourier transforms were used to analyze the residuals obtained during fitting of a volume kinetic model to 269 plasma dilution curves. Oscillating patterns were identified in two-thirds of the fluid infusion experiments. Results: The wave frequency usually had a dominating frequency of 1 h or multiples thereof. The wave amplitudes varied between 1% and 4% of the plasma volume. The "peak-to-peak" amplitudes were then twice as large, which corresponded to blood volume changes of 60–240 mL. A population kinetic analysis of the distribution of infused fluid between body fluid compartments was then applied to search for clues that could explain the oscillations. This analysis showed that amplitudes >1.5% were associated with doubled turnover of fluid in a fast-exchange interstitial fluid compartment and, together with data on plasma albumin, suggested that oscillations might represent bursts of efferent lymph. Conclusions: Oscillations with very low frequency were often observed on plasma dilution-time curves obtained during fluid therapy. They were associated with fast turnover of interstitial fluid and can possibly have resulted from accelerated lymphatic flow. [ABSTRACT FROM AUTHOR]

We consider linear schemes with several degrees of freedom for the transport equation on uniform meshes. For these schemes, the solution error is |$O(h^p + th^q)$|⁠ , where |$p$| is equal to or greater by one than the order of the truncation error and |$q \geqslant p$|⁠. We prove the existence of a mapping of smooth functions on the mesh space providing the |$q$| th order of the truncation error and deviating from the standard mapping (⁠|$L_2$| -projection for example) by |$O(h^p)$|⁠. In a one-dimensional case, this mapping can be found in the class of local mappings. In more dimensions, the existence of a local mapping with such properties is guaranteed only under additional assumptions. [ABSTRACT FROM AUTHOR]

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software disperse. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis. [ABSTRACT FROM AUTHOR]

Atmospheric drag stands out as the predominant non-gravitational force acting on satellites in Low Earth Orbit (LEO), with altitudes below 2000 km. This drag exhibits a strong dependence on the thermospheric mass density (TMD), a parameter of vital significance in the realms of orbit determination, prediction, collision avoidance, and re-entry forecasting. A multitude of empirical TMD models have been developed, incorporating contemporary data sources, including TMD measurements obtained through onboard accelerometers on LEO satellites. This paper delves into three different TMD modelling techniques, specifically, Fourier series, spherical harmonics, and artificial neural networks (ANNs), during periods of geomagnetic quiescence. The TMD data utilised for modelling and evaluation are derived from three distinct LEO satellites: GOCE (at an altitude of approximately 250 km), CHAMP (around 400 km), and GRACE (around 500 km), spanning the years 2002 to 2013. The consistent utilisation of these TMD data sets allows for a clear performance assessment of the different modelling approaches. Subsequent research will shift its focus to TMD modelling during geomagnetic disturbances, while the present work can serve as a foundation for disentangling TMD variations stemming from geomagnetic activity. Furthermore, this study undertakes precise TMD modelling during geomagnetic quiescence using data obtained from the GRACE (at an altitude of approximately 500 km), CHAMP (around 400 km), and GOCE (roughly 250 km) satellites, covering the period from 2002 to 2013. It employs three distinct methods, namely Fourier analysis, spherical harmonics (SH) analysis, and the artificial neural network (ANN) technique, which are subsequently compared to identify the most suitable methodology for TMD modelling. Additionally, various combinations of time and coordinate representations are scrutinised within the context of TMD modelling. Our results show that the precision of low-order Fourier-based models can be enhanced by up to 10 % through the utilisation of geocentric solar magnetic coordinates. Both the Fourier- and SH-based models exhibit limitations in approximating the vertical gradient of TMD. Conversely, the ANN-based model possesses the capacity to capture vertical TMD variability without manifesting sensitivity to variations in time and coordinate inputs. [ABSTRACT FROM AUTHOR]

Background: Running means for total calcium (Ca) results at our laboratory exhibit a stable time-of-day (TOD) periodic pattern. We examined use of TOD-dependent targets for running means in patient-based quality control (PBQC) for Ca. Methods: Primary data were Ca results over a 3 month interval, restricted to weekday data within the Ca reference interval (8.5–10.3 mg/dL; 2.12–2.57 mmol/L). Running means were evaluated as sliding averages of 20 samples (20-mers). Results: Data comprised 39,629 consecutive Ca measurements (75.3% inpatient (IP)) for which Ca was 9.29±0.47 mg/dL. The all data average for 20-mers was 9.29 ± 0.18 mg/dL. When parsed in 1 h TOD intervals, however, averages among 20-mers ranged from 9.1 to 9.5 mg/dL, with blocs of contiguous results above (0800–2300 h; 53.3% of results; IP = 75.3%) and below (2300–0800 h; 46.7% of results; IP = 99.9%) the all-data mean. There was thus an inherent TOD-dependent pattern of deviation of means from target when using a fixed PBQC target. Using Fourier series analysis as an example approach, characterization of the pattern to produce TOD-dependent PBQC targets eliminated this inherent inaccuracy. Conclusions: In circumstances of periodic variation in running means, simple characterization of that variation can reduce the probability of both false positive and false negative flags in PBQC. [ABSTRACT FROM AUTHOR]

This work aimed to elucidate and compare the solidification characteristics of A356.2, A356.2/5% SiC, A356.2/5% Al2O3, and A356.2/5% ZrO2 metal composites with and without adding Bi element by using the Fourier thermal analysis method. Microstructural and XRD analysis showed that reinforcement particles have been successfully embedded in the A356.2 alloy through the compo-casting route. Thermal analysis results show that the cooling rate of the A356.2 matrix alloy, as measured in the experimental set-up, was 0.8 °C/s and increased to 1.9 °C/s in the composites. The nucleation temperature of α-Al increased slightly (0.6 °C), and undercooling (8.9–11 °C) was observed for all composites. The nucleation temperature of the Mg2Si phase and solidus temperature of composites were lower than the A356.2. Moreover, the growth temperature and recalescence magnitude of eutectic Al-Si did not change remarkably. The solidification temperature range and solidification rate increased by 5% and 33%; however, the solidification time decreased by 21%. The solid fraction at the coherency point increased, which is associated with an expansion in the time difference between nucleation and the coherency point. However, adding Bi resulted in the depression of eutectic growth temperature and the refinement of eutectic Si. These data infer that the solidification kinetic of A356.2 and their composites are identical. It cannot be concluded that reinforcement particle acts as nucleation agents for both α-Al and eutectic Si. [ABSTRACT FROM AUTHOR]

Plumage patterns of melanerpine (Melanerpes - Sphyrapicus) woodpeckers are strikingly diverse. Understanding the evolution and function of this diversity is challenging because of the difficulty of quantifying plumage patterns. We use a three-dimensional space to characterize the evolution of melanerpine achromatic plumage patterns. The axes of the space are three pattern features (spatial frequency, orientation, and contrast) quantified using two-dimensional fast Fourier transformation of museum specimen images. Mapping plumage in pattern space reveals differences in how species and subclades occupy the space. To quantify these differences, we derive two new measures of pattern: pattern diversity (diversity across plumage patches within a species) and pattern uniqueness (divergence of patterns from those of other species). We estimate that the melanerpine ancestor had mottled plumage and find that pattern traits across patches and subclades evolve at different rates. We also find that smaller species are more likely to display horizontal face patterning. We promote pattern spaces as powerful tools for investigating animal pattern evolution. [ABSTRACT FROM AUTHOR]

Viazovska's solution of the sphere packing problem in eight dimensions is based on a remarkable construction of certain special functions using modular forms. Great mathematics has consequences far beyond the problems that originally inspired it, and Viazovska's work is no exception. In this article, we'll examine how it has led to new interpolation theorems in Fourier analysis, specifically a theorem of Radchenko and Viazovska. [ABSTRACT FROM AUTHOR]

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We study the asymptotic normality of two feasible estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate n 1 / 4 ⁠ , while the estimator without bias-correction has a slower convergence rate and a smaller asymptotic variance. Additionally, we provide simulation results that support the theoretical asymptotic distribution of the rate-efficient estimator and show the accuracy of the latter in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, using the rate-optimal Fourier estimator, we reconstruct the series of the daily volatility of volatility of the S&P500 and EUROSTOXX50 indices over long samples and provide novel insight into the existence of stylized facts about the volatility of volatility dynamics. [ABSTRACT FROM AUTHOR]

We present a unified approach to derive sharp isoperimetric‐type inequalities of arbitrary high order. In particular, we obtain (i) sharp high‐order discrete polygonal isoperimetric‐type inequalities, (ii) sharp high‐order isoperimetric‐type inequalities for smooth curves with both upper and lower bounds for the isoperimetric deficit, and (iii) sharp higher order Chernoff‐type inequalities involving a generalized width function and higher order locus of curvature centers. Our approach involves obtaining higher order discrete or smooth Wirtinger inequalities via Fourier analysis, by examining a family of linear operators. The key to our approach is identifying the appropriate linear operator and translating the analytic inequalities into geometric ones. [ABSTRACT FROM AUTHOR]

This is a survey of unconditional pseudorandom generators (PRGs). A PRG uses a short, truly random seed to generate a long, "pseudorandom" sequence of bits. To be more specific, for each restricted model of computation (e.g., bounded-depth circuits or read-once branching programs), we would like to design a PRG that "fools" the model, meaning that every function computable in the model behaves approximately the same when we plug in pseudorandom bits from the PRG as it does when we plug in truly random bits. In this survey, we discuss four major paradigms for designing PRGs: • We present several PRGs based on k -wise uniform generators, small-bias generators, and simple combinations thereof, including proofs of Viola's theorem on fooling low-degree polynomials [242] and Braverman's theorem on fooling AC 0 circuits [36]. • We present several PRGs based on "recycling" random bits to take advantage of communication bottlenecks, such as the Impagliazzo-Nisan-Wigderson generator [131]. • We present connections between PRGs and computational hardness, including the Nisan-Wigderson framework for converting a hard Boolean function into a PRG [183]. • We present PRG frameworks based on random restrictions, including the "polarizing random walks" framework [49]. We explain how to use these paradigms to construct PRGs that work unconditionally , with no unproven complexity-theoretic assumptions. The PRG constructions use ingredients such as finite field arithmetic, expander graphs, and randomness extractors. The analyses use techniques such as Fourier analysis, sandwiching approximators, and simplification-under-restrictions lemmas. [ABSTRACT FROM AUTHOR]

Allogenic demineralized bone matrix (DBM), processed to expose bioactive proteins imbedded by calcium salts, is widely used for bone repair and regeneration as an alternative to the autologous bone graft. However, demineralized bone matrices from tissue banks vary significantly in residual calcium content and osteogenicity for clinical bone regeneration. The present study produced DBM with various residual calcium contents by partial demineralization using ethylenediaminetetraacetic acid disodium (EDTA) and hydrochloric acid. Compositional analysis reveals that, as the percent weight loss of bone materials increases from 0% to 74.9% during demineralization, the residual calcium content of DBM decreases from 24.8% to 0.2% and collagen content increases from 29.7% to 92.6%. Calorimetrical analysis and Fourier transform infrared (FTIR) analysis demonstrated that demineralization to the residual calcium content of <4% enables the complete exposure and/or release of bone collagen fibers and other bioactive molecules. In order to evaluate the relationship between the extent of demineralization and the osteogenicity of DBM, DBM particles were fabricated with the aid of acellular dermal matrix (ADM) microfibers to form flexible foam‐like DBM/ADM composites. Proteomic analysis identified various type collagens and bone formation‐related bioactive molecules in both ADM and DBM. Using the rat bilateral Φ = 5 mm calvarium defect repair model, the study had shown that the DBM/ADM composite with ~20% DBM residual calcium (e.g., ~40% calcium being removed) maximized the osteogenicity for bone defect repair after 4 and 8 weeks. DBM with ~40% calcium removal had the maximal osteogenicity presumably through the sustained release of bioactive molecules during the process of bone regeneration. [ABSTRACT FROM AUTHOR]

Instrumental resolution of Fourier transform-charge detection mass spectrometry instruments with electrostatic ion trap detection of individual ions depends on the precision with which ion energy is determined. Energy can be selected using ion optic filters or from harmonic amplitude ratios (HARs) that provide Fellgett's advantage and eliminate the necessity of ion transmission loss to improve resolution. Unlike the ion energy-filtering method, the resolution of the HAR method increases with charge (improved S/N) and thus with mass. An analysis of the HAR method with current instrumentation indicates that higher resolution can be obtained with the HAR method than the best resolution demonstrated for instruments with energy-selective optics for ions in the low MDa range and above. However, this gain is typically unrealized because the resolution obtainable with molecular systems in this mass range is limited by sample heterogeneity. This phenomenon is illustrated with both tobacco mosaic virus (0.6-2.7 MDa) and AAV9 (3.7-4.7 MDa) samples where mass spectral resolution is limited by the sample, including salt adducts, and not by instrument resolution. Nevertheless, the ratio of full to empty AAV9 capsids and the included genome mass can be accurately obtained in a few minutes from 1× PBS buffer solution and an elution buffer containing 300+ mM nonvolatile content despite extensive adduction and lower resolution. Empty and full capsids adduct similarly indicating that salts encrust the complexes during late stages of droplet evaporation and that mass shifts can be calibrated in order to obtain accurate analyte masses even from highly salty solutions.

AbstractA novel tidal analysis package (red_tide) has been developed to characterize low-amplitude non-phase-locked tidal energy and dominant tidal peaks in noisy, irregularly sampled, or gap-prone time series. We recover tidal information by expanding conventional harmonic analysis to include prior information and assumptions about the statistics of a process, such as the assumption of a spectrally colored background, treated as nontidal noise. This is implemented using Bayesian maximum posterior estimation and assuming Gaussian prior distributions. We utilize a hierarchy of test cases, including synthetic data and observations, to evaluate this method and its relevance to analysis of data with a tidal component and an energetic nontidal background. Analysis of synthetic test cases shows that the methodology provides robust tidal estimates. When the background energy spectrum is nearly spectrally white, red_tide results replicate results from ordinary least squares (OLS) commonly used in other tidal packages. When background spectra are red (a spectral slope of −2 or steeper), red_tide’s estimates represent a measurable improvement over OLS. The approach highlights the presence of tidal variability and low-amplitude constituents in observations by allowing arbitrarily configurable fitted frequencies and prior statistics that constrain solutions. These techniques have been implemented in MATLAB in order to analyze tidal data with non-phase-locked components and an energetic background that pose challenges to the commonly used OLS approach.

In this paper, we propose and demonstrate a new method for measuring the trap frequency from the fluorescence dynamics of an ion, initiated using fast trap-center displacement. Here, we observe the coherently excited motion of an ion in a harmonic trap using time-resolved fluorescence detection. Furthermore, Fourier analysis of the ion fluorescence signal was used to determine the trap frequency of an ion with high precision and reproducibility. The results show that our proposed method can be an alternative way to determine trap frequencies in an ion trap experiment. [ABSTRACT FROM AUTHOR]