Fourier Analysis Research Articles

Refractive Astigmatism Consistency Pre- and Post-Cycloplegia in Pediatric Population

Background: Cycloplegic refraction is crucial in pediatric eye assessments. While spherical refraction changes due to cycloplegia are well-documented, astigmatic alterations remain unclear. This study assessed the agreement between spherical and astigmatic refraction pre- and post-cycloplegia. Methods: We enrolled 96 patients (mean age: 12.5 ± 2.4 years), including 35 myopes, 30 emmetropes, and 31 hyperopes. Pre- and post-cycloplegia autorefraction and keratometry (Myopia Master) were conducted using 1% cyclopentolate. Ocular residual astigmatism (ORA) was calculated as the difference between refractive and keratometric astigmatism. Astigmatism was analyzed using Fourier analysis (J0 and J45). Results: Cycloplegia resulted in a more positive spherical equivalent (SE) (+0.80 D), with myopes showing the smallest (+0.38 D) and hyperopes showing the highest variation (+1.47 D) in SE. With-the-rule (WTR) astigmatism predominated in the refractive and keratometric measurements, while ORA was against-the-rule (ATR). Cycloplegia shifted the refractive J0 (+0.06 D) towards more WTR and decreased ORA J0 (+0.05 D). No effect was observed in the J45 component. About 25% of patients exhibited astigmatism changes above 0.25 D, with refractive J0 variation being positively correlated with accommodation relaxation (0.044 D per D of relaxation). Conclusion: Cycloplegia induces clinically significant changes in the spherical component, but minimal variations in astigmatic components, predominantly in hyperopic eyes, likely reflecting alterations in crystalline lens anatomy.

Study on flow field characteristics and fluid-induced resonance analysis of swing check valve

The purpose of this study is to investigate the vibration of the valve flap and rocker arm of DN25 swing check valve in piping system caused by fluid under working condition. Computational fluid dynamics (CFD), fluid–solid coupled modal analysis and harmonic response analysis are used to carry out non-constant flow field calculations and structural modal calculations. The flow field characteristics, pressure pulsations, modal frequencies and modal vibration modes of the flap and rocker stem of the rotary check valve at different opening degrees are obtained. The results show that the fluid in front of the valve is relatively stable, while the fluid behind the valve exhibits chaos and vortex. As the valve opening increases, the vortices dissipate and the fluid becomes orderly. The pressure pulsations are mainly concentrated in the high-velocity region downstream of the valve and gradually decrease as the valve opening in the flow direction increases. The peak frequency distribution of pressure pulsations caused by eddy currents and turbulence is in the range of 30 to 1000 Hz in the valve opening range of 0% to 20%. The peak frequencies of pressure pulsations at 5% and 10% opening are 539.56 Hz and 554.24 Hz, respectively, and the intrinsic mode frequencies are 539.44 Hz and 554.1 Hz. These frequencies are similar to those of the medium frequency resonance (FIR). The maximum amplitude of the pressure pulsation in the valve is 0.1763 mm in the Y-axis and 0.10669 mm in the Z-axis.

Vibration response analysis of hydraulic pipeline based on finite element method

The oil pipeline is a critical component that influences the vibration and noise levels of the hydraulic system. Inadequate design may result in resonance or leakage issues, rendering it susceptible to external vibration excitation. To enhance the reliability of the hydraulic pipeline, simulations and analyses were conducted on its modal, harmonic response, and fatigue characteristics. Based on the results of harmonic response analysis and strength analysis, an effective reinforcement scheme was proposed and validated. By inputting the acceleration load to the pipeline system for frequency response analysis, the influence of different excitation forces on the pipeline stress can be determined. The findings indicate that pipeline vibration primarily occurs in the outlet pipe of the transmission, with significant stress and vibration displacement observed at the thermostat valve support. Following structural improvements, there was a notable reduction in stress levels at the transmission outlet pipe, along with a shift in maximum stress position due to additional support. This enhancement has improved both structural stiffness of the outlet pipe and overall stability of the pipeline system.

An Inverse Inequality for Fractional Sobolev Norms in Unbounded Domains

The nonlocal operators have found applications in various areas of contemporary science. The anomalous diffusion phenomena have been modeled by the fractional Poisson boundary-value problem. Electromagnetic fluids have been described by fractional differential equations. The fractional differential operators have found applications in material sciences, planar and space elasticity, probabilistic theory, harmonic analysis, and even in finance. The inverse inequality plays an important role in Numerical Analysis. The well-known results on inverse inequalities have been obtained in bounded domains and finite-dimensional spaces. Naturally, a new challenge arises to obtain inverse inequalities in the fractional Sobolev spaces. This paper is devoted to differential inequalities between fractional Sobolev norms. We expand the notion of a monotone function into a new notion supermonotone function and rigorously prove an inverse inequality for a class of differentiable functions in unbounded domains. Examples that demonstrate the theory are presented.

Dynamic simulation analysis of aircraft engine planetary gear system

The Geared Turbofan (GTF) engine is used for aircraft propulsion with fan drive, characterized by its complex structure and operation in challenging environmental conditions. During its operation, variations in gear meshing and loads on the transmission shaft exacerbate vibration within the transmission system, leading to a decline in engine performance. This paper established three-dimensional solid models of the X-type aviation engine planetary gear system, input shaft, and output shaft, and employed ADAMS for multibody dynamics analysis, achieving simulation of engine operational vibrations. Modal and harmonic response analyses were conducted using ANSYS to observe and analyze critical parameters such as vibration displacement, vibration acceleration, gear meshing forces, modal resonance, and harmonic resonance, evaluating the impact of vibration amplitude, frequency, and their effects on system performance and longevity, providing guidance for vibration control and optimization of aviation engine systems.

Study of the stability of the linearized compressible Navier-Stokes system

A deep analytic analysis of the stability for the one-dimensional linearized compressible Navier-Stokes system (LNSS) is presented. A very detailed study of the spectrum of the unbounded linear differential operator associated with LNSS has been completed. A Fourier analysis method and an explicit calculation using the eigenvalues of the linear operator make it possible to obtain exponential stability results with a decay rate determined solely according to the parameters of LNSS. Consequently, some exponential stability results are proved in different Hilbert spaces, (in [Formula: see text]-norm and [Formula: see text]-norm). Finally, numerical experiments are presented to verify the theoretical results.

High Data Rate MWD Mud Pulse Telemetry – From Mysteries to Discovery

Our new approach to MWD mud pulse telemetry offers significant increases over conventional data rates. Using waveguide acoustics, we show that common drilling communications channels support carrier frequencies exceeding several hundred Hertz. Such signals are prone to attenuation over large drillpipe distances. Low power, self-spinning “turbosirens” are designed, providing high torque and rotation rate performance at all flow rates without electric or hydraulic motor drives. The sirens rotate, drawing only on the kinetic energy of the mud, like flapping flags oscillating in wind. Our turbosirens are minimally affected by LCM jamming. Turbine and siren rotor components ride freely along longitudinal trenches built into rotating shafts. Both magically float into the oncoming mud as it slows down, thus, widening all gap spaces and freeing any trapped debris even as both travel opposite to the mud flow. In addition, “turbosirens in series” signal superposition, drawing on constructive wave interference, offers strong pressure signals at high frequencies without mechanical complexity. Rapid modulations are possible, also without motor drive, relying on rapidly acting electro-magneto rheological brakes powered by turbosirens. To take advantage of hardware capabilities, “Intelligent i FSK” telemetry, or Frequency Shift Keying creates clean signals without the ambiguous wave reflections found with PSK and randomized time shifts. Frequency pairs are not selected arbitrarily, but chosen from “neighboring pressure peaks and valleys” in frequency space as determined from bottomhole assembly waveguide Fourier analysis. Finally, surface signal processing and reflection removal are facilitated with time delay and differential equation algorithms. For deep wells where multiple drill pipe reflections are unlikely, analytical solutions for both are obtained assuming single reflections which do not involve windowing challenges and complicated digital filter design. Software and hardware developments patented, published and validated over the years, are integrated, refined and readied for controlled field tests.

Experimental investigation of the influence of surface topographic parameters on fluid leakage through static metallic seals

Purpose The purpose of this paper is to monitor leakage in the static sealing interface, using three-dimensional and two-dimensional surface topography parameters as indicators. Design/methodology/approach This study involved developing a test rig for examining fluid leakage in metallic seals. Leakage of water through the interface of the metallic valve and valve seats was measured. The analysis focused on the combined effect of roughness, waviness and form error of metallic seal surfaces on leakage, with a detailed emphasis on the significance of form errors through harmonic analysis. Findings The findings suggest that three-dimensional or areal surface texture parameters have more predictive control over leakage compared to two-dimensional or profile parameters, as they provide information about micro-leak channels in all directions. Moreover, it was observed that average amplitude parameters of surface topography, particularly the form error of metallic valves, are strongly correlated with leakage values compared with the roughness and waviness of the contact surface. In addition, the leakage in metallic seals is profoundly influenced by lower-order harmonics, with a corresponding increase as the average undulation number of the flatness profile rises. Originality/value This research contributes to the understanding of the relationship between surface topography and sealing performance, particularly in metallic seals. By emphasizing the importance of form errors and using advanced surface texture analysis techniques, the study offers insights that can aid in optimizing the design and performance of static seals in industrial applications. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0186/

Data-driven model for marine engine fault diagnosis using in-cylinder pressure signals

Effective diagnosis of marine engines that is crucial for safe and reliable ship operations requires fidel tools for the identification of critical faults. However, the unavailability of extensive measured data-sets corresponding to engine faulty conditions renders the development of such tools challenging. This study aims to develop a data-driven fault estimation model considering information extraction methods and regression techniques of low computational effort, namely multiple linear and polynomial regression. The required data-sets for healthy and faulty conditions for four critical faults and their combinations are generated by employing a calibrated zero-dimensional thermodynamic model representing a marine four stroke medium speed diesel engine, which is validated against engine shop trial measurements. Fourier analysis of the derived in-cylinder pressure profiles is employed to calculate the coefficients of the harmonic orders. Several harmonics coefficients sets are used as input to the regression models to estimate the severity of the four considered faults. The results demonstrate that initial 20 harmonics are sufficient to effectively estimate the severity for each fault, whereas polynomial regression is highly effective, exhibiting R 2 values greater than 98 % . This study provides insights on the data-driven simultaneous faults severity estimation, and as such it impacts the advancement of cost-effective diagnostic methods for marine engines.

Classification of leakage current odd harmonic component of aged insulator surface condition under different relative humidity using crest factor

The impact of pollution on insulator surface performance has been extensively studied to continuously improve the insulator performance using suitable condition monitoring, including using the leakage current harmonic component analysis. However, the analysis of harmonic components, particularly in relation to the odd harmonics of the leakage current in aged insulators under the influence of contamination and humidity, is still not fully understood and remains deficient. In this paper, the leakage current of aged and polluted insulators under different environmental conditions are investigated. The study was conducted experimentally using twelve samples of insulators with varying degrees of aging. The crest factor was employed as an indicator of the leakage current index. The findings showed that the odd harmonic crest factor demonstrates high sensitivity in classifying the degree of aging in contaminated insulators.

Rapid assessment of the levels, nature, and dynamics of sustainability for the United Kingdom 1992–2015 from the doughnut model perspective

The Doughnut model's application to determine sustainability outcomes has thus far been primarily based upon indirect quantitative-based approaches. Therefore, the challenge has been how to directly determine and evaluate sustainability outcomes from a Doughnut-based assessment. In this paper, a direct determination and evaluation of the sustainability of the United Kingdom's environment-human system for the period 1992–2015 from a Doughnut-based assessment is conducted, based upon the application of the Sustainability Dynamics Framework (SDF). The fundamental methodology adopted consisted of: (i). Development of a new scoring criteria framework to convert the indicator-threshold ratios of biophysical boundaries and social threshold indicators into scores; (ii). Determination of the annual indicated values of the Environment (E), Human Needs and Interests (HNI), and Sustainability (S); (iii). Fourier analysis to indicatively determine the dynamics of the UK environment-human system; and (iv). Dynamic modelling of the dynamics of Sustainability (S), Total capital (K), the Earth System (N-A) and dE/dt occurring. The results indicate that the UK's environment-human system was consistent with very weak sustainability throughout the specified period, based upon obtained S-values which were within the range of [+0.075 ≤ S(t) ≤ +0.158] over the specified period. This was due to a declining and fundamentally compromised environmental system caused by the significant exceedance of the biophysical boundaries, and the near-total to total fulfilment of the social thresholds. These outcomes were further supported by the Fourier transformation plots, which indicated increasing dynamic perturbations occurring within the UK environment-human system over the specified period. The paper concludes that the UK will not achieve a state consistent with operating within the safe and just operating space (SJOS), if it continues along its current development pathway. Without fundamental and transformative actions, then there is the realistic possibility of a systemic crisis occurring due to the UK's operating considerably beyond its SJOS.

Thermal one-point functions and their partial wave decomposition

In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on S1 × Sd−1. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant conformal blocks for an external field of arbitrary spin and with any spin exchange along the thermal circle, at least in three dimensions. This is achieved by identifying solutions to the Casimir equations with a special class of spherical functions in the harmonic analysis of the conformal group. The resulting blocks are then applied to study the decomposition of one-point functions of the scalar ϕ2 and the stress tensor T for a three-dimensional free scalar field ϕ. We are able to read off averaged OPE coefficients into exchanged fields of high weight and spin for a complete set of tensor structures. We also extract an asymptotic behaviour of conformal blocks and use it to analyse the density of heavy-heavy-light OPE coefficients for spinning operators, comparing it with semi-classical predictions, such as the dimensions of operators at large charge.

A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, which resolves the problem of harmonic analysis on the infinite-dimensional unitary group

The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to taking the reduced Palm measure at infinity for the decomposing measures in question. The proof proceeds by finite-dimensional approximation of the measures by orthogonal polynomial ensembles. The key remark is that taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.

Extreme wrinkling of the nuclear lamina is a morphological marker of cancer

Nuclear atypia is a hallmark of cancer. A recent model posits that excess surface area, visible as folds/wrinkles in the lamina of a rounded nucleus, allows the nucleus to take on diverse shapes with little mechanical resistance. Whether this model is applicable to normal and cancer nuclei in human tissues is unclear. We image nuclear lamins in patient tissues and find: (a) nuclear laminar wrinkles are present in control and cancer tissue but are obscured in hematoxylin and eosin (H&E) images, (b) nuclei rarely have a smooth lamina, and (c) wrinkled nuclei assume diverse shapes. Deep learning reveals the presence of extreme nuclear laminar wrinkling in cancer tissues, which is confirmed by Fourier analysis. These data support a model in which excess surface area in the nuclear lamina enables nuclear shape diversity in vivo. Extreme laminar wrinkling is a marker of cancer, and imaging the lamina may benefit cancer diagnosis.

Analysis of the Effectiveness of Using Active Filters and Passive Filters in Reducing Harmonics Using a Power Simulator (PSIM) at PT. Delta Jaya Mas

The Extruder Machine at PT. Delta Jaya Mas plays a critical role in the production of rubber and PVC hoses, as well as molded rubber products. This process involves the use of a 3-phase synchronous motor and Variable Frequency Drive (VFD), which can introduce harmonics into the electrical system due to their non-linear load. These harmonics can cause waveform distortion, leading to decreased efficiency and potential equipment damage. To overcome this issue, a comprehensive research is being conducted utilizing the Power Simulator (PSIM) program to analyze the impact of harmonics and evaluate the effectiveness of both active and passive filters in reducing these unwanted distortions. Initial assessments of the Extruder SDP panel revealed elevated levels of Total Harmonic Distortion (THD) in the current phases, while the voltage phases remained within acceptable thresholds. Simulation results demonstrated that the active filter was able to significantly reduce THD to an impressive 1.57%, showcasing its effectiveness in harmonic mitigation. On the other hand, the passive filter also proved beneficial, albeit to a slightly lesser extent, achieving a reduction in THD to 34.07%. This ongoing research not only aims to assist PT. Delta Jaya Mas in implementing appropriate harmonic reduction measures for their Extruder Machine but also seeks to advance the understanding of harmonic analysis and filter applications.

Fourier Analysis with Gini Coefficient: A New Approach to Assess Surface Topography in Direct Laser Interference Patterning

Fourier Analysis with Gini Coefficient: A New Approach to Assess Surface Topography in Direct Laser Interference Patterning

Examination of forces acting on two circular cylinders in tandem arrangement

Flow-induced vibrations of a two-dimensional circular cylinder in the wake of another stationary equal-sized cylinder under a Reynolds number of 150 are numerically simulated by a well-developed in-house code. The center-to-center distance between two cylinders is 4 diameters, and the downstream cylinder with a mass ratio of 50 is free to oscillate in the transverse direction only. The instantaneous frequencies of lift forces acting on both cylinders are obtained by the combined singular spectrum analysis and Hilbert transform method. The time-varying frequencies are consistent with those obtained by the wavelet transform of the original lift forces and also show very good agreement with the vortex shedding frequencies from both cylinders. The time-varying frequency and envelope of lift forces acting on the downstream cylinder are the result of nonlinear fluid–structure interactions, which is ascribed to the presence of multi-frequency components in the frequency spectrum obtained by harmonic analysis. Vibration of the downstream cylinder is the result of vortex shedding from both cylinders. The vortex shedding frequency from the downstream cylinder is greatly influenced by the wake from the upstream cylinder. On the other hand, the movement of the downstream cylinder slightly affects the vortex shedding frequency from the upstream cylinder. Consequently, the cylinder movement is locked upon the natural frequency when the vortex shedding frequency is close to the value of 0.155 in stationary situation, which results in a small synchronized region of the reduced velocity ranging from 6.2 to 6.4.

Preliminary Investigation on Local Solid Earth Tides Variations in Sumatra Island Using Ina-CORS GNSS Network

Abstract Solid earth tides refer to the periodic motion of the Earth’s crust caused by the gravitational forces of the Sun and Moon. In precise geodetic measurements, solid earth tides are a critical source of error that must be mitigated to achieve high accuracy. This study aims to observe variations in local solid earth tides during two significant time periods: when the Earth is at its closest point to the Sun (Perihelion) and at its farthest point (Aphelion). We used multi-day Kinematic Precise Point Positioning (KPPP) to process kinematic data, effectively eliminating discontinuities at day boundaries. Additionally, harmonic analysis with the least squares method was applied to extract tidal generation coefficients in three directions of motion. These coefficients were then compared with theoretical models of solid earth tides, focusing primarily on the largest tidal generation coefficients for amplitude and phase values to identify local variations. Our findings reveal that the lunar semidiurnal coefficient (M2) is the primary tide generator, exhibiting the highest energy percentage. Furthermore, during the Aphelion and Perihelion periods, our results showed no significant differences in tidal ranges at a 95 percent confidence level, indicating that the Sun’s influence on these tidal variations is minimal. Additionally, we compared the differences between observed M2 coefficients, and the theoretical model provided by the International Earth Rotation and Reference Systems Service (IERS) and found discrepancies that led to large tidal residuals, suggesting that local factors, such as geological features, are not fully captured by global models. In conclusion, this study provides valuable insights into understanding local solid earth tides on Sumatra Island.

An enhanced sliding window Fourier analysis with a time delay compensation for single-phase active power filter

An enhanced sliding window Fourier analysis with a time delay compensation for single-phase active power filter

Theoretical Framework for the Response of Barotropic Shelf Current to Along-Shelf Bathymetric Perturbations

Abstract The mechanism underlying the response of barotropic shelf current to along-shelf bathymetric perturbations is rationalized by a one-dimensional vorticity equation. Fourier analysis of the equation in the wavenumber domain suggests that bathymetric features with relatively short length scales in the alongshore direction drive steady cross-shelf velocity undulations when the shelf circulation is against the direction of Kelvin wave propagation (upwelling regime). In contrast, much weaker and nonoscillatory cross-shelf velocity is expected when the shelf circulation is in alignment with propagating Kelvin waves (downwelling regime). The velocity undulations in the upwelling regime result from a positive feedback mechanism associated with potential vorticity (PV) advection; however, the presence of bottom friction restricts such undulations within a few wavelengths. The characteristic wavelength of undulations is determined by when the normalized drag coefficient , where u is the along-shelf mean flow speed, Hs is the shelf depth, αs is the bottom slope, f is the Coriolis parameter, and r is the linear drag coefficient. Using this formula, a scale of the cross-shelf displacement distance Yt is proposed, aligning with one-layer barotropic simulations over a large parameter space. The study provides a framework for investigating barotropic cross-shelf exchange caused by shelf circulation over irregular bottom bathymetries.