Smoothing Effect Research Articles

Global Kato smoothing and Strichartz estimates for Schrödinger type equations with rough decay potentials

Let [Formula: see text] be a higher-order elliptic operator on [Formula: see text], where [Formula: see text] is a general bounded decaying potential. This paper focuses on the global Kato smoothing and Strichartz estimates for solutions to Schrödinger-type equation associated with [Formula: see text]. In particular, we first establish sharp global Kato smoothing estimates for [Formula: see text], based on uniform resolvent estimates of Kato–Yajima type for the absolutely continuous part of [Formula: see text]. As a consequence, we also obtain optimal local decay estimates. Using these local decay estimates, we then prove the full set of Strichartz estimates, including the endpoint case. Notably, we derive Strichartz estimates with sharp smoothing effects for higher-order cases with rough potentials, which are applicable to the study of nonlinear higher-order Schrödinger equations. Finally, we introduce new uniform Sobolev estimates of the Kenig–Ruiz–Sogge type, incorporating an additional derivative term, which are crucial for establishing the sharp Kato smoothing estimates.

Imaging the Northern Los Angeles Basins with Autocorrelations

Abstract We show reflectivity cross sections for the San Gabriel, Chino, and San Bernardino basins north of Los Angeles (LA), California, determined from autocorrelations of ambient noise and teleseismic earthquake waves. These basins are thought to channel the seismic energy from earthquakes on the San Andreas fault to LA, and a more accurate model of their depth is important for hazard mitigation. We use the causal side of the autocorrelation function (ACF) to determine the zero-offset reflection response. To minimize the smoothing effect of the source time function, we remove the common mode from the autocorrelation to reveal the zero-offset reflection response. We apply this to 10 temporary nodal lines consisting of a total of 758 geophones with an intraline spacing of 250–300 m. We also show that the ACF from teleseismic events can provide illumination on the subsurface that is consistent with ambient noise. Both autocorrelation results compare favorably to receiver functions.

Solving Viscous Burgers’ Equation: Hybrid Approach Combining Boundary Layer Theory and Physics-Informed Neural Networks

In this paper, we develop a hybrid approach to solve the viscous Burgers’ equation by combining classical boundary layer theory with modern Physics-Informed Neural Networks (PINNs). The boundary layer theory provides an approximate analytical solution to the equation, particularly in regimes where viscosity dominates. PINNs, on the other hand, offer a data-driven framework that can address complex boundary and initial conditions more flexibly. We demonstrate that PINNs capture the key dynamics of the Burgers’ equation, such as shock wave formation and the smoothing effects of viscosity, and show how the combination of these methods provides a powerful tool for solving nonlinear partial differential equations.

Assessing Statistical Methods for Generating Forecasts for COVID-19

The COVID-19 pandemic, a persistent global health emergency that has affected almost all facets of daily life, was initially discovered in Wuhan, China, in December 2019. Since that time, the virus has rapidly spread over the globe, causing serious social and economic upheavals necessitating the need for reliable forecasting methods. This study compares ten distinct models to predict the number of confirmed COVID-19 cases in Sri Lanka, aiming to assess the performance of statistical models using limited and volatile real-world data characterized by trends, random peaks, and autocorrelations. In addition to the classical ARIMA model, various smoothing and filtering techniques were explored to capture the unique characteristics of the data. The model consistencies in multiple-day predictions were demonstrated, and robust evaluation criteria, along with non-robust measures, were utilized to enhance the effectiveness of the evaluation process. The results highlight the effectiveness of traditional smoothing and filtering strategies such as Simple Exponential Smoothing, Holt’s Exponential Smoothing, and the Smoothing Splines technique coupled with the ARIMA model. This study also discovered that the ARIMA model, when applied directly to the original data without using any smoothing or filtering approaches, failed to forecast adequately, thereby demonstrating the insufficiency of the ARIMA model on its own to provide credible forecasts when given a volatile set of data.

Curve smoothening for the analysis of fractal dimensions of blast-cleaned steel surface textures for tribological and adhesion interfaces

Abstract Fractal dimensions are increasingly used for the characterization of surface textures for tribological and adhesion applications. The resolution of 2D profiles acquired from various measurement methods can be adjusted via curve smoothing. It is still unclear whether curve smoothing would notably affect the estimated fractal dimensions. In this communication, 2D profiles of twelve blast-cleaned surface settings were derived by means of a data manipulation software, including a curve smoothing procedure. The fractal dimensions were estimated, and Design of Experiments was applied to analyze the relationships. Factors included abrasive type, preparation grade, roughness, and curve smoothing. Analysis of Variance indicated that the contribution of curve smoothing to the regression model was as low as 1.0%. Therefore, for blast-cleaned substrates, curve smoothing effects can be neglected with respect to the contributions of roughness and abrasive type, when estimating the fractal dimensions.

Research to reduce pain and increase comfort using skin cleaning materials

During her nursing career, Professor Emeritus Hiroko Shimizu focused on the need for nursing care to promote and support patient recovery and found that the use of steam cloths helped relax patients and reduce their physical and mental pain. Shimizu is affiliated with Kagawa University and has been working to investigate the impact of skin cleaning materials on the brain waves of patients. Shimizu and her collaborators set out to create something that could warm people affected by disasters and relieve the pain of cancer patients. The researchers were the first to employ a method invented by Professor Ichirou Ishimaru to measure moisture using near-infrared two-dimensional Fourier spectrometry. They measured moisture smearing on the skin and found a softening and smoothing effect on the skin. This led them to develop a steam-generating cleaning tool that induces relaxation without a towel or cloth. Part of Shimizu’s work concentrates on developing new techniques and measurement methods needed to verify her findings. The researchers also used text analysis of the subjects’ statements and psychological images to project their thoughts and attitudes towards the care provided, as well as an electroencephalogram analysis by a neurologist, Visiting Professor Tetsuo Toge, to correlate the results. Shimizu plans to incorporate an analysis of steam volume and moisture or images with temperature and humidity into her considerations. In one study, Professor Hidekuni Takao, who shared Professor Shimizu's research, is working as the representative of a Japan Science and Technology Agency (JST)-CREST project to develop a rare device to measure the shape of the skin surface. The goal is that the integrated semiconductor tactile sensor the researchers are developing will have equal or even greater sensitivity and performance than that of a human fingerprint.

A highly naturalistic facial expression generation method with embedded vein features based on diffusion model

Abstract Facial expression generation technology has achieved notable progress in computer vision and artificial intelligence. However, challenges persist regarding background consistency, expression clarity, and detailed representation. Additionally, the instability of generative adversarial networks (GANs) during training affects both image quality and diversity. While diffusion models have demonstrated potential advantages over GANs, research on controllable expression generation remains limited. To address these challenges, this paper proposes a highly natural facial expression generation method based on denoising diffusion implicit models (DDIM) with embedded vein features. This approach avoids adversarial training by employing gradual diffusion to generate specific expressions, thereby enhancing both the diversity and authenticity of the images. Vein features are introduced and embedded within the generated expression images to protect the intellectual property of algorithm-generated digital resources. Firstly, image and expression text guide words are combined as conditional inputs to improve the authenticity and diversity of the generated images. Secondly, a classification coding network is introduced to guide expression generation, thus enhancing the accuracy and consistency of the produced expressions. Furthermore, this paper proposes a vein feature fusion method based on multi-directional local dynamic feature coding operator (MLDFO) and integrates DDIM with frequency-domain watermarking technology to achieve image intellectual property protection. Experimental results demonstrate the effectiveness of this method across several public datasets, including FFHQ, CelebA, FV-USM, and SDUMLA-HMT. Notably, in the CelebA dataset, the average expression recognition rate increased by 11.41%, with a 100.00% recognition rate for happy expressions. The generated expression images exhibit a high degree of authenticity and consistency, and the video conversion tests reveal a natural and smooth effect. These results confirm that this method not only advances facial expression generation technology but also significantly enhances the steganographic protection of images.

An Improved PINN Algorithm for Shallow Water Equations Driven by Deep Learning

Solving shallow water equations is crucial in science and engineering for understanding and predicting natural phenomena. To address the limitations of Physics-Informed Neural Network (PINN) in solving shallow water equations, we propose an improved PINN algorithm integrated with a deep learning framework. This algorithm introduces a regularization term as a penalty in the loss function, based on the PINN and Long Short-Term Memory (LSTM) models, and incorporates an attention mechanism to solve the original equation across the entire domain. Simulation experiments were conducted on one-dimensional and two-dimensional shallow water equations. The results indicate that, compared to the classical PINN algorithm, the improved algorithm shows significant advantages in handling discontinuities, such as sparse waves, in one-dimensional problems. It accurately captures sparse waves and avoids smoothing effects. In two-dimensional problems, the improved algorithm demonstrates good symmetry and effectively reduces non-physical oscillations. It also shows significant advantages in capturing details and handling complex phenomena, offering higher reliability and accuracy. The improved PINNs algorithm, which combines neural networks with physical mechanisms, can provide robust solutions and effectively avoid some of the shortcomings of classical PINNs methods. It also possesses high resolution and strong generalization capabilities, enabling accurate predictions at any given moment.

Design a novel algorithm for enhancing UWB positioning accuracy in GPS denied environments

Accurate indoor positioning is the key to the development of the Internet of Things and intelligent devices. In view of GPS-denied indoor environments, we propose to build the indoor local positioning system by using ultra-wide band (UWB) system. In order to enhance the localization accuracy of UWB system, we propose a novel algorithm which integrates the Maximum Correntropy Criterion (MCC) and unscented Kalman filter (UKF) method to reconstruct the measurement distance by using the maximum entropy principle to reduce the influence of outliers and unknown process noise on the smooth effect. Subsequently, the least square (LS) method is implemented to attain the target node (TN) initial position coordinates, and the Taylor algorithm is then performed to further optimize the localization results of the LS method. Lastly, the experimental investigation is conducted to assess the effectiveness and applicability of the developed method via the UWB system in indoor scenarios. The experimental outcomes demonstrate that the developed MCCUKF-LS method can achieve the lowest root mean square error (RMSE), and enhance the positioning accuracy of the TN compared with the LS, KF-LS, and UKF-LS methods. The overall average RMSE of MCCUKF-LS method is reduced by 45.7% contracted with the LS algorithm. The average error of x-, y- and z-axis orientation for the LS method is reduced from 0.074 m, 0.067 m, 0.098 m to 0.036 m, 0.034 m, 0.044 m, and the achieved accuracy in the orientation of the three axes is increased by 51.4%, 49.3% and 55.1% respectively, which reveals that the designed fusion technique is capable of enhancing the positioning accuracy of the TN effectively, providing a new positioning methodology and reference for indoor positioning in GPS-denied environments.

Comparison of Triple Exponential Smoothing and ARIMA in Predicting Cryptocurrency Prices

Cryptocurrency has emerged as a prominent digital asset over the past decade, but its high price volatility presents significant challenges for investors. This study evaluates and compares the effectiveness of the Triple Exponential Smoothing (TES) and Autoregressive Integrated Moving Average (ARIMA) methods in forecasting the prices of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), Solana (SOL), and Ripple (XRP). TES models trends and seasonality in time series data, while ARIMA captures autoregressive patterns and moving averages. The dataset is split into 80% for training and 20% for testing, with performance evaluated using Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE). TES outperforms ARIMA in predicting Bitcoin and Binance Coin, achieving MAPE values of 10.38% and 13.81%, and RMSE values of 3,985.55 and 41.28, respectively. However, ARIMA shows better performance for Ethereum, Solana, and Ripple, with MAPE ranging from 8.78% to 32.84% and RMSE between 0.08 and 204.59. Notably, Ethereum has the lowest MAPE at 8.78%, while Ripple exhibits the smallest RMSE at 0.08. These findings suggest that TES is more suitable for cryptocurrencies with relatively stable price patterns, while ARIMA is better adapted to forecasting highly volatile assets. This research underscores the importance of selecting forecasting models based on the specific characteristics of each cryptocurrency

The impact of spatial representation in energy transition modelling on systemwide energy return on investment

AbstractAdopting aggregation techniques in power sector modelling led to disregarding the key characteristics of regions in terms of resource use, which may not completely capture the bottlenecks in the energy transition. This study provides a holistic approach to estimate its impact on the transition of the European power system from the perspective of energy return on investment (EROI) by using six energy transition scenarios based on three different spatial representations. The findings indicate that EROI trends are highly dependent on the spatial representation, technology selection and energy mix. Further additional capacities of complementary technologies along with an upsurge in renewable capacities drive EROI values down. Disregarding the physical distances in the energy modelling results in large EROI enhancement due to the artificial smoothing effect of the aggregation method. EROI values of the aggregated scenarios remain between 18 and 24 by 2050. In the case of 20 independent sub‐regions, the lowest EROI is obtained at about 14 by 2050, due to the limitation on optimal resource utilisation. Interconnection of the sub‐regions, which represents the best proximation to the real situation, increases the EROI to 17 by 2050.

Modeling window smoothing effect hidden in fringe projection profilometry

The reconstruction using MEMS micro-vibration mirrors is the most promising. However, the influence mechanism of the line laser, which serves as the sole light source of MEMS-based systems, on reconstruction is unclear. To fill this theoretical gap, we propose the first interpretable laser influence model called the window smoothing model. This model reveals the window smoothing effect of laser beam scanning and quantifies its impact on modulation intensity through a decay factor. Given the absence of lens defocusing issues, the window smoothing effect becomes the primary factor affecting the contrast of fringe patterns. Therefore, a novel method using laser parameters to evaluate system accuracy is introduced. Leveraging these insights, we further propose an optimal fringe number calibration method, also based on laser parameters, to maximize the reconstruction accuracy of any given system. Finally, experimental results validate the effectiveness of the proposed method. As the first model tailored for MEMS systems, the window smoothing model is interpretable, highly accurate, and universal. Therefore, this model can provide new insights and a theoretical foundation for achieving high-performance MEMS-based reconstruction.

Analyzing the permeability distribution of multilayered specimens using pulsed eddy-current testing with multi-scale 1D-ResNet

The mechanical properties of steel are determined by its microstructure, which is closely related to its permeability profile. In thermal processing, layered structures are formed in steel and different layers have different mechanical and magnetic properties. Therefore, it is crucial to propose a practical method to monitor the change of permeability profile along the depth, which can indicate the evolution of the microstructure of steel during thermal processing, such as hot rolling. This paper presents a method for determining the layered structure and permeability profile of the steel by using pulsed eddy current testing (PECT), which offers better penetration ability. An analytical model has been deduced for calculating the time-domain pulsed eddy current (PEC) response from a Hall sensor of a triple-layer conductor system based on the inverse Laplace transform. It is found the Tau (τ) curve is closely related to the permeability profile of the conductor. For the inverse solution, the Simultaneous Iterative Reconstruction Technique (SIRT) is utilized to determine the permeability profile of the multilayered specimens from the measured response. The approximate Jacobian matrix (sensitivity matrix) is obtained by the perturbation method based on the Tau curve. However, the permeability profile suffers from smoothing effect and sharp features are lost. Deep learning (DL) algorithm based on the Multi-Scale 1D-ResNet model is therefore introduced to address this issue. Numerical simulations and experiments have been performed to evaluate the proposed method for permeability profile estimation with various materials and thicknesses. The DL method can achieve an accurate estimation of the plate permeability profile with a relative error under 5%.

Broad table-like magnetocaloric effect in the full hydrogen liquefaction range in Gd3Ni6XY

Gd3Ni6SiAl, Gd3Ni6SiGa, and Gd3Ni6AlGa (Ce3Ni6Si2-type, Im-3m, N 229, cI44) present a broad table-like magnetocaloric effect in the full hydrogen liquefaction range (20-77K) with a real plateau wide enough to be competitive for refrigeration devices based on the Ericsson cycle. The characterization of the magnetocaloric variables (|ΔSMpk|= 6.60J/kgK, TEC(10)= 6.44J/kgK for Gd3Ni6SiGa, |ΔSMpk|= 6.05J/kgK, TEC(10)= 6.01J/kgK for Gd3Ni6SiAl, all at μ0ΔH=5T) state that they are among the best of table-like magnetocaloric materials in this temperature range. The physical origin of this smooth and wide table-like effect is the combination of a spin reorientation transition (which appears in Gd3Ni6XY when Si or Ga is introduced) with the paramagnetic to ferromagnetic transition, close to each other. The application of the Banerjee criterion and the evolution of the critical exponent with temperature n(T) confirm that both transitions are second order, which is extremely relevant for real applications. From the study of the magnetic properties it has been inferred that the introduction of Si induces a magnetic ground state with combined ferromagnetic and antiferromagnetic components which turns to fully ferromagnetic at very low field. The critical exponents (β, γ, δ, n) have been found for the paramagnetic to ferromagnetic transitions; the values of γ (from 1.22 to 1.36) suggest that the magnetic interactions are short-range, though the ensembles do not correspond to any particular universality class.

Wind farm cluster power prediction based on graph deviation attention network with learnable graph structure and dynamic error correction during load peak and valley periods

The power prediction accuracy of wind farm cluster (WFC) seriously affects its consumption and the safe and stable operation of power system. The fluctuation of power between wind farms (WFs) significantly affects the wind power ultra-short-term prediction (WPUP) accuracy of WFC. In this regard, this paper proposes a graph deviation attention network (GDAN) considering improved clustering distance and learnable graph structure (LGS) for predicting and correcting the wind power of WFC. And used a weighted distance function combining sequence convergence smoothing effect and correlation to dynamically divide the WFC, and to learn and construct the graph structure. Proposed the GDAN with LGS to mine the convergence correlation of WF sub-clusters and establish power prediction model. Considering the characteristics of load peak and valley periods (LPVP), introduced a power correction coefficient to reduce the error, and used the successive variational mode decomposition (SVMD) to extract its key components to achieve power prediction and correction. The proposed method is applied to the WFC in Western Inner Mongolia, China. Compared with the comparison model before correction, the RMSE, MAE and MAPE are reduced by 4.27 %, 3.55 % and 17.92 % respectively, and the R2 and Pr are increased by 11.87 % and 9.88 % respectively.

Time resolution of wind speed data introduces errors in wind power density assessment

Wind energy is critical in the global shift towards renewable energy sources, necessitating accurate potential assessments for informed decision-making and strategic development in this transition. Despite the widespread use of wind speed data with varying time resolutions for estimating wind energy, the influence of this variability on the accuracy of wind energy assessment remains uncertain. In this study, we investigate the impact of wind speed data’s time resolution on wind power density (WPD) assessment, utilizing high-frequency, in-situ observations collected from eight anemometer towers in China. Through analysis of wind speed data at nine resolutions, ranging from 10-minute to monthly intervals, we uncover significant errors introduced by coarser time resolutions in WPD calculations. Specifically, it reveals a systematic underestimation of WPD with decreasing time resolution, highlighting the importance of time resolution in wind energy evaluation. While hourly wind speed data yield acceptable WPD errors, daily and monthly resolutions lead to substantial underestimation due to the smoothing effect of fluctuations. We also delve into the underlying mechanisms contributing to these errors, including variations in the power law exponent and changes in the Weibull distribution shape factor with time resolution. Furthermore, we propose a novel method to mitigate WPD calculation errors using coarse time resolution data by regressing Weibull distribution factors. The findings offer valuable insights into wind speed data selection and accurate wind energy assessment, with implications for renewable energy planning and policy-making in the context of the global energy transition.

INNOVATIVE APPROACH TO ENSURING THE QUALITY OF GAS TURBINE ENGINE PARTS PRODUCED BY SELECTIVE LASER SINTERING FOR UAV

The research objects are gas turbine engines parts, manufactured using an innovative method of additive manufacturing – selective laser sintering. The main problem solved in this work is the low quality of the surface layer and the residual porosity of the parts obtained by this method, which significantly limits their operational characteristics and durability. As a result of the experimental studies, rational operating parameters of diamond smoothing were established. This allowed to significantly improve the surface quality and increase the operational characteristics of parts made of heat-resistant alloys INCONEL 718 and an intermetallic alloy based on titanium aluminide OX45-3ODS. The effectiveness of diamond smoothing is explained by local plastic deformation and compaction of the surface layer of parts under the influence of high contact pressures and temperatures. This leads to a significant reduction in surface roughness, an increase in the surface hardness due to strain hardening and a significant reduction in the size and number of residual pores. A characteristic feature of the obtained results is the ability to control the quality parameters of the surface layer by varying the diamond smoothing operating parameters – smoothing force, feed, radius, and geometry of the smoother's working part. The established regularities of the smoothing operating parameters have an impact on the quality characteristics of the surface. This information can be utilized in the development of highly efficient technological processes for the production and restoration of gas turbine engines, critical components of unmanned aerial vehicles, obtained through selective laser sintering. Implementing the elaborated technological recommendations will permit broadening the range of goods produced by additive manufacturing and enhancing their capacity and dependability during operation under conditions of cyclical loads and extreme temperatures.

Module‐Based Supercapacitors: Potential Energy Storage Solutions for Large‐Scale Photovoltaic Systems

Intermittency is an inherent characteristic of photovoltaic (PV) power generation and results in high ramp rates of the generated power. This article explores the feasibility of integrating supercapacitors at the PV module level, aiming to reduce the power fluctuations of PV systems and control the power ramp rate into the power grid. First, an equivalent circuit model of a single‐phase grid‐connected PV system based on module‐based supercapacitors is proposed, and a power ramp rate control scheme is established. Then, experimental setups for a single‐phase grid‐connected PV system based on module‐based supercapacitors are implemented, and the computational model is verified through experiments. Finally, using the verified computational model and the proposed control scheme, the module‐based supercapacitor sizes for different PV system sizes (PV module, rooftop, small system, large system) that meet specific ramp rate requirements under different ramp rate limits (5, 10, 15% min−1) are compared. Case studies show that large‐scale PV systems with geographical smoothing effects help to reduce the size of module‐based supercapacitors per normalized power of installed PV, providing the possibility for the application of modular supercapacitors as potential energy storage solutions to improve power ramp rate performance in large‐scale PV systems.

Foreign Accent and Forensic Speaker Identification in Voice Lineups: The Influence of Acoustic Features Based on Prosody.

This research aims to examine both the prosodic-acoustic features and the perceptual correlates of foreign-accented English and foreign-accented Brazilian Portuguese and check how the speakers' productions of foreign and native accents are correlated to the listeners' perception. In the Methodology, we conducted a speech production procedure with a group of American speakers of L2 Brazilian Portuguese and a group of Brazilian speakers of L2 English, and a speech perception procedure in which we performed voice lineups for both languages.For the speech production statistical analysis, we ran Generalized Additive Models to evaluate the effect of the language groups on each class (metric or prosodic-acoustic) of features controlled for the smoothing effect of the covariate(s) of the opposite class. For the speech perception statistical analysis, we ran a Kruskal-Wallis test and a post-hoc Dunn's test to evaluate the effect of the voices of the lineups on the scores judged by the listeners. We nevertheless conducted acoustic (voice) similarity tests based on Cosine and Euclidean distances. Results showed significant acoustic differences between the language groups in terms of variability of the f0, duration, and voice quality. For the lineups, the results indicated that prosodic features of f0, intensity, and voice quality correlated to the listeners' perceived judgments.

Quantifying the effect of scanning parameters on digital volume correlation analysis for in situ X-ray imaging of concrete

The potential effects of X-ray Computed Tomography (XCT) scan settings on the kinematic field computed via Digital Volume Correlation (DVC) are discussed in this paper. A parametric sensitivity study was conducted, including a series of acquired XCT scans, probing the same volume of interest (VOI) of a concrete specimen, and applying various combinations of XCT scan settings. Different values were adopted for the number of projections acquired, the exposure time and the pixel size. The DVC results revealed a linear correlation between the mean normalised correlation residuals, designating the quality of the correlation and the reliability of the computed kinematic field and the scanning parameters. Gaussian and median filters were applied to the raw data to explore the effect of image noise smoothness in the DVC analysis. The significant reduction noted for the mean normalised correlation residuals was not accompanied by similar levels of change for the corresponding error uncertainties, as defined by the displacement magnitude. The concept was tested against a realistic loading scenario, where the DVC kinematic fields, computed for various XCT “recipes”, were compared. Slim differences in the distribution of the mean minimum principal strain were observed.