Search Results (15)

The 6061 aluminum alloy is extensively utilized in the production of aircraft components, valve parts, and maritime equipment, owing to its exceptional corrosion resistance, weldability, machinability, and anodic oxidation performance. This study investigates the effects of different heat treatment parameters on the mechanical properties of 6061 aluminum alloy. A series of orthogonal experiments were conducted, including quasi-static tensile tests using a QJBV212F-300KN universal testing machine following different solution and aging treatments. Scanning electron microscopy (SEM) was employed for microstructural characterization, revealing the mechanisms by which different heat treatment conditions impact the alloy’s mechanical properties. The test results indicate that the plasticity of 6061 aluminum alloy improves progressively within the temperature range of 510 °C to 540 °C. However, when the solution treatment temperature is elevated to 570 °C, significant grain coarsening occurs, leading to increased brittleness at the grain boundaries and reduced plasticity. Additionally, the elongation of 6061 aluminum alloy initially decreases and then increases as the aging time increases. Based on the experiments, a Hansel–Spittel constitutive model was developed, incorporating temperature, strain rate, and strain effects to accurately predict the flow stress of 6061 aluminum alloy under varying heat treatment conditions. Full article

This paper develops a new formalism to treat both infinite and finite exceptional orthogonal polynomial (EOP) sequences as X-orthogonal subsets of X-Jacobi differential polynomial systems (DPSs). The new rational canonical Sturm–Liouville equations (RCSLEs) with quasi-rational solutions (q-RSs) were obtained by applying rational Rudjak–Zakhariev transformations (RRZTs) to the Jacobi equation re-written in the canonical form. The presented analysis was focused on the RRZTs leading to the canonical form of the Heun equation. It was demonstrated that the latter equation preserves its form under the second-order Darboux–Crum transformation. The associated Sturm–Liouville problems (SLPs) were formulated for the so-called ‘prime’ SLEs solved under the Dirichlet boundary conditions (DBCs). It was proven that one of the two X₁-Jacobi DPSs composed of Heun polynomials contains both the X₁-Jacobi orthogonal polynomial system (OPS) and the finite EOP sequence composed of the pseudo-Wronskian transforms of Romanovski–Jacobi (R-Jacobi) polynomials, while the second analytically solvable Heun equation does not have the discrete energy spectrum. The quantum-mechanical realizations of the developed formalism were obtained by applying the Liouville transformation to each of the SLPs formulated in such a way. Full article

The spatial and temporal distribution of heavy rainfall across the Taihang Mountains exhibits significant variation. Due to the region’s unstable geological conditions, frequent heavy rainfall events can lead to secondary disasters such as landslides, debris flows, and floods, thus intensifying both the frequency and severity of extreme events. Understanding the spatiotemporal evolution of heavy rainfall and its response to atmospheric circulation patterns is crucial for effective disaster prevention and mitigation. This study utilized daily precipitation data from 13 meteorological stations in the Taihang Mountains spanning from 1973 to 2022, employing Rotated Empirical Orthogonal Function (REOF), the Mann–Kendall Trend Test, and Continuous Wavelet Transform (CWT) to examine the spatiotemporal characteristics of heavy rainfall and its relationship with large-scale atmospheric circulation patterns. The results reveal that: (1) Heavy rainfall in the Taihang Mountains can be categorized into six distinct regions, each demonstrating significant spatial heterogeneity. Region I, situated in the transition zone between the plains and mountains, experiences increased rainfall due to orographic lifting, while Region IV, located in the southeast, receives the highest rainfall, driven primarily by monsoon lifting. Conversely, Regions III and VI receive comparatively less precipitation, with Region VI, located in the northern hilly area, experiencing the lowest rainfall. (2) Over the past 50 years, all regions have experienced an upward trend in heavy rainfall, with Region II showing a notable increase at a rate of 14.4 mm per decade, a trend closely linked to the intensification of the hydrological cycle driven by global warming. (3) The CWT results reveal significant 2–3-year periodic fluctuations in rainfall across all regions, aligning with the quasi-biennial oscillation (QBO) characteristic of the East Asian summer monsoon, offering valuable insights for future climate predictions. (4) Correlation and wavelet coherence analyses indicate that rainfall in Regions II, III, and IV is positively correlated with the Southern Oscillation Index (SOI) and the Pacific Warm Pool (PWP), while showing a negative correlation with the Pacific Decadal Oscillation (PDO). Rainfall in Region I is negatively correlated with the Indian Ocean Dipole (IOD). These climatic factors exhibit a lag effect on rainfall patterns. Incorporating these climatic factors into future rainfall prediction models is expected to enhance forecast accuracy. This study integrates REOF analysis with large-scale circulation patterns to uncover the complex spatiotemporal relationships between heavy rainfall and climatic drivers, offering new insights into improving heavy rainfall event forecasting in the Taihang Mountains. The complex topography of the Taihang Mountains, combined with unstable geological conditions, leads to uneven spatial distribution of heavy rainfall, which can easily trigger secondary disasters such as landslides, debris flows, and floods. This, in turn, further increases the frequency and severity of extreme events. Full article

Grids such as perforated plates are of fundamental importance in flow turbulence study and are commonly utilised to promote mixing. An orificed perforated plate (OPP) and its reversed counterpart, the converging-nozzle perforated plate (CNPP), were applied to produce quasi-isotropic turbulence inside a wind tunnel. The three orthogonal velocity components were measured using a triple hotwire at 10D downstream of the perforated plate for Reynolds numbers, Re_D, 18,700 and 28,400, where D is the diameter of the perforated holes. The statistics of the grid-generated turbulence was analysed using the time-averaged local velocity profile and turbulence intensity, which revealed a more homogeneous distribution of the flow field with a higher level of turbulence for the OPP. Fourier and wavelet analyses were employed to investigate the energy of the eddies as a function of frequency and multiscale characteristics of the fluctuating velocity, respectively. At Re_D = 18,700, the turbulent energy remains prominently with large-scale vortical structures which are non-intermittently present in the flow for both perforated plates. The thickness of the converging channels of the CNPP appears to provide the venue for spawning intermittent fluctuations. At higher Re_D 28,400, the effect of this intermittent behaviour becomes evident for the CNPP, leading to a multiscale distribution of turbulent energy. Full article

Cavitation is a quasi-periodic process, and its non-stationarity leads to increasingly complex flow field structures. On the other hand, characterizing the flow field with greater precision has become increasingly feasible. However, accurately and effectively extracting the most representative vibration modes and spatial structures from these vast amounts of data has become a significant challenge. Researchers have proposed data-driven modal decomposition techniques to extract flow field information, which have been widely applied in various fields such as signal processing and fluid dynamics. This paper addresses the application of modal decomposition methods, such as dynamic mode decomposition (DMD), Proper Orthogonal Decomposition (POD), and Spectral Proper Orthogonal Decomposition (SPOD), in cavitation feature detection in hydraulic machinery. It reviews the mathematical principles of these three algorithms and a series of improvements made by researchers since their inception. It also provides examples of the applications of these three algorithms in different hydraulic machinery. Based on this, the future development trends and possible directions for the improvement of modal decomposition methods are discussed. Full article

In this article, we consider the correction of metric matrices in quasi-Newton methods (QNM) from the perspective of machine learning theory. Based on training information for estimating the matrix of the second derivatives of a function, we formulate a quality functional and minimize it by using gradient machine learning algorithms. We demonstrate that this approach leads us to the well-known ways of updating metric matrices used in QNM. The learning algorithm for finding metric matrices performs minimization along a system of directions, the orthogonality of which determines the convergence rate of the learning process. The degree of learning vectors’ orthogonality can be increased both by choosing a QNM and by using additional orthogonalization methods. It has been shown theoretically that the orthogonality degree of learning vectors in the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is higher than in the Davidon–Fletcher–Powell (DFP) method, which determines the advantage of the BFGS method. In our paper, we discuss some orthogonalization techniques. One of them is to include iterations with orthogonalization or an exact one-dimensional descent. As a result, it is theoretically possible to detect the cumulative effect of reducing the optimization space on quadratic functions. Another way to increase the orthogonality degree of learning vectors at the initial stages of the QNM is a special choice of initial metric matrices. Our computational experiments on problems with a high degree of conditionality have confirmed the stated theoretical assumptions. Full article

The pair-interaction force profiles for two non-magnetic colloids immersed in a suspension of ferromagnetic colloidal polymers are investigated via Langevin simulations. A quasi-two-dimensional approach is taken to study the interface case and a range of colloidal size ratios (non-magnetic:magnetic) from 6:1 up to 20:1 have been considered in this work. Simulations show that when compared with non-magnetic suspensions, the magnetic polymers strongly modify the depletion force profiles leading to strongly oscillatory behavior. Larger polymer densities and size ratios increase the range of the depletion forces, and in general, also their strength; the force barrier peaks at short distances show more complex behavior. As the length of the ferromagnetic polymers increases, the force profiles become more regular, and stable points with their corresponding attraction basins develop. The number of stable points and the distance at which they occur can be tuned through the modification of the field strength H and the angle $\theta$ formed by the field and the imaginary axis joining the centers of the two non-magnetic colloids. When not constrained, the net forces acting on the two colloids tend to align them with the field till $\theta =0^{\circ }$. At this angle, the force profiles turn out to be purely attractive, and therefore, these systems could be used as a funneling tool to form long linear arrays of non-magnetic particles. Torsional forces peak at $\theta ={45}^{\circ }$ and have minimums at $\theta =0^{\circ }$ as well as $\theta ={90}^{\circ }$ which is an unstable orientation as slight deviations will evolve towards $\theta \to 0^{\circ }$. Nonetheless, results suggest that the $\theta ={90}^{\circ }$ orientation could be easily stabilized in several ways. In such a case, the stable points that the radial force profiles exhibit for this orthogonal orientation to the field could be used to control the distance between the two large colloids: their position and number can be controlled via H. Therefore, suspensions made of ferromagnetic colloidal polymers can be also useful in the creation of magnetic colloidal tweezers or ratchets. A qualitative explanation of all the observed phenomena can be provided in terms of how the geometrical constraints and the external field modify the conformations of the ferromagnetic polymers near the two large particles, and in turn, how both factors combine to create unbalanced Kelvin forces that oscillate in strength with the distance between the two non-magnetic colloids. Full article

We provide new analytical results for the implementation of the Hausman specification test statistic in a standard panel data model, comparing the version based on the estimators computed from the untransformed random effects model specification under Feasible Generalized Least Squares and the one computed from the quasi-demeaned model estimated by Ordinary Least Squares. We show that the quasi-demeaned model cannot provide a reliable magnitude when implementing the Hausman test in a finite sample setting, although it is the most common approach used to produce the test statistic in econometric software. The difference between the Hausman statistics computed under the two methods can be substantial and even lead to opposite conclusions for the test of orthogonality between the regressors and the individual-specific effects. Furthermore, this difference remains important even with large cross-sectional dimensions as it mainly depends on the within-between structure of the regressors and on the presence of a significant correlation between the individual effects and the covariates in the data. We propose to supplement the test outcomes that are provided in the main econometric software packages with some metrics to address the issue at hand. Full article

The aim of this study is to investigate the characteristics of the intraseasonal oscillation (ISO) with a 10–30-day cycle over mid-high-latitude Eurasia during boreal summer. The leading mode of this ISO is determined using an extended empirical orthogonal function analysis. Through a phase composite analysis, it is observed that a southeastward-propagating wave train with a quasi-barotropic structure is present in Eurasia. The dynamical mechanism and energy conversion affecting its propagation are also analyzed. The negative (positive) temperature tendency appears in the southeastern part of the temperature anomaly in the lower troposphere (upper troposphere), resulting in further southeastward displacement of the temperature perturbation. A diagnosis of temperature tendency shows that the main cause of the southeastward movement is the advection of anomalous temperature by the mean zonal wind. The energy conversion analysis reveals that by converting kinetic energy and potential energy, the ISO perturbation acquires energy from the summertime mean flow during its southeastward movement. Full article

The features of polarization control of multiple multiresonances for quasi-trapped modes excited by synchronization of bianisotropic dipole responses in MoS${}_2$ disks with a hole are considered. Using numerical calculations with analytical multipole analysis, we showed that the presence of a strong optical anisotropy of MoS${}_2$ nanoparticles provides an additional degree of freedom and makes it possible to observe several resonances of electric and magnetic dipoles at once in a narrow spectral range. Based on the simulation results, we obtained the frequency dependences for the dipole polarizabilities of the MoS${}_2$ disk with a hole, which can be used to distinguish the contributions of the nonlocal and bianisotropic dipole responses and possessing several features in the near-infrared range. Using the polarizability spectra of single nanoparticles and applying the tuning strategy, the design of the MoS${}_2$ metasurface placed in air and supporting three resonances of quasi-trapped modes at once in a narrow spectral range was developed. One of these resonances corresponds to the telecom wavelength of about 1550 nm. The spectrum of light reflection for the MoS${}_2$ metasurface is characterized by three narrowband dips corresponding to the wavelengths of the quasi-trapped modes. It was shown that a change in the polarization of a wave normally incident on the metasurface to orthogonal one leads to a change in the type of bianisotropic response excited in each MoS${}_2$ disk and to the excitation of three other features in the reflection spectrum of the metasurface at wavelengths close to the initial values. Full article

The nanostructuring of the (100) PbS single crystal surface was studied under varying argon plasma treatment conditions. The initial PbS single crystals were grown by high-pressure vertical zone melting, cut into wafer samples, and polished. Subsequently, the PbS single crystals were treated with inductively coupled argon plasma under varying treatment parameters such as ion energy and sputtering time. Plasma treatment with ions at a minimum energy of 25 eV resulted in the formation of nanotips with heights of 30–50 nm. When the ion energy was increased to 75–200 eV, two types of structures formed on the surface: high submicron cones and arrays of nanostructures with various shapes. In particular, the 120 s plasma treatment formed specific cruciform nanostructures with lateral orthogonal elements oriented in four <100> directions. In contrast, plasma treatment with an ion energy of 75 eV for 180 s led to the formation of submicron quasi-spherical lead structures with diameters of 250–600 nm. The nanostructuring mechanisms included a surface micromasking mechanism with lead formation and the vapor–liquid–solid mechanism, with liquid lead droplets acting as self-forming micromasks and growth catalysts depending on the plasma treatment conditions (sputtering time and rate). Full article

We report a quasi T-channel electrokinetics-based micromixer with electrically conductive sidewalls, where the electric field is in the transverse direction of the flow and parallel to the conductivity gradient at the interface between two fluids to be mixed. Mixing results are first compared with another widely studied micromixer configuration, where electrodes are located at the inlet and outlet of the channel with electric field parallel to bulk flow direction but orthogonal to the conductivity gradient at the interface between the two fluids to be mixed. Faster mixing is achieved in the micromixer with conductive sidewalls. Effects of Re numbers, applied AC voltage and frequency, and conductivity ratio of the two fluids to be mixed on mixing results were investigated. The results reveal that the mixing length becomes shorter with low Re number and mixing with increased voltage and decreased frequency. Higher conductivity ratio leads to stronger mixing result. It was also found that, under low conductivity ratio, compared with the case where electrodes are located at the end of the channel, the conductive sidewalls can generate fast mixing at much lower voltage, higher frequency, and lower conductivity ratio. The study of this micromixer could broaden our understanding of electrokinetic phenomena and provide new tools for sample preparation in applications such as organ-on-a-chip where fast mixing is required. Full article

We present a compact optical head design for wide-range and low noise displacement sensing using deep frequency modulation interferometry (DFMI). The on-axis beam topology is realised in a quasi-monolithic component and relies on cube beamsplitters and beam transmission through perpendicular surfaces to keep angular alignment constant when operating in air or in a vacuum, which leads to the generation of ghost beams that can limit the phase readout linearity. We investigated the coupling of these beams into the non-linear phase readout scheme of DFMI and implemented adjustments of the phase estimation algorithm to reduce this effect. This was done through a combination of balanced detection and the inherent orthogonality of beat signals with different relative time-delays in deep frequency modulation interferometry, which is a unique feature not available for heterodyne, quadrature or homodyne interferometry. Full article

This paper deals with transformations from electrocardiographic (ECG) to vectorcardiographic (VCG) leads. VCG provides better sensitivity, for example for the detection of myocardial infarction, ischemia, and hypertrophy. However, in clinical practice, measurement of VCG is not usually used because it requires additional electrodes placed on the patient’s body. Instead, mathematical transformations are used for deriving VCG from 12-leads ECG. In this work, Kors quasi-orthogonal transformation, inverse Dower transformation, Kors regression transformation, and linear regression-based transformations for deriving P wave (PLSV) and QRS complex (QLSV) are implemented and compared. These transformation methods were not yet compared before, so we have selected them for this paper. Transformation methods were compared for the data from the Physikalisch-Technische Bundesanstalt (PTB) database and their accuracy was evaluated using a mean squared error (MSE) and a correlation coefficient (R) between the derived and directly measured Frank’s leads. Based on the statistical analysis, Kors regression transformation was significantly more accurate for the derivation of the X and Y leads than the others. For the Z lead, there were no statistically significant differences in the medians between Kors regression transformation and the PLSV and QLSV methods. This paper thoroughly compared multiple VCG transformation methods to conventional VCG Frank’s orthogonal lead system, used in clinical practice. Full article

Flow field in the inter-stage is of great importance to jet engine turbine performance and efficiency. Investigation of flow fields is limited by the complex geometrical structure. Traditional measurement techniques, such as hot wire, pressure probe and laser Doppler velocimetry (LDV) can hardly obtain a planar information of the flow field simultaneously. To overcome this difficulty, an instantaneous planar velocimetry technique, the particle image velocimetry (PIV) technique is widely employed. However, there is no publication that studied the detailed flow field by PIV in a turbine inter-stage with the consideration of the influence of rotor blade and purge flow. This paper presents a quasi-three dimensional perspective of flow field between inlet guide vane (IGV) and rotor blade in a research turbine inter-stage by using a 2D PIV system. Coherent structures in the flow field are extracted by the proper orthogonal decomposition (POD) method. Time-averaged results show the ellipsoid structures caused by secondary flow in the inter-stage. Rotor blade influence to axial and radial flow is evaluated by time-averaged data and the first order POD mode. Egress of purge flow (9.4% of main annulus flow rate) leads to a domain with 60% axial velocity loss near hub and a growth over three times in radial velocity. POD analysis of purge flow shows detailed flow migration in the whole measurement plane. Full article