Time Difference Method Research Articles

Greedy trial subspace selection in meshfree time-stepping scheme with applications in coupled bulk-surface pattern formations

Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels with high orders of smoothness on some sufficiently dense set of trial centers provides high spatial approximation accuracy that can exceed the accuracy of finite difference methods in time. The paper proposes a greedy approach for selecting trial subspaces in the kernel-based collocation method applied to time-stepping to balance errors in both well-conditioned and ill-conditioned scenarios. The approach involves selecting trial centers using a fast block-greedy algorithm with new stopping criteria that aim to balance temporal and spatial errors. Numerical simulations of coupled bulk-surface pattern formations, a system involving two functions in the domain and two on the boundary, illustrate the effectiveness of the proposed method in reducing trial space dimensions while maintaining accuracy.

Effect of internal fluid and external shear flow on vortex-induced vibration response of drilling riser

This study introduces a new numerical tool for exploring the impact of various dimensionless parameters on vortex-induced vibration in risers. The tool is based on an innovative coupled model of a riser and a modified wake oscillator, which integrates the effects of internal axial flow and external cross flow. The dynamic equations are discretized using a second-order finite difference method in both time and space domains. Simulations reveal multi-modal behavior in the riser's vortex-induced vibration response, including lock-in and synchronous vibration. It is demonstrated that increasing internal flow velocity reduces response mode number and periodicity, and the riser becomes unstable when centrifugal force equals axial tension. The study also shows that higher maximum external flow velocities increase the frequency components of the riser's response and vortex shedding frequency range. A quarter-period phase difference between structural displacement and lift coefficient is observed, while lift coefficient and structural velocity remain synchronous. The lift frequency, as a function of position, jumps between neighboring sections of the riser. This tool provides a foundation for future research, with the cases explored serving as examples of its potential applications in investigating VIV phenomena.

Exponential time difference methods with spatial exponential approximations for solving boundary layer problems

AbstractIn this work, an efficient and stable exponential time difference method is presented for solving boundary layer problems. By combining exponential time difference schemes with spatial direct discontinuous Galerkin discretization based on exponential boundary layer approximations, the proposed algorithm not only may admit large time step sizes but also could provide good spatial approximations even if on rather coarse spatial grids in the boundary layer. Some energy stabilities of the numerical scheme are rigorously derived. Numerical examples illustrate the accuracy, stability and efficiency of the algorithm.

Fourier spectral exponential time-differencing method for space-fractional generalized wave equations

Fourier spectral exponential time-differencing method for space-fractional generalized wave equations

Enhanced Area Defense: Magnetic Launcher and Sensor Integration

In this article, the most appropriate design method for a field defense system that operates with magnetic field laws by taking audio and video signals as reference is described. The study is important because it eliminates the operator (soldier) factor in the battlefield. Taking into account the effect of capacitor voltage, capacitance value and accelerator winding inductance value, the main criteria for determining the power supply and armature structure of the electromagnetic launcher are proposed. This proposal is made with MATLAB/Simulink software based mathematical model and the differences are explained by comparing with ANSYS Maxwell simulation. The simulated results show that the speed difference between the models is 7%. Additionally, the design methods of the audio and video-based positioning systems that control the system are explained in the study. In this system where signal receiving microphones are positioned in triangular form, a linear algorithm using the time difference method is utilized. By comparing the theoretical mathematical model with the experimental simulation model, the accuracy of the method and the method function is proved. In this study, a deep learning-based target detection system that operates with the YOLO v2 algorithm is used to increase the system's mission execution capacity. The operator is eliminated by switching the system with the signal received from the positioning systems.

The effect of micro-nanostructural changes on the absorption and emission characteristics of InGaAsP photocathodes

In this paper, three structures (cylinder, square column, and hexagonal prism) of InGaAsP nanowire arrays are designed based on the excellent light trapping effect of nanostructures. The effects of nanowire aperture, array period, and nanowire height on the light absorption properties are simulated and analyzed using the finite-domain time-difference (FDTD) method. The photoelectron emission capacity of the nanowire arrays was also calculated using MATLAB. The results show that the cylindrical nanowire array has phenomenon of resonance enhancement (absorption peak) in the near-infrared band of 820–1000[Formula: see text]nm, and the shift of absorption peaks can be achieved by adjusting the geometric parameters. Meanwhile, the quantum efficiency is taken to 9.98%. These simulation results provide some reference for the photocathode design of InGaAsP in the near-infrared band.

Petroleum System Analysis and Burial History of Middle Permian Source Rock in Turpan–Hami Basin, NW China

The pre-Jurassic in the north depression of the Tuha depression is the most favorable replacement strata to obtain new reserves in the Turpan–Hami Basin. (Pre-Jurassic, in this paper, refers to the Permian and Triassic.) The main source rocks are the Taodonggou Group, of which the burial history and hydrocarbon generation potential remain unconfirmed. The investigation of the burial and thermal history is vital for the basin analysis and hydrocarbon exploration. Therefore, in this paper, by using the acoustic time difference method, vitrinite reflectance method, stratigraphic trend method and PetroMod-1D software, the differential characteristics of denudation thickness, burial history and thermal evolution history of different tectonic units in different periods of Taibei Sag in the Turpan–Hami basin are studied, and their influence on the petroleum system is analyzed, and then the zones with exploration potential are optimized. The results show that the Taibei Sag has experienced multiple tectonic uplift events. The Late Indosinian movement has profound effects on the Taodonggou Group source rocks. The rather large uplift amplitude postpones the maturation of source rocks. In addition, the Turpan–Hami Basin is a typical cold basin. Therefore, the thermal maturity of the source rocks is relatively low, with respect to the relatively deep burial. The thermal histories of the different sub-sags in the study area are slightly differentiated from each other. The Taodonggou Group source rocks in the Taibei Sag generally became mature during the Mid–Late Jurassic epoch, except for those in the Central–Southern Shanbei sub-sag, represented by Well LT-1, which reached the mature stage during the Late Triassic epoch. The study area has well-developed reservoir rocks, and effective reservoir bodies are formed in the slope zone and near the Tainan Sag, due to the higher porosity and permeability of reservoir rocks. The statistics related to the faults and an analysis of the structural styles of oil reservoirs indicate that the structural slope and anticline of the Huobei, Lianbei and Shanbei sub-sags are favorable for increasing reserves and production of hydrocarbons.

Early pitting fault detection for polymer gears using kurtosis-VMD based condition indicators

The vibration signals of a polymer gear are considerably weak and susceptible to ambient noise at the early stage of the fault, which makes the fault difficult to detect. Efficient detection of an early fault in a polymer gear may improve the operation safety of the machinery system that utilizes it for power transmission. This study introduces an innovative approach for the early detection of pitting faults in polymer gears, utilizing condition indicators (CIs) derived from kurtosis-variational mode decomposition (VMD). First, the vibration signal of the polymer gear is decomposed using VMD into several components. Second, the sensitive components are selected to construct a new signal from the first two largest kurtosis values. Third, the CIs are extracted from newly constructed signals, and envelope spectrum analysis is performed. It is observed from the results that the kurtosis-VMD based CIs are effective in the early pitting fault detection of polymer gears. Finally, it is found that the proposed method performs better in all operating conditions considered in the experiment, compared with raw signal and kurtosis-empirical mode decomposition (EMD) based analysis. The proposed method’s response to noise is also explored. Furthermore, the proposed method is compared with the existing time synchronous averaging (TSA), difference, and residual methods.

Solution of The Duffing Equation Using Exponential Time Differencing Method

To describe the spring stiffening effect that occurs in physics and engineering problems, Georg Duffing added the cubic stiffness term to the linear harmonic oscillator equation and is now known as the Duffing oscillator. Despite its simplicity, its dynamic behavior is very diverse. In this research, the Exponential Time Difference method is introduced to solve the Duffing oscillator numerically. To formulate the ETD method, we were using the integration factors. It is a function which, when multiplied by an ordinary differential equation, produces a differential equation that can be integrated. This method is an effective numerical method for solving complex differential equations, especially equations that have strong non-linearity The ETD method delivers highly accurate numerical solutions for the Duffing oscillator, with minimal discrepancy from the analytical results. Through parameter variation, the ETD method's applicability extends to diverse Duffing oscillator configurations.

Аналитическое решение задачи оценки местоположения источника радиоизлучения разностно-дальномерным методом

The problem of calculating the coordinates of a radio source by the time-difference method based on the results of measuring the distance differences of three pairs of receiving stations is considered. In contrast to the known solutions, analytical relations have been obtained for the case when the distance differences were determined by five receiving stations, in which two pairs contain one common receiving station, and the third pair was formed by two receiving stations with arbitrary coordinates. A numerical example of calculation, illustrating the performance of the method is given.

Evaluation of the Time Difference Method in Identifying Hepatocellular Carcinoma in Current CEUS LR-M Category Nodules

ObjectiveTo explore a potential method for improving the diagnostic detection hepatocellular carcinoma (HCC) based on the contrast-enhanced ultrasound (CEUS) liver imaging reporting and data system (LI-RADS) version 2017. MethodsWe retrospectively evaluated 585 liver nodules in 427 patients with HCC risk from December 2020 to March 2023. The nodules were categorized as LR-1 to LR-M based on CEUS LI-RADS version 2017 and were randomly subclassified into a developmental cohort (DC) and a validation cohort (VC) at 3:1. In the DC, the cutoff value of the time difference (∆T) for differentiating HCC from other malignancies in LR-M was calculated, which was used to reclassify nodules in the VC. The diagnostic effect on HCC detection before and after reclassification was further assessed. ResultsAccording to the current CEUS LI-RADS, 140 of 426 (32.9%) confirmed HCC nodules were misclassified as LR-M. In the DC (439 nodules), the receiver operating characteristic (ROC) curve showed that the cutoff value of ∆T (washout onset time minus contrast arrival time) recommended for HCC diagnosis was greater than 21 s. In the VC (146 nodules), 34 HCCs were correctly categorized as LR-5 according to the cutoff value and after reclassification LR-5 had higher accuracy (67.1% vs. 89.0%, p < 0.001) and sensitivity (56.0% vs. 87.2%, p < 0.001) for HCC diagnosis with high specificity (100% vs. 94.6%, p = 0.500) remained. ConclusionUsing the time difference method could identify HCC nodules misdiagnosed as LR-M and improve the diagnostic performance for current CEUS LI-RADS.

Application of a hybrid pseudospectral method to a new two-dimensional multi-term mixed sub-diffusion and wave-diffusion equation of fractional order

&lt;abstract&gt;&lt;p&gt;In the current study, a novel multi-term mixed sub-diffusion and wave-diffusion model was considered. The new model has a unique time-space coupled derivative in addition to having the diffusion-wave and sub-diffusion terms concurrently. Typically, an elliptic equation in the space variable is obtained by applying a finite difference time-stepping procedure. The severe stability restrictions are the main disadvantage of the finite difference method in time. It has been demonstrated that the Laplace transform is an excellent choice for solving diffusion problems and offers a substitute to the finite difference approach. In this paper, a method based on Laplace transform coupled with the pseudospectral method was developed for the novel model. The proposed method has three main steps: First, the model was reduced to a time-independent model via Laplace transform; second, the pseudospectral method was employed for spatial discretization; and finally, the inverse Laplace transform was applied to transform the obtained solution in Laplace transform domain back into a real domain. We also presented the numerical scheme's stability and convergence analysis. To demonstrate our method's efficacy, four problems were examined.&lt;/p&gt;&lt;/abstract&gt;

Optimization design and research of ultrasonic flowmeter based on time difference method

Optimization design and research of ultrasonic flowmeter based on time difference method

Runge–Kutta type Time Stepping Methods for Space Fractional Reaction Diffusion Model with Restricted Padé Approximation

A new numerical method that solves a time-space-fractional reaction-diffusion equation effectively is presented. The space-fractional Riesz operator is first discretized using fourth order compact finite differences, resulting in a system with a linear stiff term. The system of differential equations is then solved through time integration using an exponential time difference method, which explicitly handles the nonlinear non-stiff term. Restricted Padé rational approximation of a single real pole is used to approximate the matrix exponential e-A. The problems concerning the stability and computational efficiency of this new approach are tackled by means of a splitting technique. Based on compact finite differences with third-order accuracy in time and restricted Padé approximation, this novel efficient technique reduces computing cost and effectively tackles the problems with non-smooth initial data. The superiority of new method in terms of accuracy, reliability, and computational efficiency is finally shown by numerical examples.

Study on detection of intracerebral hemorrhage based on frequency difference of permittivity

Introduction: Current detection of intracerebral hemorrhage (ICH), whether employing Electrical Capacitance Tomography (ECT) or other electrical imaging techniques, rely on time-difference measurements. The time-difference methods necessitate baseline measurements from the patient in a non-hemorrhagic state, which is impractical to obtain, rendering rapid detection of ICH unfeasible.Methods: This study introduces a novel approach that capitalizes on the distinct dispersion characteristics of the permittivity in brain tissue and the spectral variance of the permittivity between blood and other brain components. Specifically, the frequency-dependent variations in the permittivity are employed to achieve absolute detection of ICH, thereby eliminating the need for non-hemorrhagic baseline data. The methodology entails identification of two frequency points that the frequency-dependent variation in the permittivity at these two frequency points manifest the maximal difference between blood and other brain tissues. Subsequently, this permittivity differential at the two identified frequency points is utilized for hemorrhage detection. Experimental measurements were conducted using an impedance analyzer and a parallel plate capacitor to capture the capacitance in four single-component substances—distilled water, sheep blood, isolated pig fat, and isolated pig brain—as well as three mixed blood compounds—distilled water enveloping sheep blood, pig fat encapsulating sheep blood, and pig brain surrounding sheep blood—across a frequency range of 10 kHz to 20 MHz.Results: The results show that in different frequency bands, it is indeed possible to distinguish single-component substances from mixed substances by the frequency difference of capacitance variation. Comparative analysis reveals that the 1 MHz to 5 MHz frequency range is most effective for detecting blood in distilled water. For blood detection in pig fat, a 10 kHz to 1 MHz frequency range is identified as optimal, while a 10 kHz to 0.5 MHz frequency range is advantageous for blood detection in pig brain tissue.Discussion: The findings confirm that absolute detection of ICH is achievable through frequency-dependent variations in the permittivity. However, this necessitates the identification of the frequency band manifesting the largest difference of frequency-dependent variation between single-component and mixed substances. The study acknowledges limitations primarily due to the use of anticoagulant-altered sheep blood, which exhibits permittivity divergent from those of natural blood. Additionally, the in vitro pig fat and pig brain samples, having been subjected to freeze-thaw cycles, also demonstrate permittivity unrepresentative of in vivo tissue.

Pointwise second order convergence of structure-preserving scheme for the triple-coupled nonlinear Schrödinger equations

In this paper, we present a finite difference scheme for the triple-coupled Schrödinger equations (T-CNLS) in optics. The T-CNLS is approximated by Crank-Nicolson scheme in time and finite difference method in space. Some mathematical characters are investigated, such as structure-preserving properties, unique solvability, convergence in L∞ norm. Some numerical examples are reported to illustrate the theoretical results.

Bayesian acoustic emission time-difference method for locating the collision point of sweeping robot shell

The existing source localization based on acoustic emission technology often depends on the assumption of constant wave velocity inside the material. However, this assumption is hardly satisfied in actual engineering. The uncertainty of wave velocity can easily lead to low localization accuracy of sweeping robots. To overcome these deficiencies, a complete probability multi-directional measurement method based on the Bayesian inference mechanism is proposed. In the proposed method, based on the Bayesian probabilistic model, the extracted sensor time difference is subjected to probabilistic inference using the coordinate input model to determine the posterior distribution of the source’s position and wave velocity of the given arrival time. Compared with the traditional time-difference method, the proposed method achieves excellent results and outperforms the standard time-difference method in localization accuracy and anti-interference. In addition, the proposed method can conveniently, quickly, and effectively determine the location of the colliding point without considering the source emission time and wave velocity. The research in this paper provides an effective method for solving the collision localization problem of the sweeping robot shell under the acoustic emission time and wave velocity are unknown.

Ultrasonic gas flow metering in hydrogen-mixed natural gas using Lamb waves

Hydrogen mixing in existing natural gas pipelines efficiently achieves large-scale, long-distance, and low-cost hydrogen delivery. The physical properties of hydrogen and natural gas differ significantly. Hydrogen-mixed natural gas modifies the flow state and thermodynamic properties of the original natural gas in the pipeline. Hydrogen-mixed natural gas can lead to increased errors in ultrasonic flow metering because of the high sound speed and low density of hydrogen. Ultrasonic flowmeter installation distances need to be re-determined. In this study, a Lamb wave non-contact ultrasonic gas flow meter is used to measure the flow of hydrogen-mixed natural gas in a T-type pipeline. The greater the hydrogen mixing ratio, the higher the flow rate of the branch pipeline, and the shorter the installation distance of the ultrasonic flow meter, for example, 10% at 150D, 20% at 110D, and 30% at 20D. The time-difference method with high accuracy and broad applicability is used to calculate the flow rates of COMSOL simulated values. The errors between COMSOL simulation and theoretical flow rates at the shortest installation distance downstream do not exceed 3%. The errors at the position where the mixing uniformity is 80% are significantly higher than those at the shortest installation distance, and the maximum error is about 7.7%. The COMSOL simulation results show the feasibility and accuracy of ultrasonic gas flow metering of hydrogen-mixed natural gas.

One-dimensional position-sensitive detector for alpha particles using an outer-layer scintillating fiber

For applications of detecting alpha contamination and identifying its location over a wide area at a time in nuclear plants and radiation facilities, a position-sensitive detector for α-rays based on an outer-layer scintillating (OLS) fiber with silicon photomultiplier (SiPM) readout was developed. While a standard scintillating fiber is unable to detect α-rays due to their short range, the OLS fiber has a thin scintillation layer on its surface that enhances its potential for α-ray measurements. We initially performed measurements using an Am-241 source to compare the α-ray-detection capability of the OLS fiber with that of a conventional scintillating fiber. Subsequently, a position-sensitive detector employing the time-difference method was developed to measure the radiation distribution along the fiber in a one-dimensional format. The time and spatial resolutions of the measurement system, which used a single 2.2-m-long fiber, were estimated to be approximately 3.6 ns and 290 mm full width at half maximum (FWHM), respectively. Results from two Am-241 sources placed simultaneously indicated that the resolving capability to distinguish the two sources of the measurement system was <300 mm.

Real Time Measurement of Multiphase Flow Velocity using Electrical Capacitance Tomography

Accurate and real-time measurement of fluid flow velocity is crucial in various industrial processes, especially when dealing with multiple phase fluids. Traditional flow measurement methods often struggle to accurately quantify the velocity of complex multiphase flows within pipes. This challenge necessitates the exploration of innovative techniques capable of providing reliable measurements. This paper proposes the utilization of Electrical Capacitance Tomography (ECT) as a promising approach for measuring the velocity of multiple phase fluids in pipes. The ECT technique involves the non-intrusive imaging of the electrical capacitance distribution within the pipe. By utilizing an array of electrodes placed around the pipe circumference, the capacitance distribution can be reconstructed, offering insight into the fluid flow patterns. By analyzing the temporal changes in the capacitance distribution, the velocity of different phases within the pipe can be estimated. To achieve accurate velocity measurements, an ECT system needs to account for the complexities introduced by multiphase flows. Various image reconstruction algorithms, such as linear back-projection and iterative algorithms like Gauss-Newton and Levenberg-Marquardt, are employed to reconstruct the capacitance distribution. Additionally, advanced signal processing techniques, such as cross-correlation analysis and time-difference methods, are used to extract velocity information from the reconstructed images. This paper presents an experimental investigation of measuring the velocity of multiple-phase fluids in pipes using the ECT technique. The study aims to address the challenges associated with different flow regimes, fluid properties, and pipe geometries by exploring advancements in electrode design, system calibration, and data processing techniques to enhance the accuracy and robustness of ECT-based velocity measurements.