Spatial Step Research Articles

Enhancing Performance of Single-Channel SSVEP-Based Visual Acuity Assessment via Mode Decomposition.

This study aimed to improve the performance of single-channel steady-state visual evoked potential (SSVEP)-based visual acuity assessment by mode decomposition methods. Using the SSVEP dataset induced by the vertical sinusoidal gratings at six spatial frequency steps from 11 subjects, 3-40-Hz band-pass filtering and other four mode decomposition methods, i.e., empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), and variational mode decomposition (VMD), were used to preprocess the single-channel SSVEP signals from Oz electrode. After comparing the SSVEP signal characteristics corresponding to each mode decomposition method, the visual acuity threshold estimation criterion was used to obtain the final visual acuity results. The agreement between subjective Freiburg Visual Acuity and Contrast Test (FrACT) and SSVEP visual acuity for band-pass filtering (-0.095 logMAR), EMD (-0.112 logMAR), EEMD (-0.098 logMAR), ICEEMDAN (-0.093 logMAR), and VMD (-0.090 logMAR) was all pretty good, with an acceptable difference between FrACT and SSVEP acuity for band-pass filtering (0.129 logMAR), EMD (0.083 logMAR), EEMD (0.120 logMAR), ICEEMDAN (0.103 logMAR), and VMD (0.108 logMAR), finding that the visual acuity obtained by these four mode decompositions had a lower limit of agreement and a lower or close difference compared to the traditional band-pass filtering method. This study proved that the mode decomposition methods can enhance the performance of single-channel SSVEP-based visual acuity assessment, and also recommended ICEEEMDAN as the mode decomposition method for single-channel electroencephalography (EEG) signal denoising in the SSVEP visual acuity assessment.

Continuous Change Detection of Flood Extents With Multisource Heterogeneous Satellite Image Time Series

Flood monitoring is of crucial importance for protecting lives and properties. Change detection (CD) methods on multi-source remote sensing images have been widely used for flood extent monitoring. In this paper, we propose a spatiotemporal fusion CD (STFCD) algorithm, exploiting the spatial dependence and temporal interaction of multi-source heterogeneous (MSH) satellite image time series (SITS), to realize improved flood CD performance in comparison with existing methods. The proposed STFCD algorithm mainly contains two steps, i.e., spatial clustering and temporal fusion. In the spatial clustering step, we propose a sparse Markov random field (MRF)-based strategy to exploit contextually spatial features in each image of MSH-SITS, which provides a larger local receptive field than the commonly used MRF. In the temporal fusion step, the historical information of flood detection results is employed as constraints to effectively reduce the effects of terrain shadows in synthetic aperture radar (SAR) images and cloud shadows and topography shadows in optical images on flood CD results of existing methods in accordance with the temporal dependence among MSH-SITS. Experiments on real MSH-SITS (containing Gaofen-1, Gaofen-3, Gaofen-6, Sentinel-1, and Sentinel-2 satellite images) covering Chinese Amur and Huma Rivers show that the overall flood CD accuracy of our proposed STFCD algorithm is higher than the other commonly used algorithms for CD of flood extents and demonstrate the robustness of our proposed STFCD algorithm.

A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion

In this paper, we propose an efficient numerical method for a comprehensive infection model that is formulated by a system of nonlinear coupling advection-diffusion-reaction equations. Using some subtle mixed explicit-implicit treatments, we construct a linearized and decoupled discrete scheme. Moreover, the proposed scheme is capable of preserving the positivity of variables, which is an essential requirement of the model under consideration. The proposed scheme uses the cell-centered finite difference method for the spatial discretization, and thus, it is easy to implement. The diffusion terms are treated implicitly to improve the robustness of the scheme. A semi-implicit upwind approach is proposed to discretize the advection terms, and a distinctive feature of the resulting scheme is to preserve the positivity of variables without any restriction on the spatial mesh size and time step size. We rigorously prove the unique existence of discrete solutions and positivity-preserving property of the proposed scheme without requirements for the mesh size and time step size. It is worthwhile to note that these properties are proved using the discrete variational principles rather than the conventional approaches of matrix analysis. Numerical results are also provided to assess the performance of the proposed scheme.

Predviđanje hrapavosti površine tankih delovi sa zidovima na koje utiču varijacije radijalne dubine rezanja tokom perifernog procesa glodanja

During the peripheral milling process, great transverse displacement vibrations of the thin-walled part are occurred under the acting of milling tool edge forcesdue to their low dynamic rigidity and the radial depth of cut ae variations. In this work, the main surface roughness parameters are evaluated for stable milling process conditions through maximum radial displacements determined by a theoretical method and a finite element (FE) computation utilizing numerical simulations. The cutting tooth edge forces are calculated along the effective part for each tooth tool engaged into part material in discrete spatial and time steps using flat-end mills. Finally, the radial displacements are confronted, which are close in magnitude and in profile shape trend. Therefore, the generated cutting tooth edge forces showed gradual stabilities while changing the parameter ae from 05 mm to 0.75 mm, respectively. Then, the parameters Ra and Rq contribute more to these stabilities than Rv.

On the Characteristics of EMTR as a Correlation-Estimator-Based Fault Location Method in Transmission Lines

Methods based on electromagnetic time reversal (EMTR) have recently demonstrated promising results. In particular, EMTR, as a correlation estimator metric, has offered a quantitative definition for fault location candidates. As the correlation estimator already obtains the system transfer functions by simulating fault occurrences, these functions are subsequently correlated with the fault-generated transfer function. Therefore, it is necessary to explore the analysis related to the pre-fault processing of this metric. Firstly, the impact of fault impedance mismatch between the fault occurrence and fault estimation stages was investigated, and a simple approach is presented after observing the fault locations’ error. Secondly, it was noticed that the existing correlation estimator approach does not accurately identify fault types; therefore, a pseudo approach was developed to address this issue. Finally, the spatial step considered during the fault estimation stage was investigated. It is demonstrated that larger spatial steps result in inaccuracies in fault location. The smaller spatial steps improved the performance, but increased the memory burden on the data storage devices, especially when simple and pseudo approaches must be employed. The memory issue was resolved by presenting a hybrid approach that makes use of regression analysis. A single-phase and a three-phase lossy transmission line system were used to illustrate the proposed analyses.

Thermo-hydraulic coupled analysis of long-distance district heating systems based on a fully-dynamic model

The long-distance district heating pipeline (LDHP) system is a key solution for transporting the renewable heat from the suburban to urban areas. In LDHP, thermal and hydraulic characteristics are coupled. Developing effective thermo-hydraulic co-simulation method is vital to enhance LDHP’s operation performance and to enhance its flexibility. As the pressure wave travels much faster than the hot water in the district heating (DH) pipeline, the research in this regard mainly focuses on pseudo-dynamic model, in which the calculation of thermal dynamics only adopts the static hydraulic conditions. In this paper, a novel fully-dynamic model considering both the hydraulic transients and thermal dynamics is developed. The model is solved using the method of characteristic (MOC). The optimal spatial and temporal step sizes for the thermal dynamic modeling are analyzed and studied. Next, we compared our proposed model with the conventional pseudo-dynamic model on a 20 km LDHP. Results show that the simulated temperature fluctuations of the two models are close to each other, but the predicted temperature arriving at the heat exchange station is up to 28 s earlier than the pseudo-dynamic model, indicating that hydraulic transients have some influence thermal dynamics. Moreover, the fully-dynamic model has capability to predict the temperature and flow rate transport of the system in both disturbance state and steady state, which is important for the rapid and accurate analysis of the operation of LDHP.

Assessing the impact of climate change on Combined Sewer Overflows based on small time step future rainfall timeseries and long-term continuous sewer network modelling

The evolution of the climate in the future will probably lead to an increase in extreme rainfall events, particularly in the Mediterranean regions. This change in rainfall patterns will have impacts on combined sewer systems operation with a possible increase of spilled flows, leading to an increase of untreated water volumes released to the receiving water. Due to the impact of overflows on the water cycle, local authorities managing combined sewer systems are wondering about the extent of these changes and the possibility of taking it into account in stormwater management structure design. To do this, rainfall data with a fine time step are required to better master the shape of the hyetographs that are crucial to get a relevant rainfall/runoff relationship in an urban environment. However, there are currently no simulations of future rainfall series available at a time step compatible with the needs in urban drainage field. In this work, future rainfall time series with a fine time step are elaborated with the aim to be used in urban hydrology. The proposed approach is based on simulations results from five regional climate models in the framework of the Euro-Cordex program. It consists in a spatial downscaling step followed by a temporal disaggregation. The rainfall time series obtained are then used as input for a calibrated and validated hydrological model to investigate the evolution of annual CSO volumes and frequencies by 2100. The results show an increase of annual spilled volumes between 13% and 52% according to the considered climate model. This increase will most likely be a problem regarding compliance of sewer networks in line with the water framework directive, particularly the current French regulations. No clear trends were observed on the CSO frequencies. If there is a consensus for all the carried-out simulations to conclude that the CSO volumes will increase, we must remember that actual regional climate models suffer from limited spatial and temporal resolution and don't explicitly solve convection processes. Due to this point uncertainty concerning the evolution rate remains important particularly for intense rainfall episodes. New generations of climate models are needed to accurately predict intense episodes.

Numerical Modeling of Pollutant Transport: Results and Optimal Parameters

In this work, we used three finite difference schemes to solve 1D and 2D convective diffusion equations. The three methods are the Kowalic–Murty scheme, Lax–Wendroff scheme, and nonstandard finite difference (NSFD) scheme. We considered a total of four numerical experiments; in all of these cases, the initial conditions consisted of symmetrical profiles. We looked at cases when the advection velocity was much greater than the diffusion of the coefficient and cases when the coefficient of diffusion was much greater than the advection velocity. The dispersion analysis of the three methods was studied for one of the cases and the optimal value of the time step size k, minimizing the dispersion error at a given value of the spatial step size. From our findings, we conclude that Lax–Wendroff is the most efficient scheme for all four cases. We also show that the optimal value of k computed by minimizing the dispersion error at a given value of a spacial step size gave the lowest l2 and l∞ errors.

Условия формирования опасных отложений зернистой изморози на Полярном Урале

Synoptic conditions for the formation of high-intensity hard rime accretion on the territory of the Polar Urals are considered. A leading role of mesoscale processes primarily related to the terrain features in the formation of hard rime is revealed. Numerical experiments are implemented to reproduce the cases of hard rime formation on the territory of the Rai-Iz mountain range using the WRF-ARW mesoscale model. The simulation results and the methods used to interpret them made it possible to obtain detailed fields of meteorological parameters necessary for the correct assessment of the probability and intensity of the hard rime formation. It was also shown that it is reasonable to use model spatial steps of not more than 2 km for successful modeling of ice accretion in the form of hard rime. Keywords: severe weather events, ice accretion, icing, rime, hard rime, numerical weather prediction, WRF-ARW

Unconditional superconvergence analysis of two modified finite element fully discrete schemes for nonlinear Burgers' equation

In this paper, two modified nonconforming finite element fully discrete schemes are considered for solving the nonlinear Burgers' equation. The schemes are constructed by using the nonconforming Wilson element approximation in space combining with the backward Euler(BE) and 2-step backward differentiation formula (BDF2) respectively in time. We present the superconvergence results of the two proposed schemes in modified energy norm of order O(h2+τ) and O(h2+τ2), where h and τ are the space subdivision parameter and time step respectively. The proof involves the time-space error splitting technique, the discrete embedding inequality, the technique of taking difference between two time, the discrete derivative transfer technique and a new modified projection operator. Our analysis not only gets rid of the restriction between temporal and spatial step sizes, but also provides one order higher error estimate results than that of corresponding traditional finite element fully discrete schemes. Finally, numerical experiments are carried out to demonstrate the effective of theoretical analysis.

Small-data-driven fast seismic simulations for complex media using physics-informed Fourier neural operators

Deep learning (DL) seismic simulations have become a leading-edge field that could provide an effective alternative to traditional numerical solvers. We have developed a small-data-driven time-domain method for fast seismic simulations in complex media based on the physics-informed Fourier neural operator (FNO). Unlike most DL-based modeling schemes that either solve wave equations by embedding the physical constraints into the cost function or conduct physics-informed learning by incorporating the wave functions into convolutional neural networks (CNNs), the FNO uses a learning architecture similar to the structure of split-step Fourier wave propagators, which is composed of two CNNs formulated in the space and wavenumber domains, respectively. The space-domain CNN acts as a local trainable phase-screen compensation. The wavenumber-domain CNN represents a nonlocal spatial convolutional operator acting as a trainable wavenumber filter for the phase-shift process. The FNO method approximates the mathematical-physical behavior of wave equations through learning the mapping between seismic wavefields at different time/locations from training seismic data. That is, the learning process parameterizes the integral kernel directly in the Fourier space, so that we can establish an expressive and efficient architecture for a better balance between accuracy and performance than the traditional spatial CNNs. Applications to gradient, layered, and Marmousi velocity models demonstrate its performance in accuracy and efficiency. The FNO seismic simulation is a data-driven method that needs a small amount of training data, especially when using blended source training data. It is a discretization-independent method that is not subject to the limitation of spatial sampling and time steps imposed on traditional numerical solvers, implying that the training data can be discretized arbitrarily. It also is a model-independent method that can include absorption attenuation into seismic modeling without the need of viscoelastic wave equations.

Maximum error estimates of two linearized compact difference schemes for two-dimensional nonlinear Sobolev equations

In this paper, two classes of high-order numerical schemes on the time discretization for the solutions of two-dimensional nonlinear Sobolev equations are analyzed. The two-level Newton linearized difference scheme had been established in the previous literature, in which the error estimates in L2-norm and H1-norm are obtained, but that in L∞-norm remains unsolved. The second difference scheme is established based on a three-level linearized difference technique in temporal direction. The numerical discretization in spatial dimension for both schemes utilizes the compact difference operator. We prove that the orders of convergence for both difference schemes in L∞-norm are O(τ2+h14+h24) based on the energy argument, where τ denotes the temporal step size, h1 and h2 denote the spatial step sizes in x-direction and y-direction, respectively. The numerical tests further verify the theoretical results and demonstrate the efficiency of both difference schemes.

A general Lagrangian tracking methodology for riverine flow and transport

AbstractThis article presents a new public domain tool for generalized Lagrangian particle tracking in rivers. The approach can be applied with a variety of two‐ and three‐dimensional flow solvers. Particle advection by the flow is incorporated using flow fields from the chosen solver assuming particles follow the Reynolds‐averaged flow, although some other simple passive and active particle behaviors are also treated. Turbulence effects are treated using a random walk algorithm with spatial step lengths randomly chosen from Gaussian distributions characterized by the diffusivity from the flow solver. Our work extends this concept to a general framework that is solver and coordinate system independent to allow easy comparisons between differing flow treatments. To better treat problems where detailed information is required in specific regions, the approach includes novel cloning and colligation algorithms which enhance local resolution at modest computational expense. We also provide tools for computing local concentrations and total exposure over a user‐specified time interval. Several examples of predictions are provided to illustrate applications of the technique, including examination of the role of curvature‐driven secondary flows, storage in lateral separation eddies, treatment of larval drift, treatment of fuel spill dispersion, river‐floodplain connections, and sedimentation in floodplain ponds by tie channel connections. We also demonstrate that the model can reproduce analytically derived concentration profiles for simple diffusivities. These examples show that the Lagrangian particle tracking approach and the extensions proposed here are broadly applicable and viable for treating difficult river problems with multiple temporal and spatial scales. The examples also illustrate the utility of the cloning/colligation extensions and show how these can decrease the computational effort required on problems where high local resolution is required. Enhancement of the tools and even broader applicability can be achieved through the inclusion of multiple particle populations and particle–particle interactions.

The element-free Galerkin method for the variational–hemivariational inequality of the dynamic Signorini–Tresca contact problems with friction in elastic materials

The element-free Galerkin method is presented for the variational–hemivariational inequality of the dynamic Signorini–Tresca contact problems with friction in elastic materials. The Dirichlet boundary conditions and the constrained conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method indicate that the convergence order depends on the spatial step, the time step, the largest degree of basis functions in the moving least-squares approximation and the penalty factor. Numerical examples verify our theoretical results.

Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme

In this paper, we present a fourth-order difference scheme for solving the Allen-Cahn equation in both 1D and 2D. The proposed scheme is described by the compact difference operators together with the additional stabilized term. As a matter of fact, the Allen-Cahn equation contains the nonlinear reaction term which is eminently proved that numerical schemes are mostly nonlinear. To solve the complexity of nonlinearity, the Crank-Nicolson/Adams-Bashforth method is applied in order to deal with the nonlinear terms with the linear implicit scheme. The well-known energy-decaying property of the equation is maintained by the proposed scheme in the discrete sense. Additionally, the L∞ error analysis is carried out in the 1D case in a rigorous way to show that the method is fourth-order and second-order accuracy for the spatial and temporal step sizes, respectively. Concurrently, we examine the L2 and H1 error analysis for the scheme in the case of 2D. We consider the impact of the additional stabilized term on numerical solutions. The consequences confirm that an appropriate value of the stabilized term yields a significant improvement. Moreover, relevant results are carried out in the numerical simulations to illustrate the faithfulness of the present method by the confirmation of existing pieces of evidence.

Variable Interfacial Water Nanosized Arrangements Measured by Atomic Force Microscopy.

While there seems to be broad agreement that cluster formation does exist near solid surfaces, its presence at the liquid/vapor interface is controversial. We report experimental studies we have carried out on interfacial water attached on hydrophobic and hydrophilic surfaces. Nanosized steps in the measured force vs distance to the surface curves characterize water cluster profiles. An expansion of the interfacial structure with time is observed; the initial profile extent is typically ∼1 nm, and for longer times expanded structures of ∼70 nm are observed. Our previous results showed that the interfacial water structure has a relative permittivity of ε ≈ 3 at the air/water interface homogeneously increasing to ε ≈ 80 at 300 nm inside the bulk, but here we have shown that the interfacial dielectric permittivity may have an oscillating profile describing the spatial steps in the force vs distance curves. This low dielectric permittivity arrangements of clusters extend the region with ε ≈ 3 inside bulk water and exhibit a behavior similar to that of water networks that expand in time.

Convergence Analysis and Approximate Optimal Temporal Step Sizes for Some Finite Difference Methods Discretising Fisher's Equation

In this study, we obtain a numerical solution for Fisher's equation using a numerical experiment with three different cases. The three cases correspond to different coefficients for the reaction term. We use three numerical methods namely; Forward-Time Central Space (FTCS) scheme, a Nonstandard Finite Difference (NSFD) scheme, and the Explicit Exponential Finite Difference (EEFD) scheme. We first study the properties of the schemes such as positivity, boundedness, and stability and obtain convergence estimates. We then obtain values of L1 and L∞ errors in order to obtain an estimate of the optimal time step size at a given value of spatial step size. We determine if the optimal time step size is influenced by the choice of the numerical methods or the coefficient of reaction term used. Finally, we compute the rate of convergence in time using L1 and L∞ errors for all three methods for the three cases.

An IDDES study of the near-wake flow topology of a simplified heavy vehicle

Abstract The complex wake flow of a GTS (ground transportation system) model contributes to large percentage of the aerodynamic drag force. Therefore, predicting accurate wake flow will help carry out the drag reduction strategies. In this paper, the near-wake flow topology of the GTS was studied at Re = 2.7×104 to assess the capability of a hybrid RANS/LES (Reynolds-averaged Navier–Stokes/large eddy simulation) approach, known as IDDES (improved delayed detached eddy simulation). The current study also aims to understand the effects of different computational parameters, e.g. the spatial resolution, time step, residual level, discretization scheme and turbulence model, on this asymmetrical wake flow configuration. A comparison of IDDES with previous water channel tests, well-resolved LES, partially averaged Navier–Stokes and URANS (unsteady RANS) was included to better understand the benefits of this hybrid RANS/LES approach. The results show that on the medium and fine grids, the IDDES produces an asymmetrical flow topology (known as flow state I) in the near-wake of the vertical midplane, as reported in previous studies. The recommended parameters for the time step (1×10–4 s) and residual level (1×10–4) provide sufficient accuracy of wake predictions to show good agreement with experiments. For the convective term of the momentum equation in IDDES, the bounded central difference discretization scheme is proposed to be adopted for discretization. Additionally, URANS cannot accurately capture this asymmetrical flow field. IDDES proves to be capable of predicting the wake flow field of this simplified heavy vehicle with high accuracy. All obtained conclusions can provide references for the aerodynamic drag reduction of the GTS.

High Sensing Accuracy Realisation With Millimetre/Sub-Millimetre Resolution in Optical Frequency Domain Reflectometer

By effectively suppressing the nonlinear sweep noise and random range of wavelength sweep in the optical frequency domain reflectometer, the theoretical spatial resolution and uniform sweep distribution are delivered for high sensing accuracy. A strain accuracy of ±0.51 μϵ is realised with a 5 mm sensing resolution, while the accuracy is ±5.89 μϵ with a 1 mm sensing resolution. Theoretical limitation between the strain accuracy and sensing resolution is further studied for the sub-millimetre resolution sensing. It is found that signal to noise ratio and frequency bandwidth of the calculated cross-correlation are critical factors in measuring accuracy. Increasing the sweep range can provide a better spatial frequency step for a high signal to noise ratio in the cross-correlation. With a 130 nm sweep range, the measurement accuracy is limited to ±19.31 μϵ with a 0.5 mm sensing resolution. Besides, for the long-distance sensing of 104 m, the measurement accuracy is ±8.72 μϵ with a 1 mm sensing resolution.

High-order finite difference method based on linear barycentric rational interpolation for Caputo type sub-diffusion equation

The main aim of this paper is to develop a class of high-order finite difference method for the numerical solution of Caputo type time-fractional sub-diffusion equation. In the time direction, the Caputo derivative is discretized by employing a numerical technique based on the fractional linear barycentric rational interpolation method (FLBRI). The stability properties and the convergence analysis of the proposed scheme are considered based on the energy method. As a result, the order of convergence is O(Δt)p+(Δx)2 for 1≤p≤7, in which Δt is the temporal step size, Δx is the spatial step size, and p is the order of accuracy in the time direction. Finally, numerical experiment is provided to show that the results confirm the theoretical analysis, perfectly.