Difference Method Research Articles

Manning Coefficient Effect on the Shallow Water Flow Equation

This work will seek to solve shallow water equations, using numerical integration methods, to solve partial differential equations (PDEs) and subsequently present a brief physical interpretation of the solutions. The derivation of the equations is demonstrated, along with the explanation of each physical quantity present. The discretization of non-conservative shallow water equations is carried out using the method of finite differences advanced in time and central in space (FTCS), in explicit form. With the deductions, different Manning coefficients will be addressed in the solutions, verifying their effects.

A novel unified variational finite difference (VFD) solution method for optimal control problems

This article is aimed to propose a simple yet efficient unified numerical strategy for solving both linear and non-linear optimal control problems. To do so, the general form of quadratic performance index function and nonlinear state equations are considered first. Then, the idea of variational differential quadrature method is used to convert the integral/differential equations to the equivalent algebraic form. Since time is the only independent variable is this research, the finite difference method with an equally-spaced discretization scheme would be a more appropriate technique rather than the differential quadrature approach. So, the implemented numerical solution is called now as the variational finite difference method. The method of Lagrange multipliers is then utilized for minimization purpose and, as a result, the final set of nonlinear algebraic equations are obtained. Finally, the quadratic and triadic forms of non-linearity are considered and an explicit formulation is represented for the residual and Jacobian of the Newton-based iterative solution procedure. To demonstrate the accuracy and efficiency of the proposed approach in the quadratic optimal control area, several benchmark problems involving linear time-invariant, linear time-variant and nonlinear examples are successfully solved and the results are confirmed with those existed in the literature.

A front-fixing numerical method for a fluvio-deltaic sedimentation process with thespace fractional derivative and variable sediment flux

This paper centers around a space-fractional mathematical model for a fluvio-deltaic sedimentation process which involves a space-fractional derivative (Caputo derivative) and time dependent variable sediment flux to investigates the movement of shoreline in a sedimentary ocean basin. This model is a specific case of a basic shoreline model and analogous to a Stefan problem. The numerical solution to the problem is acquired by employing a front-fixing explicit finite difference method. The consistency, stability and convergence of the numerical scheme are theoretically analyzed. The effects of variable sediment flux on the movement of shoreline position and the height of sediments are also assessed for different cases.

Modelling of non-linear elastic constitutive relationship and numerical simulation of rocks based on the Preisach-Mayergoyz space model

Summary The existence of pores, cracks, and cleavage in rocks results in significant non-linear elastic phenomena. One important non-linear elastic characteristic is the deviation of the stress-strain curve from the linear path predicted by Hooke's law. To provide a more accurate description of the non-linear elastic characteristics of rocks and to characterize the propagation of non-linear elastic waves, we introduce the Preisach-Mayergoyz space model. This model effectively captures the non-linear mesoscopic elasticity of rocks, allowing us to observe the stress-strain and modulus-stress relationships under different stress protocols. Additionally, we analyze the discrete memory characteristics of rocks subjected to cyclic loading. Based on the Preisach-Mayergoyz space model, we develop a new non-linear elastic constitutive relationship in the form of an exponential function. The new constitutive relationship is validated through copropagating acousto-elastic testing, and the experimental result is highly consistent with the data predicted by the theoretical non-linear elastic constitutive relationship. By combining the new non-linear elastic constitutive relationship with the strain-displacement formula and the differential equation of motion, we derive the non-linear elastic wave equation. We numerically solve the non-linear elastic wave equation with the finite difference method and observe two important deformations during the propagation of non-linear elastic waves: amplitude attenuation and dispersion. We also observe wavefront discontinuities and uneven energy distribution in the 2-D wavefield snapshot, which are different from those of linear elastic waves. We qualitatively explain these special manifestations of non-linear elastic wave propagation.

Numerical simulation of heat transfer properties of skin tissue acted on repetitive laser irradiation

Pulsed laser has been widely used in the clinical treatment of various diseases and injuries due to its unique advantages in the process of interaction with skin tissue. In order to ensure the therapeutic effect and patient safety, it is necessary to accurately monitor the time-space response of the whole-field temperature of the target tissue irradiated by pulsed laser. A research strategy to explore the thermal response and incidental thermal damage of skin tissue induced by repeated pulses laser has been proposed in present work. A theoretical model involved variable physical properties was first proposed, in which the dual-phase lag (DPL) equation and Henrique burn equation were employed to evaluate the tissue temperature and thermal damage induced by repeated pulse laser irradiation. With the help of finite difference method, the governing equation with variable physical properties was then numerical solved to obtain the time-space distribution of tissue temperature, and the evolution process of the thermal damage was further calculated. The effects of laser input parameters and variable physical parameters on the laser penetration depth, temperature distribution and burn degree of the irradiated tissue were analyzed.

Vibration response of piles at different distances induced by shield tunneling in hard rock strata

Excavation of subway tunnels in hard rock generates strong vibration waves that pose potential risks to the stability of surrounding structures. In this study, the discrete element method-finite difference method (DEM-FDM) coupling was adopted to build the model of tunnel structure-rock-pile, which was validated by field monitoring data. Then, the vibration response of piles under various pile-tunnel spacings was analyzed, revealing the occurrence of vibration peak rebound phenomena within certain distance ranges. The range of vibration effects was categorized. Furthermore, in shield tunneling construction, the energy induced by vibrations was mainly concentrated within the 50 Hz range. Low-frequency vibrations result in a wider effect range. The study also demonstrated that within a 1d (tunnel diameter) range of the pile-tunnel spacing, the vibration induced by shield tunneling construction had a more significant effect. As the pile-tunnel spacing increased, the piles transitioned from being subjected to bending forces to experiencing bending-shear forces. Finally, the vibration effects on the existing piles were evaluated under field working conditions. It also provided suggestions for construction based on the effects and laws of the pile dynamic response.

PSI-26 Effects of particle size and enzyme supplementation on the energy value of field peas fed to growing pigs

Abstract An experiment was conducted to determine if particle size and enzyme supplementation affects the digestible energy (DE), metabolizable energy (ME), and net energy (NE) contents in field peas fed to growing pigs. Male weaned pigs [n = 30; TN70 × TN Tempo; body weight (BW) = 16.5 ± 0.4 kg] were assigned to 1 of 5 dietary treatments: 4 consisting of 50% peas and a corn-soybean meal basal diet. The experiment was carried out as a completely randomized design with treatments arranged in a 2 × 2 factorial design, based on two particle sizes (500μm, 700μm) and two levels of carbohydrase supplementation (0 g/mt, 1,000 g/mt) to give 6 replicates per treatment. Diets were formulated to meet or exceed NRC (2012) requirements. The study was carried out in 3 consecutive periods, each consisting of 15 d; the first 10 d were for adaptation, followed by 5 d of total fecal and urine collection (marker to marker procedure) to calculate DE and ME of diets. The energy content of peas was determined using the difference method. Data were analyzed using the MIXED procedure of SAS. The model included the particle size, enzyme supplementation, and their interaction as a fixed effect. The period was included as a random effect. Least squares means for each treatment were adjusted using Tukey post-hoc test. Dry matter (DM), acid detergent fiber, neutral detergent fiber, gross energy, starch, ash, crude protein, and ether extract contents were analyzed to allow for the prediction of NE content of peas. There were no interactions between particle size and enzyme supplementation on dietary energy values. Also, no main effects of particle size and enzyme supplementation were observed. The average DE, ME, and predicted NE contents for peas were determined to be 3,848, 3,735, and 2,691 kcal/kg DM, respectively. In conclusion, enzyme supplementation and particle size did not influence the DE, ME, and NE contents of the peas.

Identification and Application of Wave Field Characteristics of Channel Waves in Extra-Thick Coal Seams

Channel wave seismic activity often occurs with thin and medium-thick coal seams being the main target layer. To address the problem of channel wave applicability detection in extremely thick coal seams, the propagation and identification characteristics of channel waves remain the focus of research. Therefore, this paper takes the in-seam wave exploration of a 27 m extremely thick coal seam as an example and uses the staggered mesh finite difference method to construct a three-dimensional medium model for numerical simulation. An analysis of the physical parameters of coal and rock, along with the dispersion characteristics of channel waves in extra-thick coal seams, is utilized, through the Zoeppritz equation and the total reflection propagation method, to calculate the imaging. We found the following: (1) The dispersion areas and weak dispersion areas along the detection direction are extremely thick coal seams. (2) There are apparent channel waves in extra-thick coal seams, with a waveform similar to body waves; the length of the wave train is shorter than that of the conventional channel wave, and the arrival time can be estimated accurately. The amplitude of the apparent channel wave is affected by the degree of dispersion, with lower attenuation and higher resolution. The characteristic of total reflection in extremely thick coal seams is that the incident angle is equal to the critical angle, and the dispersion characteristics are weak. (3) The channel waves with weak dispersion characteristics in extra-thick coal seams are mainly Love-type waves.

Modeling obliquely incident seismic wave propagation in rocks via the FDM-DEM coupling scheme: Algorithms and applications

The incidence angle of seismic waves plays a pivotal role in the stability analysis of structures in near-field zones. Despite its importance, the application of obliquely incident seismic waves within models of discontinuous media has been limited. This study introduces a novel approach that integrates the oblique incidence of seismic waves into a coupled model employing both the Finite Difference Method (FDM) and the Discrete Element Method (DEM). We validate the accuracy of seismic wave propagation under oblique incidence in two FDM-DEM coupling models—overlapping coupling and interface coupling—through comparisons with theoretical solutions. For vertically incident seismic P-waves, both models yield similar results. However, under oblique incidence, the overlapping coupling model demonstrates superior accuracy, with a maximum error of approximately 4.217 %, compared to about 10 % in the interface coupling model. Our findings also show that while the relative sizes of particle diameter and overlap length minimally affect accuracy, the arrangement of particles markedly influences the results. Furthermore, we apply this method to a slope model to investigate the failure process, revealing that the nature of the sliding body shifts from tensile sliding to tensile ejection as the incidence angle increases.

A theoretical model for the load-transfer analyses of load distributive compression anchor integrating DSC-based interface nonlinear model

An innovative anchorage technology named load distributive compression anchor (LDCA) has recently been employed in a multitude of geotechnical engineering. The anchoring structure comprises multiple anchor bodies, thereby overcoming the bearing defects associated with conventional load-concentrated anchors and providing superior bearing performance. The complex structural configuration of LDCA considerably complicates the process of load-transfer theoretical modeling. A lack of relevant studies from theoretical solution perspective is yet evident in previous works. In this paper, a theoretical model was proposed for the load-transfer analyses of LDCA, of which the soil-anchor interface mechanical behavior was specially characterized by a disturbed state concept (DSC)-based nonlinear model. The mechanical simulation for the connections in different anchor bodies was incorporated into the theoretical analysis framework through the utilization of finite difference method. Three groups of 3D finite element (FE) models were established to simulate the load-transfer behaviors of LDCAs with different numbers of anchor bodies. The theoretical calculations agree well with the FE numerical results and the in-situ pullout test data, thereby confirming the applicability of the load-transfer theoretical model. The axial force and interface shear stress distributions, as well as the bearing capacity for LDCAs, were discussed based on theoretical calculations and FE simulations. Sensitivity analysis of several key design parameters was conducted to investigate their effects on the bearing capacity of LDCAs. The findings achieved in this study can provide insights into the understanding of the load-transfer behaviors of LDCA, and contribute to the bearing performance evaluation.

An Eulerian formulation for the computational modeling of phase-contrast MRI.

Computational simulation of phase-contrast MRI (PC-MRI) is an attractive way to physically interpret properties and errors in MRI-reconstructed flow velocity fields. Recent studies have developed PC-MRI simulators that solve the Bloch equation, with the magnetization transport being modeled using a Lagrangian approach. Because this method expresses the magnetization as spatial distribution of particles, influences of particle densities and their spatial uniformities on numerical accuracy are well known. This study developed an alternative method for PC-MRI modeling using an Eulerian approach in which the magnetization is expressed as a spatially smooth continuous function. The magnetization motion was described using the Bloch equation with an advection term and computed on a fixed grid using a finite difference method, and k-space sampling was implemented using the spoiled gradient echo sequence. PC-MRI scans of a fully developed flow in straight and stenosed cylinders were acquired to provide numerical examples. Reconstructed flow in a straight cylinder showed excellent agreement with input velocity profiles and mean errors were less than 0.5% of the maximum velocity. Numerical cases of flow in a stenosed cylinder successfully demonstrated the velocity profiles, with displacement artifacts being dependent on scan parameters and intravoxel dephasing due to flow disturbances. These results were in good agreement with those obtained using the Lagrangian approach with a sufficient particle density. The feasibility of the Eulerian approach to PC-MRI modeling was successfully demonstrated.

Deep learning method for finding eigenpairs in Sturm-Liouville eigenvalue problems

Solving the eigenvalue problem for differential equations in inhomogeneous media poses a significant challenge across diverse scientific fields. While classical finite difference methods and finite element methods have produced numerous outcomes, they heavily rely on discretizing the computational domain, which can introduce complexities and limitations. In this study, we present an unsupervised neural network approach tailored for finding eigenpairs in Sturm-Liouville eigenvalue problems within inhomogeneous media. Our method introduces eigenvalues as trainable parameters, crafts a novel cost function, incorporates an adaptive hyper-parameter tuning strategy, and sequentially trains the eigenpairs. The simplicity, accuracy, and interpretability of our approach significantly expand its applicability across various domains. The method we present in this paper can easily tackle boundary value conditions with derivatives, resulting in orthogonal eigenfunctions. This is a very important advantage of deep learning methods that has not yet been noticed. Quantitative estimation of eigenpairs is given for the Sturm-Liouville eigenvalue problems. Furthermore, we extend the proposed methodology to tackle two-dimensional cases, periodic scenarios, demonstrating its versatility and broad potential. For more information see https://ejde.math.txstate.edu/Volumes/2024/53/abstr.html

Influence of surface texture on pocket pairs lubrication performance of cylindrical roller bearings

Purpose This paper aims to reveal the influence of the grooved texture parameters on the lubrication performance of circular pocket-roller pairs in cylindrical roller bearings. Design/methodology/approach In this paper, the thermal elastohydrodynamic lubrication mathematical model of the grooved texture circular pocket-roller pair was established, the finite difference method and successive over-relaxation method were used to solve the model, the influence of texture quantity, texture depth and texture area ratio on circumferential bearing capacity, friction coefficient, maximum temperature rise, stiffness and damping of the circular pocket-roller pairs were analyzed. Findings The results show that texture quantity, texture depth and texture area ratio significantly influence the static and dynamic characteristics of circular pocket-roller pairs. The suitable surface groove texture parameters can dramatically improve the circumferential bearing capacity, reduce the friction coefficient, inhibit the maximum temperature rise and increase the stiffness and damping of the circular pocket-roller pairs. Originality/value The research in this paper can provide a theoretical basis for the optimization design of pockets in cylindrical roller bearings to reduce friction and vibration.

Propagation characteristics of show sea seismic wave in different underwater media

The propagation characteristics of sea seismic wave (SSSW) in different underwater media are different. This study mainly focuses on the propagation characteristics of SSSW in different underwater media to improve the detection ability of SSSW mines. The propagation of SSSW in different underwater media, including clay, sandy clay, sandstone, mudstone, hard stone, and dolomite, is simulated using the staggered grid finite difference method. The dispersive energy maps of different underwater media are extracted using the f-k dispersive energy extraction method. Compared with the results of Scholte wave dispersion characteristic equations, the simulation results are consistent with the theoretical results. At the same time, the attenuation law of the SSSW train is obtained. The results provide a theoretical basis for developing SSSW mine fuses.

Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning

A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set.

ANALISIS PROBABILITAS PEMILIHAN MODA PUBLIC BOAT DAN FAST BOAT RUTE PENYEBERANGAN BANGSAL – GILI INDAH

The most popular modes of transportation on the crossing from Bangsal Harbor to Gili Indah are public boats and fast boats. The respective advantages and disadvantages of these two modes are that fast boats excel in fast travel times, while public boats excel in cheaper travel costs. The aim of this research is to obtain factors that influence passengers' decisions in choosing a mode, to find out user characteristics and to obtain the probability that passengers choose public boats and fast boats.Data was obtained from the results of a questionnaire using the stated preference method which offers 7 change scenarios and related choices such as cost (X1), travel time (X2), and waiting time (X3) regarding the choice of public boat and fast boat modes (Y). The results of the choices of public boat and fast boat users will be known through the proportion of public interest in each scenario. Factors that influence mode choice can be identified using multiple linear regression analysis. Then a binary logit analysis of the difference is carried out to obtain the probability of mode choice. The research results show that the utility function equation is Y = -0.3864 – 0.04299X1 – 0.06177X2 – 0.02577X3. Factors that influence passengers' decisions in choosing public and fast boats are cost (X1), travel time (X2), and waiting time (X3). Using the binary logit difference method, the probability of choosing the mode for the Bangsal-Gili Indah crossing route is public boat 79% and fast boat 21%.

Spatiotemporal Evolution and Influencing Factors of Heat Island Intensity in the Yangtze River Delta Urban Agglomeration Based on GEE

Urban agglomerations significantly alter the regional thermal environment. It is urgent to investigate the evolution and influence mechanisms of urban agglomeration heat island intensity from a regional perspective. This study is supported by Google Earth Engine long-term MODIS data series. On the basis of estimating surface urban heat island intensity (SUHI) in the Yangtze River Delta urban agglomeration from 2001 to 2020 based on the suburban temperature difference method, the causes of heat islands in the urban agglomeration were analyzed by using geographical detector analysis. Additionally, the heat island proportion (PHI) and SUHI indicators were used to compare and analyze the changing characteristics of the urban heat island effect of ten representative cities. The research reveals the following: (1) The average SUHI of the study area increased from 0.11 °C in 2001 to 0.29 °C in 2020, with an average annual increase rate of 0.009 °C. (2) According to the results of the geographical detector analysis, SUHI was influenced by several driving factors exhibiting obvious seasonal variations. (3) SUHI difference between cities is significant in the summer (1.52 °C), but smallest in the winter; the PHI difference between cities is larger in the autumn (46.7%), while it is smaller in the summer. The research findings aim to effectively serve the formulation of collaborative development plans for the Yangtze River Delta urban agglomeration.

Can institutional opening-up promote green development in cities? Evidence from China's Pilot Free Trade Zones

As a testing ground for China's institutional opening-up, Pilot Free Trade Zones (PFTZs) are of great significance in shaping a new global economic governance framework, addressing pollution and carbon reduction challenges, and fostering green economic development and transition. This study empirically assesses the influence of PFTZs establishment on urban green development (GD) using panel data from 284 Chinese cities between 2007 and 2020, using the asymptotic Difference in Differences (DID) method. The results indicate that the creation of PFTZs greatly encourages cities to develop green sustainably. In comparison to cities without PFTZs, the presence of PFTZs results in a notable average increase of 9.5% in urban green total factor productivity (GTFP). The impact of PFTZs on urban GD varies significantly across different geographical areas and city resource endowment conditions. Institutional innovation has a positive moderating effect on the PFTZs' promotion of urban GD. The influence mechanisms that PFTZs support urban GD mainly include the effects of green innovation, economic agglomeration, and environmental regulation. This paper provides crucial policy insights for advancing PFTZ construction, promoting urban green growth, and ultimately achieving the coexistence of human beings and nature in harmony.

A two-stage defect detection method for unevenly illuminated self-adhesive printed materials

The process of printing defect detection usually suffers from challenges such as inaccurate defect extraction and localization, caused by uneven illumination and complex textures. Moreover, image difference-based defect detection methods often result in numerous small-scale pseudo defects. To address these challenges, this paper proposes a comprehensive defect detection approach that integrates brightness correction and a two-stage defect detection strategy for self-adhesive printed materials. Concretely, a joint bilateral filter coupled with brightness correction corrects uneven brightness properly, meanwhile smoothing the grid-like texture in complex printed material images. Then, in the first detection stage, an image difference method based on a bright–dark difference template group is designed to effectively locate printing defects despite slight brightness fluctuations. Afterward, a discriminative method based on feature similarity is employed to filter out small-scale pseudo-defects in the second detection stage. The experimental results show that the improved difference method achieves an average precision of 99.1% in defect localization on five different printing pattern samples. Furthermore, the second stage reduces the false detection rate to under 0.5% while maintaining the low missed rate.

Home-based EXercise and motivAtional programme before and after Liver Transplantation (EXALT): study protocol for phase II two-centre, randomised controlled trial

IntroductionPhysical frailty is associated with increased mortality and poor quality of life (QoL) before and after liver transplantation (LT). Evidence is lacking on how to tailor exercise and behavioural techniques...