Discreteness Criterion for Subgroups in PU（1,n;C）

In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.

Natural Numbers Applied to Physical Constants: Spacetime Discreteness

We analyze some physical concepts only using natural numbers. We assume a dis-crete space. Physical variables such as speed and momentum are considered as result of the sum of discrete contributions. Such discrete contributions can be calculated with natural numbers only. Elementary algebra is used in the analysis of physical subjects.

Spacetime Discreteness: Shedding Light on Two of the Simplest Observations in Physics

Loop quantum gravity is considered to be one of the two major candidates for a theory of quantum gravity. The most appealing aspect about this theory is it predicts that spacetime is not continuous;both space and time have a discrete nature. Simply, space is not infinitely divisible, but it has a granular structure, and time does not flow continuously like a smooth river. This paper demonstrates a review for two missed (unnoted) observations that support the discreteness of the spacetime. The content of this paper does not validate the specific model of quantized geometry of the spacetime which is predicted by the theory itself. Instead, it proves that time does not flow continuously. But it flows in certain, discrete steps, like a ticking of a clock, due to a simple observation which is absence of any possible value of time that can exist between the present and the future. Regarding space, it validates the spatial discreteness, and the existence of spatial granules (space quanta) due to a simple observation which is the existence of the origin position in a coordinates system. All of this is achieved by reviewing the concept of discreteness itself, and applied directly to the observations.

An MPI parallel DEM-IMB-LBM framework for simulating fluid-solid interaction problems

The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.

Production induced fracture closure of deep shale gas well under thermo-hydro-mechanical conditions

Deep shale gas reservoirs have geological characteristics of high temperature,high pressure,high stress,and inferior ability to pass through fluids.The multi-stage fractured horizontal well is the key to exploiting the deep shale gas reservoir.However,during the production process,the effectiveness of the hydraulic fracture network decreases with the closure of fractures,which accelerates the decline of shale gas production.In this paper,we addressed the problems of unclear fracture closure mechanisms and low accuracy of shale gas production prediction during deep shale gas production.Then we established the fluid—solid—heat coupled model coupling the deformation and fluid flow among the fracture surface,proppant and the shale matrix.When the fluid—solid—heat coupled model was applied to the fracture network,it was well solved by our numerical method named discontinuous discrete fracture method.Compared with the conventional discrete fracture method,the discontinuous discrete fracture method can describe the three-dimensional morphology of the fracture while considering the effect of the change of fracture surface permeation coefficient on the coupled fracture—matrix flow and describing the displacement discontinuity across the fracture.Numerical simulations revealed that the degree of fracture closure increases as the production time proceeds,and the degree of closure of the secondary fractures is higher than that of the primary fractures.Shale creep and proppant embedment both increase the degree of fracture closure.The reduction in fracture surface permeability due to proppant embedment reduces the rate of fluid transfer between matrix and fracture,which has often been overlooked in the past.However,it significantly impacts shale gas production,with calculations showing a 24.7%cumulative three-year yield reduction.This study is helpful to understand the mechanism of hydraulic fracture closure.Therefore,it provides the theoretical guidance for maintaining the long-term effectiveness of hydraulic fractures.

Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

An Intelligent Sensor Data Preprocessing Method for OCT Fundus Image Watermarking Using an RCNN

Watermarks can provide reliable and secure copyright protection for optical coherence tomography(OCT)fundus images.The effective image segmentation is helpful for promoting OCT image watermarking.However,OCT images have a large amount of low-quality data,which seriously affects the performance of segmentationmethods.Therefore,this paper proposes an effective segmentation method for OCT fundus image watermarking using a rough convolutional neural network(RCNN).First,the rough-set-based feature discretization module is designed to preprocess the input data.Second,a dual attention mechanism for feature channels and spatial regions in the CNN is added to enable the model to adaptively select important information for fusion.Finally,the refinement module for enhancing the extraction power of multi-scale information is added to improve the edge accuracy in segmentation.RCNN is compared with CE-Net and MultiResUNet on 83 gold standard 3D retinal OCT data samples.The average dice similarly coefficient(DSC)obtained by RCNN is 6%higher than that of CE-Net.The average 95 percent Hausdorff distance(95HD)and average symmetric surface distance(ASD)obtained by RCNN are 32.4%and 33.3%lower than those of MultiResUNet,respectively.We also evaluate the effect of feature discretization,as well as analyze the initial learning rate of RCNN and conduct ablation experiments with the four different models.The experimental results indicate that our method can improve the segmentation accuracy of OCT fundus images,providing strong support for its application in medical image watermarking.

Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Analysis of mesoscopic mechanical dynamic characteristics of ballast bed with under sleeper pads

The meso-dynamical behaviour of a high-speed rail ballast bed with under sleeper pads(USPs)was studied.The geometrically irregular refined discrete element model of the ballast particles was constructed using 3D scanning techniques,and the 3D dynamic model of the rail-sleeper-ballast bed was constructed using the coupled discrete element method-multiflexible-body dynamics(DEM-MFBD)approach.We analyse the meso-mechanical dynamics of the ballast bed with USPs under dynamic load on a train and verify the correctness of the model in laboratory tests.It is shown that the deformation of the USPs increases the contact area between the sleeper and the ballast particles,and subsequently the number of contacts between them.As the depth of the granular ballast bed increases,the contact area becomes larger,and the contact force between the ballast particles gradually decreases.Under the action of the elastic USPs,the contact forces between ballast particles are reduced and the overall vibration level of the ballast bed can be reduced.The settlement of the granular ballast bed occurs mainly at the shallow position of the sleeper bottom,and the installation of the elastic USPs can be effective in reducing the stress on the ballast particles and the settlement of the ballast bed.

Computer vision-aided DEM study on the compaction characteristics of graded subgrade filler considering realistic coarse particle shapes

The compaction quality of subgrade filler strongly affects subgrade settlement.The main objective of this research is to analyze the macro-and micro-mechanical compaction characteristics of subgrade filler based on the real shape of coarse particles.First,an improved Viola-Jones algorithm is employed to establish a digitalized 2D particle database for coarse particle shape evaluation and discrete modeling purposes of subgrade filler.Shape indexes of 2D subgrade filler are then computed and statistically analyzed.Finally,numerical simulations are performed to quantitatively investigate the effects of the aspect ratio(AR)and interparticle friction coefficient(μ)on the macro-and micro-mechanical compaction characteristics of subgrade filler based on the discrete element method(DEM).The results show that with the increasing AR,the coarse particles are narrower,leading to the increasing movement of fine particles during compaction,which indicates that it is difficult for slender coarse particles to inhibit the migration of fine particles.Moreover,the average displacement of particles is strongly influenced by the AR,indicating that their occlusion under power relies on particle shapes.The dis-placement and velocity of fine particles are much greater than those of the coarse particles,which shows that compaction is primarily a migration of fine particles.Under the cyclic load,the interparticle friction coefficientμhas little effect on the internal structure of the sample;under the quasi-static loads,however,the increase inμwill lead to a significant increase in the porosity of the sample.This study could not only provide a novel approach to investigate the compaction mechanism but also establish a new theoretical basis for the evaluation of intelligent subgrade compaction.

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Assessment of commutation failure in HVDC systems considering spatial-temporal discreteness of AC system faults

This paper presents a novel commutation failure(CF) assessment method considering the influences of voltage magnitude drop, phase shift, and spatial-temporal discreteness of AC system faults. The commutating voltage-time area is employed to analyze the spatial-temporal discreteness of AC system faults causing CF in high-voltage direct current systems, and the influences of fault position and fault time on CF are revealed. Based on this, a novel CF criterion is proposed, further considering the influence of voltage phase shift and the spatial-temporal discreteness. Then this research develops a new CF assessment method, which does not rely on electromagnetic transient simulations. A real case from the China Southern Power Grid is used to verify the practicability of the proposed method by comparing with simulation results obtained using PSCAD/EMTDC.

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Research on discrete memristor-based neural networks has received much attention.However,current research mainly focuses on memristor–based discrete homogeneous neuron networks,while memristor-coupled discrete heterogeneous neuron networks are rarely reported.In this study,a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V–I diagram.Based on two-dimensional(2D)discrete Izhikevich neuron and 2D discrete Chialvo neuron,a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons.Considering the coupling strength as the control parameter,chaotic firing,periodic firing,and hyperchaotic firing patterns are revealed.In particular,multiple coexisting firing patterns are observed,which are induced by different initial values of the memristor.Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength.Furthermore,the effect of Gaussian white noise on synchronization behaviors is also explored.We demonstrate that the presence of noise not only leads to the transition of firing patterns,but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

Protective effects of baffles with different positions,row spacings,heights on debris flow impact

The baffle effectively slowed down debris flow velocity,reduced its kinetic energy,and significantly shortened the distance of debris flow movement.Consequently,they are widely used for protection against natural hazards such as landslides and mudslides.This study,based on the threedimensional DEM(Discrete Element Method),investigated the impact of different baffle positions on debris flow protection.Debris flow velocity and kinetic energy variations were studied through single-factor experiments.Suitable baffle positions were preliminarily selected by analyzing the influence of the first-row baffle position on the impact force and accumulation mass of debris flow.Subsequently,based on the selected baffle positions and four factors influencing the effectiveness of baffle protection(baffle position(P),baffle height(h),row spacing(S_(r)),and angle of transit area(α)),an orthogonal design was employed to further explore the optimal arrangement of baffles.The research results indicate that the use of a baffle structure could effectively slow down the motion velocity of debris flows and dissipate their energy.When the baffle is placed in the transit area,the impact force on the first-row baffle is greater than that when the baffle is placed in the deposition area.Similarly,when the baffle is placed in the transit area,the obstruction effect on debris flow mass is also greater than that when the baffle is placed in the deposition area.Through orthogonal experimental range analysis,when the impact on the first row of baffles is used as the evaluation criterion,the importance of each influencing factor is ranked asα>P>S_(r)>h.When the mass of debris flow behind the baffle is regarded as the evaluation criterion,the rank is changed to P>α>S_(r)>h.The experimental simulation results show that the optimal baffle arrangement is:P_(5),S_(r)=16,α=35°,h=9.

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Synaptic crosstalk is a prevalent phenomenon among neuronal synapses,playing a crucial role in the transmission of neural signals.Therefore,considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks are highly necessary.In this paper,we propose a heterogeneous discrete neural network(HDNN)consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron.These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered.The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents.It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths.Furthermore,the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated,revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

Effect mechanism of seepage force on the hydraulic fracture propagation

The flow of fluid through the porous matrix of a reservoir rock applies a seepage force to the solid rock matrix.Although the seepage force exerted by fluid flow through the porous matrix of a reservoir rock has a notable influence on rock deformation and failure,its effect on hydraulic fracture(HF)propagation remains ambiguous.Therefore,in this study,we improved a traditional fluid–solid coupling method by incorporating the role of seepage force during the fracturing fluid seepage,using the discrete element method.First,we validated the simulation results of the improved method by comparing them with an analytical solution of the seepage force and published experimental results.Next,we conducted numerical simulations in both homogeneous and heterogeneous sandstone formations to investigate the influence of seepage force on HF propagation.Our results indicate that fluid viscosity has a greater impact on the magnitude and extent of seepage force compared to injection rate,and that lower viscosity and injection rate correspond to shorter hydraulic fracture lengths.Furthermore,seepage force influences the direction of HF propagation,causing HFs to deflect towards the side of the reservoir with weaker cementation and higher permeability.

Failure mechanism and simulation for long run-out of the catastrophic rock landslide in the Shanyang Vanadium Mine,China

On 12th August 2015,a massive rapid long run-out rock landslide occurred in the Shanyang Vanadium Mine in Shaanxi Province,China,which claimed the lives of 65 miners.No heavy rainfalls,earthquakes,and mining blasts were recorded before the incident.Therefore,the failure mechanism and the cause of the long run-out movement are always in arguments.In this paper,we conducted a detailed field investigation,laboratory tests,block theory analysis,and numerical simulation to investigate the failure and long run-out mechanisms of the landslide.The field investigation results show that the source material of the rock landslide is a huge dolomite wedge block bedding on siliceous shale layers.Uniaxial compression tests indicate that the uniaxial compression strength of the intact dolomite is 130-140MPa and the dolomite shows a brittle failure mode.Due to the progressive downward erosion of the gully,the dolomite rock bridge at the slope toe became thinner.As the compression stress in the dolomite bridge increased to surpass its strength,the brittle failure of the bridge occurred.Then huge potential energy was released following the disintegration of the landslide,which led to the high acceleration of this rock landslide.The 3D discrete element simulation results suggest that the low intergranular friction contributes to the long run-out movement of this rock landslide.

An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.