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.

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.

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.

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.

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.

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 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.

Damage Mechanism of Ultra-thin Asphalt Overlay(UTAO) based on Discrete Element Method

Aiming to analyze the damage mechanism of UTAO from the perspective of meso-mechanical mechanism using discrete element method(DEM),we conducted study of diseases problems of UTAO in several provinces in China,and found that aggregate spalling was one of the main disease types of UTAO.A discrete element model of UTAO pavement structure was constructed to explore the meso-mechanical mechanism of UTAO damage under the influence of layer thickness,gradation,and bonding modulus.The experimental results show that,as the thickness of UTAO decreasing,the maximum value and the mean value of the contact force between all aggregate particles gradually increase,which leads to aggregates more prone to spalling.Compared with OGFC-5 UTAO,AC-5 UTAO presents smaller maximum and average values of all contact forces,and the loading pressure in AC-5 UTAO is fully diffused in the lateral direction.In addition,the increment of pavement modulus strengthens the overall force of aggregate particles inside UTAO,resulting in aggregate particles peeling off more easily.The increase of bonding modulus changes the position where the maximum value of the tangential force appears,whereas has no effect on the normal force.

A lightweight symmetric image encryption cryptosystem in wavelet domain based on an improved sine map

In the era of big data,the number of images transmitted over the public channel increases exponentially.As a result,it is crucial to devise the efficient and highly secure encryption method to safeguard the sensitive image.In this paper,an improved sine map(ISM)possessing a larger chaotic region,more complex chaotic behavior and greater unpredictability is proposed and extensively tested.Drawing upon the strengths of ISM,we introduce a lightweight symmetric image encryption cryptosystem in wavelet domain(WDLIC).The WDLIC employs selective encryption to strike a satisfactory balance between security and speed.Initially,only the low-frequency-low-frequency component is chosen to encrypt utilizing classic permutation and diffusion.Then leveraging the statistical properties in wavelet domain,Gaussianization operation which opens the minds of encrypting image information in wavelet domain is first proposed and employed to all sub-bands.Simulations and theoretical analysis demonstrate the high speed and the remarkable effectiveness of WDLIC.

Particle size spatial distribution in landslide dams

The particle composition and spatial distribution of landslide-induced dam bodies are critical geotechnical parameters for studying the hazards of dam-break floods.However,current research often neglects the influence of the initial particle composition and spatial distribution of the landslide on the particle composition and spatial distribution of the landslide dam.This study investigated the impact of initial particle size distribution,volume,and sliding length on the energy and velocity changes of characteristic particles during the sliding process and the spatial distribution of particle sizes in the landslide dam body.Numerical simulations and physical models were employed to examine the effects of sequential gradient arrangements(where particle sizes decrease from top to bottom)and four other different initial particle arrangements on the energy and velocity changes of particles and the spatial distribution of particle sizes in the dam body.The study reveals the characteristics of translational and rotational energy of different particles and the laws of mechanical energy conversion,obtaining the spatial distribution patterns of particle sizes in landslide-induced dams.The results show that under the sequential gradient arrangement,the energy dissipation of the landslide movement is lower,with larger particles mainly distributed at the distal end and smaller particles at the proximal end of the landslide dam.In contrast,under the reverse gradient arrangement,the energy dissipation of the landslide movement is higher,and the distribution pattern of the dam particles is opposite to that of the sequential gradient arrangement.For the other arrangement modes,the spatial distribution of dam particles falls between the aforementioned two.There is a positive correlation between particle size and translational kinetic energy within the particle flow during the landslide process,and rotational motion increases energy dissipation.Under constant slope conditions,sliding length does not affect the movement pattern of the particle flow or the spatial distribution of particles in the dam body.The findings of this study provide a scientific basis for the accurate simulation and prediction of dam-break flood processes.

An Innovative Coupled Common-Node Discrete Element Method-Smoothed Particle Hydrodynamics Model Developed with LS-DYNA and Its Applications

In this study,a common-node DEM-SPH coupling model based on the shared node method is proposed,and a fluid–structure coupling method using the common-node discrete element method-smoothed particle hydrodynamics(DS-SPH)method is developed using LS-DYNA software.The DEM and SPH are established on the same node to create common-node DEM-SPH particles,allowing for fluid–structure interactions.Numerical simulations of various scenarios,including water entry of a rigid sphere,dam-break propagation over wet beds,impact on an ice plate floating on water and ice accumulation on offshore structures,are conducted.The interaction between DS particles and SPH fluid and the crack generation mechanism and expansion characteristics of the ice plate under the interaction of structure and fluid are also studied.The results are compared with available data to verify the proposed coupling method.Notably,the simulation results demonstrated that controlling the cutoff pressure of internal SPH particles could effectively control particle splashing during ice crushing failure.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling(FBCM)of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging.The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis.A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid(i.e.no re-meshing).Further,multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid.The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously:initially without permeating fluids into the rock,to seed fractures uniformly and at high density in the wall rock of the wells;followed by fluid injection to propagate the seeded fracture density hydraulically.FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly.Fractures are modeled as piecewise planar based on intersections with domain elements;fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures;and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock.Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal,shallow-dipping,steeply dipping,or vertical orientation.Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design.The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells:for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures,and in situ vertical compressive stress greater than horizontal.If preexisting fractures are steeply dipping or vertical,and considering the same in situ stress condition,well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

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.