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.

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.

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.

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.

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.

Discrete multi-step phase hologram for high frequency acoustic modulation

Acoustic holograms can recover wavefront stored acoustic field information and produce high-fidelity complex acoustic fields. Benefiting from the huge spatial information that traditional acoustic elements cannot match, acoustic holograms pursue the realization of high-resolution complex acoustic fields and gradually tend to high-frequency ultrasound applications. However, conventional continuous phase holograms are limited by three-dimensional(3D) printing size, and the presence of unavoidable small printing errors makes it difficult to achieve acoustic field reconstruction at high frequency accuracy. Here, we present an optimized discrete multi-step phase hologram. It can ensure the reconstruction quality of image with high robustness, and properly lower the requirement for the 3D printing accuracy. Meanwhile, the concept of reconstruction similarity is proposed to refine a measure of acoustic field quality. In addition, the realized complex acoustic field at 20 MHz promotes the application of acoustic holograms at high frequencies and provides a new way to generate high-fidelity acoustic fields.

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

Numerical modeling techniques for noise emission of free railway wheels

In this article,we consider the numerical prediction of the noise emission from a wheelset in laboratory conditions.We focus on the fluid-structure interaction leading to sound emission in the fluid domain by analyzing three different methods to account for acoustic sources.These are a discretized baffled piston using the discrete calculation method(DCM),a closed cylindrical volume using the boundary element method(BEM)and radiating elastic disks in a cubic enclosure solved with the finite element method(FEM).We provide the validation of the baffled piston and the BEM using measurements of the noise emission of a railway wheel by considering ground reflections in the numerical models.Selected space-resolved waveforms are compared with experimental results as well as with a fluid-structure interaction finite element model.The computational advantage of a discretized disk mounted on a baffle and BEM compared to FEM is highlighted,and the baffled pistons limitations caused by a lack of edge radiation effects are investigated.

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.

Effect of particle composition and consolidation degree on the wave-induced liquefaction of soil beds

The wave-induced liquefaction of seabed is responsible for causing damage to marine structures.Particle composition and consolidation degree are the key factors affecting the pore water pressure response and liquefaction behavior of the seabed under wave action.The present study conducted wave flume experiments on silt and silty fine sand beds with varying particle compositions.Furthermore,a comprehensive analysis of the differences and underlying reasons for liquefaction behavior in two different types of soil was conducted from both macroscopic and microscopic perspectives.The experimental results indicate that the silt bed necessitates a lower wave load intensity to attain the liquefaction state in comparison to the silty fine sand bed.Additionally,the duration and development depth of liquefaction are greater in the silt bed.The dissimilarity in liquefaction behavior between the two types of soil can be attributed to the variation in their permeability and plastic deformation capacity.The permeability coefficient and compression modulus of silt are lower than those of silty fine sand.Consequently,silt is more prone to the accumulation of pore pressure and subsequent liquefaction under external loading.Prior research has demonstrated that silt beds with varying consolidation degrees exhibit distinct initial failure modes.Specifically,a dense bed undergoes shear failure,whereas a loose bed experiences initial liquefaction failure.This study utilized discrete element simulation to examine the microscopic mechanisms that underlie this phenomenon.

CAW-YOLO:Cross-Layer Fusion and Weighted Receptive Field-Based YOLO for Small Object Detection in Remote Sensing

In recent years,there has been extensive research on object detection methods applied to optical remote sensing images utilizing convolutional neural networks.Despite these efforts,the detection of small objects in remote sensing remains a formidable challenge.The deep network structure will bring about the loss of object features,resulting in the loss of object features and the near elimination of some subtle features associated with small objects in deep layers.Additionally,the features of small objects are susceptible to interference from background features contained within the image,leading to a decline in detection accuracy.Moreover,the sensitivity of small objects to the bounding box perturbation further increases the detection difficulty.In this paper,we introduce a novel approach,Cross-Layer Fusion and Weighted Receptive Field-based YOLO(CAW-YOLO),specifically designed for small object detection in remote sensing.To address feature loss in deep layers,we have devised a cross-layer attention fusion module.Background noise is effectively filtered through the incorporation of Bi-Level Routing Attention(BRA).To enhance the model’s capacity to perceive multi-scale objects,particularly small-scale objects,we introduce a weightedmulti-receptive field atrous spatial pyramid poolingmodule.Furthermore,wemitigate the sensitivity arising from bounding box perturbation by incorporating the joint Normalized Wasserstein Distance(NWD)and Efficient Intersection over Union(EIoU)losses.The efficacy of the proposedmodel in detecting small objects in remote sensing has been validated through experiments conducted on three publicly available datasets.The experimental results unequivocally demonstrate the model’s pronounced advantages in small object detection for remote sensing,surpassing the performance of current mainstream models.

Discrete Element Modelling of Damage Evolution of Concrete Considering Meso-Structure of ITZ

The mechanical properties of interfacial transition zones(ITZs)have traditionally been simplified by reducing the stiffness of cement in previous simulation methods.A novel approach based on the discrete element method(DEM)has been developed for modeling concrete.This new approach efficiently simulates the meso-structure of ITZs,accurately capturing their heterogeneous properties.Validation against established uniaxial compression experiments confirms the precision of thismodel.The proposedmodel canmodel the process of damage evolution containing cracks initiation,propagation and penetration.Under increasing loads,cracks within ITZs progressively accumulate,culminating in macroscopic fractures that traverse themortarmatrix,forming the complex,serpentine path of cracks.This study reveals four distinct displacement patterns:tensile compliant,tensile opposite,mixed tensile-shear,and shear opposite patterns,each indicative of different stages in concrete’s damage evolution.The widening angle of these patterns delineates the progression of cracks,with the tensile compliant pattern signaling the initial crack appearance and the shear opposite pattern indicating the concrete model’s ultimate failure.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.