A multithreaded parallel upwind sweep algorithm for the S_(N) transport equations discretized with discontinuous finite elements

The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.

Darboux Transformation and Explicit Solutions for Discretized Modified Korteweg-de Vries Lattice Equation

The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.

Dynamic Analysis of the Seafloor Pilot Miner Based on Single-Body Vehicle Model and Discretized Track-Terrain Interaction Model

In order to achieve the complex dynamic analysis of the self-propelled seafloor pilot miner moving on the seafloor of extremely cohesive soft soil and further to make it possible to integrate the miner system with some subsystems to form the complete integrated deep ocean mining pilot system and perform dynamic analysis, a new method for the dynamic modeling and analysis of the miner is proposed and developed in this paper, resulting in a simplified 3D single-body vehicle model with three translational and three rotational degrees of freedom, while the track-terrain interaction model is built by partitioning the track-terrain interface into discrete elements with parameterized force dements built on the theory of terramechanics acting on each discrete dement. To evaluate and verify the correctness and effectiveness of this new modeling and analysis method, typical comparative studies with regard to computational efficiency and solution accuracy are carried out between the traditional modeling method of building the tracked vehicle as a multi-body model and the new modeling method. In full consideration of the particMar structure design of the pilot miner, the special characteristics of the seafioor soil and the hydrodynamic force of near-seafloor currnt, the dynamic simulation analysis of the miner is performed and discussed, which can provide useful guidance and reference for the practical miner system in design and operation. This new method can not only realize the rapid dynamic simulation analysis of the miner but also make possible the integration and rapid dynamic analysis of the complete integrated deep ocean mining pilot system in further researches.

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.

Modeling rock fragmentation by coupling Voronoi diagram and discretized virtual internal bond

The rock fragmentation involves the inter-block and the intra-block fracture.A simulation method for rock fragmentation is developed by coupling Voronoi diagram(VD)and discretized virtual internal bond(DVIB).The DVIB is a lattice model that consists of bonds.The VD is used to generate the potential block structure in the DVIB mesh.Each potential block may contain any number of bond cells.To characterize the inter-block fracture,a hyperelastic bond potential is employed for the bond cells that are cut by the VD edges.While to characterize the intra-block fracture,an elastobrittle bond potential is adopted for the bonds in a block.By this method,both the inter-block and intra-block fracture can be well simulated.The simulation results suggest that this method is a simple and efficient approach to rock fragmentation simulation with block smash.

A Bootstrapping Approach for Software Reliability Measurement Based on a Discretized NHPP Model

Discrete software reliability measurement has a proper characteristic for describing a software reliability growth process which depends on a unit of the software fault-detection period, such as the number of test runs, the number of executed test cases. This paper discusses discrete software reliability measurement based on a discretized nonhomogeneous Poisson process (NHPP) model. Especially, we use a bootstrapping method in our discrete software reliability measurement for discussing the statistical inference on parameters and software reliability assessment measures of our model. Finally we show numerical examples of interval estimations based on our bootstrapping method for the several software reliability assessment measures by using actual data.

THE ACTIVATION METHOD FOR DISCRETIZED CONSERVATIVE NONLINEAR STABILITY PROBLEMS WITH MULTIPLE PARAMETER AND STATE VARIABLES

For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables, the activation method is put forward, by which activated potential functions and activated equilibrium equations are derived. The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory. It is more generalized and more normalized than conventional perturbation methods. The activated potential functions may be transformed into normalized catastrophe potential functions. The activated equilibrium equations may be treated as bifurcation equations. The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory

An Improved Method to an Impulsive and Delayed Discretized Model

In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R*, and further prove that the disease-free periodic solution is globally attractive if R* is less than unit and the disease can invade if R* is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.

Elastic scattering and total reaction cross sections of^(6)Li examined via a microscopic continuum discretized coupled-channels model

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels(CDCC)framework,where 6Li is treated in anα+d two-body model.Collisions with 27Al,64Zn,138Ba,and 208Pa are analyzed.The microscopic optical potentials(MOP)based on Skyrme nucleon-nucleon interaction forαand d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs.For comparison,αand d global phenomenological optical potentials(GOP)are also used in CDCC analysis and a reduction of no less than 50%on the surface imaginary part of deuteron GOP is required for describing the data.In all cases,the 6Li breakup effect is significant and provides repulsive correction to the folding model potential.The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron.Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach,and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

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 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.

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.

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.

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.

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.

Bifurcation behaviors of an Euler discretized inertial delayed neuron model

This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one(flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation(1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.

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.