Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Clicking through the Clickstream: A Novel Statistical Modeling Approach to Improve Information Usage of Clickstream Data by E-Commerce Entities

Success or failure of an E-commerce platform is often reduced to its ability to maximize the conversion rate of its visitors. This is commonly regarded as the capacity to induce a purchase from a visitor. Visitors possess individual characteristics, histories, and objectives which complicate the choice of what platform features that maximize the conversion rate. Modern web technology has made clickstream data accessible allowing a complete record of a visitor’s actions on a website to be analyzed. What remains poorly constrained is what parts of the clickstream data are meaningful information and what parts are accidental for the problem of platform design. In this research, clickstream data from an online retailer was examined to demonstrate how statistical modeling can improve clickstream information usage. A conceptual model was developed that conjectured relationships between visitor and platform variables, visitors’ platform exit rate, boune rate, and decision to purchase. Several hypotheses on the nature of the clickstream relationships were posited and tested with the models. A discrete choice logit model showed that the content of a website, the history of website use, and the exit rate of pages visited had marginal effects on derived utility for the visitor. Exit rate and bounce rate were modeled as beta distributed random variables. It was found that exit rate and its variability for pages visited were associated with site content, site quality, prior visitor history on the site, and technological preferences of the visitor. Bounce rate was also found to be influenced by the same factors but was in a direction opposite to the registered hypotheses. Most findings supported that clickstream data is amenable to statistical modeling with interpretable and comprehensible models.

CO_(2)flooding in shale oil reservoir with radial borehole fracturing for CO_(2)storage and enhanced oil recovery

This study introduces a novel method integrating CO_(2)flooding with radial borehole fracturing for enhanced oil recovery and CO_(2)underground storage,a solution to the limited vertical stimulation reservoir volume in horizontal well fracturing.A numerical model is established to investigate the production rate,reservoir pressure field,and CO_(2)saturation distribution corresponding to changing time of CO_(2)flooding with radial borehole fracturing.A sensitivity analysis on the influence of CO_(2)injection location,layer spacing,pressure difference,borehole number,and hydraulic fractures on oil production and CO_(2)storage is conducted.The CO_(2)flooding process is divided into four stages.Reductions in layer spacing will significantly improve oil production rate and gas storage capacity.However,serious gas channeling can occur when the spacing is lower than 20 m.Increasing the pressure difference between the producer and injector,the borehole number,the hydraulic fracture height,and the fracture width can also increase the oil production rate and gas storage rate.Sensitivity analysis shows that layer spacing and fracture height greatly influence gas storage and oil production.Research outcomes are expected to provide a theoretical basis for the efficient development of shale oil reservoirs in the vertical direction.

Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

具有食饵避难所的离散捕食者-食饵模型的余维二分支分析

In this paper,a discrete predator-prey model with prey refuge is investigated.It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances.The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors,such as limit cycle,periodic solutions,chaos and codimension-1 bifurcations.

Discrete Choice Analysis of Temporal Factors on Social Network Growth

Social networks like Facebook, X (Twitter), and LinkedIn provide an interaction and communication environment for users to generate and share content, allowing for the observation of social behaviours in the digital world. These networks can be viewed as a collection of nodes and edges, where users and their interactions are represented as nodes and the connections between them as edges. Understanding the factors that contribute to the formation of these edges is important for studying network structure and processes. This knowledge can be applied to various areas such as identifying communities, recommending friends, and targeting online advertisements. Several factors, including node popularity and friends-of-friends relationships, influence edge formation and network growth. This research focuses on the temporal activity of nodes and its impact on edge formation. Specifically, the study examines how the minimum age of friends-of-friends edges and the average age of all edges connected to potential target nodes influence the formation of network edges. Discrete choice analysis is used to analyse the combined effect of these temporal factors and other well-known attributes like node degree (i.e., the number of connections a node has) and network distance between nodes. The findings reveal that temporal properties have a similar impact as network proximity in predicting the creation of links. By incorporating temporal features into the models, the accuracy of link prediction can be further improved.

A three-dimensional feature extraction-based method for coal cleat characterization using X-ray μCT and its application to a Bowen Basin coal specimen

Cleats are the dominant micro-fracture network controlling the macro-mechanical behavior of coal.Improved understanding of the spatial characteristics of cleat networks is therefore important to the coal mining industry.Discrete fracture networks(DFNs)are increasingly used in engineering analyses to spatially model fractures at various scales.The reliability of coal DFNs largely depends on the confidence in the input cleat statistics.Estimates of these parameters can be made from image-based three-dimensional(3D)characterization of coal cleats using X-ray micro-computed tomography(m CT).One key step in this process,after cleat extraction,is the separation of individual cleats,without which the cleats are a connected network and statistics for different cleat sets cannot be measured.In this paper,a feature extraction-based image processing method is introduced to identify and separate distinct cleat groups from 3D X-ray m CT images.Kernels(filters)representing explicit cleat features of coal are built and cleat separation is successfully achieved by convolutional operations on 3D coal images.The new method is applied to a coal specimen with 80 mm in diameter and 100 mm in length acquired from an Anglo American Steelmaking Coal mine in the Bowen Basin,Queensland,Australia.It is demonstrated that the new method produces reliable cleat separation capable of defining individual cleats and preserving 3D topology after separation.Bedding-parallel fractures are also identified and separated,which has his-torically been challenging to delineate and rarely reported.A variety of cleat/fracture statistics is measured which not only can quantitatively characterize the cleat/fracture system but also can be used for DFN modeling.Finally,variability and heterogeneity with respect to the core axis are investigated.Significant heterogeneity is observed and suggests that the representative elementary volume(REV)of the cleat groups for engineering purposes may be a complex problem requiring careful consideration.

IN-PLANE WAVE MOTION IN FINITE ELEMENT MODEL

The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

A modified discrete element model for sea ice dynamics

Considering the discontinuous characteristics of sea ice on various scales,a modified discrete element model（DEM） for sea ice dynamics is developed based on the granular material rheology.In this modified DEM,a soft sea ice particle element is introduced as a self-adjustive particle size function.Each ice particle can be treated as an assembly of ice floes,with its concentration and thickness changing to variable sizes under the conservation of mass.In this model,the contact forces among ice particles are calculated using a viscous-elastic-plastic model,while the maximum shear forces are described with the Mohr-Coulomb friction law.With this modified DEM,the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths.The thicknesses,concentrations and velocities of ice particles are obtained,and then reasonable dynamic process is analyzed.The sea ice dynamic process is also simulated in a vortex wind field.Taking the influence of thermodynamics into account,this modified DEM will be improved in the future work.

Evaluating the mechanical properties of anisotropic shale containing bedding and natural fractures with discrete element modeling

Natural fracture data from one of the Carboniferous shale masses in the eastern Qaidam Basin were used to establish a stochastic model of a discrete fracture network and to perform discrete element simulation research on the size efect and mechanical parameters of shale.Analytical solutions of fctitious joints in transversely isotropic media were derived,which made it possible for the proposed numerical model to simulate the bedding and natural fractures in shale masses.The results indicate that there are two main factors infuencing the representative elementary volume(REV)size of a shale mass.The frst and most decisive factor is the presence of natural fractures in the block itself.The second is the anisotropy ratio:the greater the anisotropy is,the larger the REV.The bedding angle has little infuence on the REV size,whereas it has a certain infuence on the mechanical parameters of the rock mass.When the bedding angle approaches the average orientation of the natural fractures,the mechanical parameters of the shale blocks decrease greatly.The REV representing the mechanical properties of the Carboniferous shale masses in the eastern Qaidam Basin were comprehensively identifed by considering the infuence of bedding and natural fractures.When the numerical model size is larger than the REV,the fractured rock mass discontinuities can be transformed into equivalent continuities,which provides a method for simulating shale with natural fractures and bedding to analyze the stability of a borehole wall in shale.

Very Large Eddy Simulation of Cavitation from Inception to Sheet/Cloud Regimes by A Multiscale Model

The cavitating flow in different regimes has the intricate flow structure with multiple time and space scales.The present work develops a multiscale model by coupling the volume of fluid(VOF)method and a discrete bubble model(DBM),to simulate the cavitating flow in a convergent-divergent test section.The Schnerr-Sauer cavitation model is used to calculate the mass transfer rate to obtain the macroscale phase structure,and the simplified Rayleigh-Plesset equation is applied to simulate the growing and collapsing of discrete bubbles.An algorithm for bridging between the macroscale cavities and microscale bubbles is also developed to achieve the multiscale simulation.For the flow field,the very large eddy simulation(VLES)approach is applied.Conditions from inception to sheet/cloud cavitation regimes are taken into account and simulations are conducted.Compared with the experimental observations,it is shown that the cavitation inception,bubble clouds formation and glass cavity generation are all well represented,indicating that the proposed VOF-DBM model is a promising approach to accurately and comprehensively reveal the multiscale phase field induced by cavitation.

Research on SINS Error Recursive Model of Ballistic Missile

The strap-down inertial navigation system (SINS) error of ballistic missile is generated by the mutual influence of gyroscope and accelerometer, and the recursive model is completely different from that of gimbaled INS. In the paper, a discrete error recursive model was obtained by studying the applied SINS error model of ballistic missile, and the discrete Kalman filtering simulation based on the model was carried out. The simulated results show that the model can depict the SINS error exactly and provide the advantages for research on integrated guidance and improved hit accuracy.

An Integrated Dynamic Model of Ocean Mining System and Fast Simulation of Its Longitudinal Reciprocating Motion

An integrated dynamic model of China＇s deep ocean mining system is developed and the fast simulation analysis of its longitudinal reciprocating motion operation processes is achieved. The seafloor tracked miner is built as a three-dimensional single-body model with six-degree-of-freedom. The track-terrain interaction is modeled by partitioning the track-terrain interface into a certain number of mesh elements with three mutually perpendicular forces, including the normal force, the longitudinal shear force and the lateral shear force, acting on the center point of each mesh element. The hydrodynamic force of the miner is considered and applied. By considering the operational safety and collection efficiency, two new mining paths for the miner on the seafloor are proposed, which can be simulated with the established single-body dynamic model of the miner. The pipeline subsystem is built as a three-dimensional multi-body discrete element model, which is divided into rigid elements linked by flexible connectors. The flexible connector without mass is represented by six spring-damper elements. The external hydrodynamic forces of the ocean current from the longitudinal and lateral directions are both considered and modeled based on the Morison formula and applied to the mass center of each corresponding discrete rigid element. The mining ship is simplified and represented by a general kinematic point, whose heave motion induced by the ocean waves and the longitudinal and lateral towing motions are considered and applied. By integrating the single-body dynamic model of the miner and the multi-body discrete element dynamic model of the pipeline, and defining the kinematic equations of the mining ship, the integrated dynamic model of the total deep ocean mining system is formed. The longitudinal reciprocating motion operation modes of the total mining system, which combine the active straight-line and turning motions of the miner and the ship, and the passive towed motions of the pipeline, are proposed and simulated with the developed 3D dynamic model. Some critical simulation results are obtained and analyzed, such as the motion trajectories of key subsystems, the velocities of the buoyancy modules and the interaction forces between subsystems, which in a way can provide important theoretical basis and useful technical reference for the practical deep ocean mining system analysis, operation and control.

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.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

A discrete model for response estimation of soil-structure systems with embedded foundations

The need for simplified physical models representing frequency dependent soil impedances has been the motivation behind many researches throughout history. Generally, such models are generated to capture impedance functions in a wide range of excitation frequencies, which leads to relatively complex models. That is while there is just a limited range of frequencies that really influence the response of the structure. Here, a new methodology based on the response-matching concept is proposed, which can lead to the development of simpler discrete models. The idea is then used to upgrade an existing simple model of surface foundations to the case of embedded foundations. The applicability of the model in both frequency domain and time domain analyses of soil-structure systems with embedded foundations is discussed. Moreover, the accuracy of the results is compared with another existing discrete model for embedded foundations.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Discrete event model-based simulation for train movement on a single-line railway

The aim of this paper is to present a discrete event model-based approach to simulate train movement with the con- sidered energy-saving factor. We conduct extensive case studies to show the dynamic characteristics of the traffic flow and demonstrate the effectiveness of the proposed approach. The simulation results indicate that the proposed discrete event model-based simulation approach is suitable for characterizing the movements of a group of trains on a single railway line with less iterations and CPU time. Additionally, some other qualitative and quantitative characteristics are investigated. In particular, because of the cumulative influence from the previous trains, the following trains should be accelerated or braked frequently to control the headway distance, leading to more energy consumption.