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.

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.

Some discrete SI and SIS epidemic models

The probability is introduced to formulate the death of individuals, the recovery of the infected individuals and incidence of epidemic disease. Based on the assumption that the number of individuals in a population is a constant, discrete-time SI and SIS epidemic models with vital dynamics are established respectively corresponding to the case that the infectives can recover from the disease or not. For these two models. the results obtained in this paper show that there is the same dynarfiical behavior as their corresponding continuous ones. and the threshold determining its dynamical behavior is found. Below the threshold the epidemic disease dies out eventually, above the threshold the epidemic disease becomes an endemic eventually, and the number of the infectives approaches a positive constant.

Comparative study on mode split discrete choice models

Discrete choice model acts as one of the most important tools for studies involving mode split in the context of transport demand forecast. As different types of discrete choice models display their merits and restrictions diversely, how to properly select the specific type among discrete choice models for realistic application still remains to be a tough problem. In this article, five typical discrete choice models for transport mode split are, respectively, discussed, which includes multinomial logit model, nested logit model （NL）, heteroscedastic extreme value model, multinominal probit model and mixed multinomial logit model （MMNL）. The theoretical basis and application attributes of these five models are especially analysed with great attention, and they are also applied to a realistic intercity case of mode split forecast, which results indi- cating that NL model does well in accommodating similarity and heterogeneity across alternatives, while MMNL model serves as the most effective method for mode choice prediction since it shows the highest reliability with the least significant prediction errors and even outperforms the other four models in solving the heterogeneity and similarity problems. This study indicates that conclusions derived from a single discrete choice model are not reliable, and it is better to choose the proper model based on its characteristics.

Experiments of Reconstructing Discrete Atmospheric Dynamic Models from Data (I)

In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, xn +1= 1-uxn2 could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.

A Study on the Physical Properties of Banana Straw Based on the Discrete Element Method

To improve the application of discrete element models(DEM)to the design of agricultural crushers,in this study a new highly accurate model is elaborated.The model takes into account the fiber structure,porous nature of the material and the leaf sheath coating structure.Dedicated experimental tests are conducted to determine the required“intrinsic”and basic contact parameters of the considered banana straw materials.A large number of bonding parameters are examined in relation to the particle aggregation model in order to characterize different actual banana straws.Using the particle surface energy contact model,the viscosity characteristics of the crushed material are determined together with the related stacking angle(considered as the main response factor).Through single factor experiment analysis,it is found that when the surface energy is 0.9 J·m-2,the relative error between simulations and physical experiments is 5.288%.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

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.

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.

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.

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.

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.

Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.

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 Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

Research regarding coal-bed wellbore stability based on a discrete element model

Wellbore instability is a key problem restricting efficient production of coal-bed methane. In order to perform thorough and systematic research regarding coal-bed wellbore stability problems, a new discrete element model which fully considers the features of cleat coal-beds is established based on the Kirsch equation. With this model, the safe pipe tripping speed, drilling fluid density window and coal- bed collapse/fracture pressure are determined; in addition, the relationships between pipe tripping speed and pipe size, cleat size, etc. and wellbore stability are analyzed in the coal-bed drilling and pipe tripping processes. The case studies show the following results： the wellbore collapses （collapse pressure： 4.33 MPa） or fractures （fracture pressure： 12.7 MPa） in certain directions as a result of swab or surge pressure when the pipe tripping speed is higher than a certain value; the cleat face size has a great influence on wellbore stability, and if the drilling fluid pressure is too low, the wellbore is prone to collapse when the ratio of the face cleat size to butt cleat size is reduced; however, if the drilling fluid pressure is high enough, the butt cleat size has no influence on the wellbore fracture; the factors influencing coal-bed stability include the movement length, pipe size, borehole size.

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.

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.