Effect of boundary conditions on shakedown analysis of heterogeneous materials

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.

Assessment and Visualization of Ki67 Heterogeneity in Breast Cancers through Digital Image Analysis

The Ki67 index (KI) is a standard clinical marker for tumor proliferation;however, its application is hindered by intratumoral heterogeneity. In this study, we used digital image analysis to comprehensively analyze Ki67 heterogeneity and distribution patterns in breast carcinoma. Using Smart Pathology software, we digitized and analyzed 42 excised breast carcinoma Ki67 slides. Boxplots, histograms, and heat maps were generated to illustrate the KI distribution. We found that 30% of cases (13/42) exhibited discrepancies between global and hotspot KI when using a 14% KI threshold for classification. Patients with higher global or hotspot KI values displayed greater heterogenicity. Ki67 distribution patterns were categorized as randomly distributed (52%, 22/42), peripheral (43%, 18/42), and centered (5%, 2/42). Our sampling simulator indicated analyzing more than 10 high-power fields was typically required to accurately estimate global KI, with sampling size being correlated with heterogeneity. In conclusion, using digital image analysis in whole-slide images allows for comprehensive Ki67 profile assessment, shedding light on heterogeneity and distribution patterns. This spatial information can facilitate KI surveys of breast cancer and other malignancies.

Spatial Heterogeneity and Risk Factors of Dental Caries in 12-Year-Old Children in Shanxi Province,China

Objective This study aimed to explore the spatial heterogeneity and risk factors for dental caries in 12-year-old children in Shanxi province,China.Methods The data encompassed 3,721 participants from the two most recent oral health surveys conducted across 16 districts in Shanxi Province in 2015 and 2018.Eighteen specific variables were analyzed to examine the interplay between socioeconomic factors,medical resources and environmental conditions.The Geo-detector model was employed to assess the impacts and interactions of these ecological factors.Results Socioeconomic factors(Q=0.30,P<0.05)exhibited a more substantial impact compared to environmental(Q=0.19,P<0.05)and medical resource factors(Q=0.25,P<0.05).Notably,the urban population percentage(UPP)demonstrated the most significant explanatory power for the spatial heterogeneity in caries prevalence,as denoted by its highest q-value(q=0.51,P<0.05).Additionally,the spatial distribution’s heterogeneity of caries was significantly affected by SO2 concentration(q=0.39,P<0.05)and water fluoride levels(q=0.27,P<0.05)among environmental factors.Conclusion The prevalence of caries exhibited spatial heterogeneity,escalating from North to South in Shanxi Province,China,influenced by socioeconomic factors,medical resources,and environmental conditions to varying extents.

Heterogeneity of mature oligodendrocytes in the central nervous system

Mature oligodendrocytes form myelin sheaths that are crucial for the insulation of axons and efficient signal transmission in the central nervous system.Recent evidence has challenged the classical view of the functionally static mature oligodendrocyte and revealed a gamut of dynamic functions such as the ability to modulate neuronal circuitry and provide metabolic support to axons.Despite the recognition of potential heterogeneity in mature oligodendrocyte function,a comprehensive summary of mature oligodendrocyte diversity is lacking.We delve into early 20th-century studies by Robertson and Río-Hortega that laid the foundation for the modern identification of regional and morphological heterogeneity in mature oligodendrocytes.Indeed,recent morphologic and functional studies call into question the long-assumed homogeneity of mature oligodendrocyte function through the identification of distinct subtypes with varying myelination preferences.Furthermore,modern molecular investigations,employing techniques such as single cell/nucleus RNA sequencing,consistently unveil at least six mature oligodendrocyte subpopulations in the human central nervous system that are highly transcriptomically diverse and vary with central nervous system region.Age and disease related mature oligodendrocyte variation denotes the impact of pathological conditions such as multiple sclerosis,Alzheimer's disease,and psychiatric disorders.Nevertheless,caution is warranted when subclassifying mature oligodendrocytes because of the simplification needed to make conclusions about cell identity from temporally confined investigations.Future studies leveraging advanced techniques like spatial transcriptomics and single-cell proteomics promise a more nuanced understanding of mature oligodendrocyte heterogeneity.Such research avenues that precisely evaluate mature oligodendrocyte heterogeneity with care to understand the mitigating influence of species,sex,central nervous system region,age,and disease,hold promise for the development of therapeutic interventions targeting varied central nervous system pathology.

Characterizing heterogeneity in vehicular traffic speed using two-step cluster analysis

In order to analyze the heterogeneity in vehicular traffic speed, a new method that integrates cluster analysis and probability distribution function fitting is presented. First, for identifying the optimal number of clusters, the two-step cluster method is applied to analyze actual speed data, which suggests that dividing speed data into two clusters can best reflect the intrinsic patterns of traffic flows. Such information is then taken as guidance in probability distribution function fitting. The normal, skew-normal and skew-t distribution functions are used to fit the probability distribution of each cluster respectively, which suggests that the skew-t distribution has the highest fitting accuracy; the second is skew-normal distribution; the worst is normal distribution. Model analysis results demonstrate that the proposed mixture model has a better fitting and generalization capability than the conventional single model. In addition, the new method is more flexible in terms of data fitting and can provide a more accurate model of speed distribution.

Multivariate adaptive regression splines analysis for 3D slope stability in anisotropic and heterogenous clay

Little research can be found in relation to the stability of anisotropic and heterogenous soils in three dimensions.In this paper,we propose a study on the three-dimensional(3D)undrained slopes in anisotropic and heterogenous clay using advanced upper and lower bounds finite element limit analysis(FELA).The obtained stability solutions are normalized,and presented by a stability number that is a function of three geometrical ratios and two material ratios,i.e.depth ratio,length ratio,slope angle,shear strength gradient ratio and anisotropic strength ratio.Numerical results are compared with experimental data in the literature,and charts are presented to cover a wide range of design parameters.Using the multivariate adaptive regression splines(MARS)analysis,the respective influence and sensitivity of each design parameter on the stability number and the failure mechanism are investigated.An empirical equation is also developed to effectively estimate the stability number.

A New Hybrid Hierarchical Parallel Algorithm to Enhance the Performance of Large-Scale Structural Analysis Based on Heterogeneous Multicore Clusters

Heterogeneous multicore clusters are becoming more popular for high-performance computing due to their great computing power and cost-to-performance effectiveness nowadays.Nevertheless,parallel efficiency degradation is still a problem in large-scale structural analysis based on heterogeneousmulticore clusters.To solve it,a hybrid hierarchical parallel algorithm(HHPA)is proposed on the basis of the conventional domain decomposition algorithm(CDDA)and the parallel sparse solver.In this new algorithm,a three-layer parallelization of the computational procedure is introduced to enable the separation of the communication of inter-nodes,heterogeneous-core-groups(HCGs)and inside-heterogeneous-core-groups through mapping computing tasks to various hardware layers.This approach can not only achieve load balancing at different layers efficiently but can also improve the communication rate significantly through hierarchical communication.Additionally,the proposed hybrid parallel approach in this article can reduce the interface equation size and further reduce the solution time,which can make up for the shortcoming of growing communication overheads with the increase of interface equation size when employing CDDA.Moreover,the distributed sparse storage of a large amount of data is introduced to improve memory access.By solving benchmark instances on the Shenwei-Taihuzhiguang supercomputer,the results show that the proposed method can obtain higher speedup and parallel efficiency compared with CDDA and more superior extensibility of parallel partition compared with the two-level parallel computing algorithm(TPCA).

Typhoon Case Comparison Analysis Between Heterogeneous Many-Core and Homogenous Multicore Supercomputing Platforms

In this paper,a typical experiment is carried out based on a high-resolution air-sea coupled model,namely,the coupled ocean-atmosphere-wave-sediment transport(COAWST)model,on both heterogeneous many-core(SW)and homogenous multicore(Intel)supercomputing platforms.We construct a hindcast of Typhoon Lekima on both the SW and Intel platforms,compare the simulation results between these two platforms and compare the key elements of the atmospheric and ocean modules to reanalysis data.The comparative experiment in this typhoon case indicates that the domestic many-core computing platform and general cluster yield almost no differences in the simulated typhoon path and intensity,and the differences in surface pressure(PSFC)in the WRF model and sea surface temperature(SST)in the short-range forecast are very small,whereas a major difference can be identified at high latitudes after the first 10 days.Further heat budget analysis verifies that the differences in SST after 10 days are mainly caused by shortwave radiation variations,as influenced by subsequently generated typhoons in the system.These typhoons generated in the hindcast after the first 10 days attain obviously different trajectories between the two platforms.

Comprehensive security risk factor identification for small reservoirs with heterogeneous data based on grey relational analysis model

Identification of security risk factors for small reservoirs is the basis for implementation of early warning systems.The manner of identification of the factors for small reservoirs is of practical significance when data are incomplete.The existing grey relational models have some disadvantages in measuring the correlation between categorical data sequences.To this end,this paper introduces a new grey relational model to analyze heterogeneous data.In this study,a set of security risk factors for small reservoirs was first constructed based on theoretical analysis,and heterogeneous data of these factors were recorded as sequences.The sequences were regarded as random variables,and the information entropy and conditional entropy between sequences were measured to analyze the relational degree between risk factors.Then,a new grey relational analysis model for heterogeneous data was constructed,and a comprehensive security risk factor identification method was developed.A case study of small reservoirs in Guangxi Zhuang Autonomous Region in China shows that the model constructed in this study is applicable to security risk factor identification for small reservoirs with heterogeneous and sparse data.

Heterogeneity analysis of gas-solid flow hydrodynamics in a pilot-scale fluidized bed reactor

Mesoscale drag model is of crucial significance for the reliability and accuracy in coarse-grid EulerianEulerian two-fluid model(TFM)simulations of gas-solid flow hydrodynamics in fluidized bed reactors.Although numerous mesoscale drag models have been reported in the literature,a systematic comparison of their prediction capability from the perspective of heterogeneity analysis is still lacking.In this study,in order to investigate the effect of several typical drag models on the hydrodynamic behaviors,the nonuniformity analysis and the sensitivity to material properties,extensive coarse-grid TFM simulations of a bubbling pilot-scale fluidized bed reactor are carried out.The results demonstrate that the mesoscale drag models outperform the empirical drag model in terms of nonuniformity due to the consideration of the influence of the mesoscale structures on the drag force in the bubbling region.Furthermore,the results reveal that our previously developed three-marker gradient-based drag model considering the solid concentration gradient exhibits satisfactory performance in predicting the bubbling flow hydrodynamics.Besides,the material-property-dependent drag model considering the explicit effect of material properties on drag corrections is most sensitive to the particle diameter.This work provides guideline for possible future improvements of mesoscale models to simulate gas-solid flow more accurately and universally.

Reliability Analysis of Heterogeneous Sensor-Cloud Systems against Targeted Attacks

Based on the wide application of cloud computing and wireless sensor networks in various fields,the Sensor-Cloud System(SCS)plays an indispensable role between the physical world and the network world.However,due to the close connection and interdependence between the physical resource network and computing resource network,there are security problems such as cascading failures between systems in the SCS.In this paper,we propose a model with two interdependent networks to represent a sensor-cloud system.Besides,based on the percolation theory,we have carried out a formulaic theoretical analysis of the whole process of cascading failure.When the system’s subnetwork presents a steady state where there is no further collapse,we can obtain the largest remaining connected subgroup components and the penetration threshold.Theoretically,this result is the critical maximum that the coupled SCS can withstand.To verify the correctness of the theoretical results,we further carried out actual simulation experiments.The results show that a scale-free network priority attack’s percolation threshold is always less than that of ER network which is priority attacked.Similarly,when the scale-free network is attacked first,adding the power law exponentλcan be more intuitive and more effective to improve the network’s reliability.

Spatial Heterogeneity Analysis of PM2.5 Concentration in Central Plains Economic Region

The research of the spatial heterogeneity of PM2.5 concentration in an area, is of great significance for understanding its regional spatial distribution structure, exploring the transmission relationship between regions, in order to formulate joint prevention and control measures within the entire area. Based on the daily monitoring data of PM2.5 concentration in the Central Plains Economic Region in 2019, this paper utilizes cluster analysis to divide the regional PM2.5 concentration into 5 classes, builds their spatial semi-variogram model, and then utilizes interpolation analysis method to study the regional overall distribution characteristics and transmission law. The results show that the PM2.5 concentration in the Central Plains Economic Region has a medium or higher spatial autocorrelation. The critical value of the overall PM2.5 concentration in the area is 150 μg/m3, as the overall PM2.5 concentration less than the value, the PM2.5 in a region mainly comes from local emissions, as the overall PM2.5 concentration higher than the value, the influence of spatial structure on the distribution of PM2.5 concentration is gradually obvious. PM2.5 has a certain degree of spatial transmission, which mainly includes two routes as Puyang-Xingtai and Puyang-Zhengzhou, and the transmission intensity of the former is greater than the latter.

Sub-Homogeneous Peridynamic Model for Fracture and Failure Analysis of Roadway Surrounding Rock

The surrounding rock of roadways exhibits intricate characteristics of discontinuity and heterogeneity.To address these complexities,this study employs non-local Peridynamics(PD)theory and reconstructs the kernel function to represent accurately the spatial decline of long-range force.Additionally,modifications to the traditional bondbased PD model are made.By considering the micro-structure of coal-rock materials within a uniform discrete model,heterogeneity characterized by bond random pre-breaking is introduced.This approach facilitates the proposal of a novel model capable of handling the random distribution characteristics of material heterogeneity,rendering the PD model suitable for analyzing the deformation and failure of heterogeneous layered coal-rock mass structures.The established numerical model and simulation method,termed the sub-homogeneous PD model,not only incorporates the support effect but also captures accurately the random heterogeneous micro-structure of roadway surrounding rock.The simulation results obtained using this model show good agreement with field measurements from the Fucun coal mine,effectively validating the model’s capability in accurately reproducing the deformation and failure mode of surrounding rock under bolt-supported(anchor cable).The proposed subhomogeneous PD model presents a valuable and effective simulation tool for studying the deformation and failure of roadway surrounding rock in coal mines,offering new insights and potential advancements.

Spatial patterns of Picea crassifolia driven by environmental heterogeneity and intraspecifi c interactions

Research on the spatial patterns of tree populations is critical for understanding the structure and dynamic processes of forests.However,little is known about how the underlying drivers shape these patterns and species interactions in forest systems.In this study,spatial point pattern analysis investigated the combined eff ects of intraspecifi c interactions and environmental heterogeneity on the spatial structure and internal maintenance mechanisms of Picea crassifolia in the Qilian Mountain National Nature Reserve,China.Data were obtained from a 10.2-ha dynamic monitoring plot(DMP)and sixteen 0.04-ha elevation gradient plots(EGPs).Under complete spatial randomness,both mature trees and saplings in the DMP demonstratedlarge-scale aggregation with negative correlations.In EGPs,saplings were clustered in small mesoscales,mature trees were randomly distributed,and the interactions of saplingstrees at all elevations were not correlated.By eliminating the interference of environmental heterogeneity through the inhomogeneous Poisson process,saplings in the DMP and EGPs were clustered in small scales and trees randomly distributed.Intraspecifi c associations were negatively correlated,in the DMP and at low elevations,and no correlations in high elevations of EGPs.In the vertical scale,saplings showed a small-scale aggregation pattern with increase in elevation,and the aggregation degree fi rst decreased and then increased.The interactions of saplings-trees and saplings–saplings showed inhibitions at small scales,with the degree of inhibition gradually decreasing.Spatial patterns and associations of adults–adults did not change signifi-cantly.The results revealed that intraspecifi c interactions and environmental heterogeneity regulated the spatial patterns of P.crassifolia at small and large scales,respectively.Environmental heterogeneity might be the most decisive factor aff ecting the spatial patterns of saplings,while trees were more aff ected by intraspecifi c interactions.Moreover,competition between trees in this area could be more common than facilitation for the growth and development of individuals.

Spatial Analysis of the Aging Population and Socio-economic Factors of China:Global and Local Perspectives

Population aging has become an inevitable trend and exerted profound influences on socio-economic development in China.In this study,we utilized data from national population census and statistical yearbooks in 2010 and 2020 to explore spatio-temporal patterns of aging population and its coupling correlations with socio-economic factors from both global and local perspectives.The results from Local Indicators of Spatial Association(LISA)uncover notable spatial disparities in aging population rates,with higher rates concentrated in the eastern regions and lower rates in the western areas of the Chinese mainland.The results from the global correlation analysis with the changes in aging population rates show significant positive correlations with government interventions and industrial structures,but negatively correlated with economic development,social consumption,and medical facilities.From a local perspective,a Geographically Weighted(GW)correlation analysis is employed to uncover local correlations between aging trends and socio-economic factors.The insights gained from this technique not only underscore the complexity and diversity of economic implications stemming from population aging,but also provide invaluable guidance for crafting region-specific economic policies tailored to various stages of population aging.

Spatial and temporal heterogeneity of the impact of per capita income on household indirect carbon emissions in western China

With China entering the stage of high-quality development,the issue of carbon emission has become a hot research topic.This paper analyzes the different temporal and spatial effects of per capita income on household indirect carbon emissions in western China.Based on the data of Chinese Family Panel Studies(CFPS)in 2016 and 2018 in the western China,this paper uses Regression analysis and Bayesian correlation analysis to study the relationship between per capita income and household indirect carbon emissions.The results showed that the indirect carbon emissions generated by the expenditure on food,housing and household equipment in the household consumption structure in the western China were relatively high.In 2016-2018,the per capita income and per capita household consumption indirect carbon emissions in the western China showed an increasing trend.There was a positive correlation between per capita income and indirect carbon emissions of per capita household consumption,and its correlation was gradually enhanced in time dimension.In the spatial dimension,the household indirect carbon emissions in Yunnan,Qinghai,Guangxi Zhuang and Ningxia in the western China were greatly affected by per capita income,while the household indirect carbon emissions in Guizhou was least affected by per capita income.Finally,the paper puts forward some problems that we should consider in the process of facing the per capita income growth and climate change:the collection of carbon tax,the optimization of household consumption structure,the research and development of low-carbon products,and the differentiated carbon reduction.

Multi-Scale Analysis of Fretting Fatigue in Heterogeneous Materials Using Computational Homogenization

This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.

TWO-STEP MECHANISM IN HETEROGENEOUS CATALYSIS AND DYNAMIC ANALYSIS

Recent development of the dynamic analysis technique has made it possible to measure separately kinetic parameters of a catalytic reaction as well as to study the effect of catalyst preparation parameters. But its application is still limned to first-order reaction. This work is aimed to demonstrate in some detail that,by comparison of the reaction rate expressions with the two-step mechanism used in catalytic kinetics and dynamic analysis, these methods can be extended to non-first-order reaction, and the kinetic parameters measured by dynamic techniques are interpreted for different reaction mechanisms.

Dynamic Modeling of Heterogeneous Spatial Analysis for Energy and Natural Resources in Grid Integration Environment

With the high-tech industrialization of earth observation satellite remote sensing and the implementation of digital earth strategy,the energy and natural resources have been decided to be the key research fields in China.In these fields,from the model based on topology data,through simple feature data model to rule-based data model,the basic spatial analysis algorithms have been developed

Feedback Between Influent Condition Heterogeneity and Diversity of Bacterial Community in Bioreactor at Low Substrate Concentration

In order to investigate the effect of influent condition heterogeneity on diversity of the bacterial community,the degree of microbial resolution and effluent quality,biological treatment of micro-polluted source water is proposed. Scanning Electron Microscopy( SEM) analysis reflects that influent conditions change the morphologies of biofilm. Denaturing Gradient Gel Electrophoresis( DGGE) analysis shows differences of H values are due to succession of functional bacterial communities. Microbial resolution values and species identifications reveal organic carbon is the main cause of community differentiation and bacterial migration.