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The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO₂ transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.

Anomalous dispersion behaviors of CO₂ transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.

The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.

To the best of the authors’ knowledge, first time these results are presented.

The aim of this study is to numerically simulate the density-driven convection in heterogeneous porous media associated with anisotropic permeability field, which is important to the safe and stable long term CO₂ storage in laminar saline aquifers.

The study uses compact finite difference and the pseudospectral method to solve Darcy’s law.

The presence of heterogeneous anisotropy may result in non-monotonic trend of the breakthrough time and quantity of CO₂ dissolved in the porous medium, which are important to the CO₂ underground storage.

The manuscript numerically study the convective phenomena of mixture contained CO₂ and brine. The phenomena are important to the process of CO₂ enhanced oil recovery. Interesting qualitative patterns and quantitative trends are revealed in the manuscript.

The elevator installation in old communities (EIOC) can effectively improve the public infrastructure of urban communities. However, differences in the decision-making behaviours of stakeholders lead to frequent conflicts, thereby hindering the implementation of EIOC. The purpose of this study is to explore the decision-making behavior of core stakeholders which are the government, community owners and elevator enterprises at different stages in the EIOC using the evolutionary game method.

A tripartite evolutionary game model involving the government, community owners and elevator enterprises was developed, and their evolutionary stabilisation strategies were explored in different stages. The dynamic change of the stakeholders' decision-making behaviours at different stages of the project and the influencing mechanism of the key factors on the decision-making behaviours of the three stakeholders were analysed through numerical simulation.

The results of this study showed that: Divergent interests led the government, community owners and elevator enterprises to adopt distinct decision-making behaviours at different stages, resulting in diverse attitudes and actions among stakeholders. A dynamic reward and penalty mechanism effectively motivated community owners and elevator enterprises to engage actively, fostering broad participation. However, the high regulatory cost diminished the government's regulatory effectiveness. This imbalance between penalties and incentives posed a challenge, impacting the overall effectiveness and efficiency of implementing the EIOC.

Existing research lacks exploration of the decision-making behaviours of stakeholders in community public infrastructure. This study developed a dynamic tripartite evolutionary game model in the EIOC from the gaming perspective. The results of this study provide a reference for dealing with the stakeholders' interests in the community public infrastructure and contribute to the theoretical basis for establishing an effective supervision mechanism.

Perceived justice is crucial to achieving public–private partnership (PPP) projects’ goals, but little is known about the transmission mechanism of perceived justice that affects added value in PPP projects. Therefore, this research intends to investigate the link between perceived justice and PPP projects’ added value and their underlying mechanism by analysing the mediating role of cooperative behaviour.

Based on 246 valid survey data collected from the Chinese PPP professionals, structural equation modelling was adopted to analyse and test the proposed hypotheses.

The results show all three dimensions of perceived justice positively correlated with PPP projects’ added value. The influence effect from high to low was determined to be as follows: interactive, distributive and procedural justice. Moreover, both perfunctory and consummate performance were found to be positively correlated with and thus of great importance to PPP projects’ added value, but perfunctory performance was found to have a greater influence coefficient. The relationship between perceived justice and PPP projects’ added value is mediated by perfunctory and consummate performance. Therefore, the strategies of perceived justice in improving added value are verified in the context of Chinese PPP projects.

The findings of this study can help realise added value in three ways. Firstly, new perspectives for PPP project added value should be proposed by combining the improvement of project basic objectives and the realisation of the participants’ implicit demands. Secondly, the effects of different perceived justice on added value should be analysed instead of a single dimension of perceived justice. Thirdly, the mediating effects of different types of cooperative behaviour that may influence the relationship between perceived justice and added value should be evaluated.

This study contributes to a better understanding of the relationship between perceived justice and PPP projects’ added value and provides a reliable reference for project managers to achieve added value outcomes in PPP projects. In addition, this study reveals the impact of perceived justice on PPP projects’ added value and the path of perceived justice transformation. This provides a useful reference for project managers to take advantage of the positive effects of distributive, interactive and procedural justice to enhance inter-organizational cooperative behaviour. This study thus helps improve the practice and value of PPP projects by using the right strategy of perceived justice.

The research clarifies the impacts of multidimensional perceived justice for added value of PPP projects throughout the implementation process. It offers a new perspective on PPP projects’ added value by combining the improvement of the realisation of participants’ implicit claims.

Due to extensive industrial activities, the manufacturing sector is deteriorating the environment through resource depletion and rising pollution levels which led to a significant transition toward green supply chain practices (GSCP). Therefore, internal and external GSCP and green training (GT) gaining momentous attention. This study aims to explore the interconnections among the internal and external GSCP, GT, green innovation (GI), pro-environmental behavior (PEB), competitive advantage (CA), green knowledge sharing (GKS), green self-efficacy (GSE), environmental and financial performance (EP) and (FP).

To check the hypothesized model, researchers used cross-sectional data based on survey questionnaires which were gathered from Pakistani manufacturing firms. The theoretical framework was validated through the utilization of partial least square structural equation modeling.

The findings suggest that internal and external GSCP and GT are correlated with GI, PEB, CA, EP and FP. Additionally, this study discovers that PEB and GI act as intermediaries among internal and external GSCP, GT and CA. GKS positively moderates the connection among internal and external GSCP, and GT, GI, and PEB. Similarly, GSE also serves as a moderator among between PEB and GI.

This study is a significant contribution to the literature by studying potential mediators and moderators that improve the association among outlined constructs. Moreover, findings suggest that firms should adopt an integrated and holistic green approach to combat environmental deterioration, maintain environmental integrity and attain sustainable development.

There is a scarcity of studies concerning the holistic framework of interrelated constructs studied in this research and it is the pioneer research to offer insights with an innovative model and empirical evidence.

The shapes of surface textures have been designed to control the leakage of mechanical seals in recent years. The purpose of this paper is to demonstrate the influence of geometric properties of elliptical dimples on the leakage rate.

A new geometric feature point is expressed using an analytical solution to locate the high-pressure zones. Furthermore, a numerical model of the three-dimensional flow field for the mechanical seal with elliptical dimples is developed using ANSYS Fluent to demonstrate the influencing mechanism.

The location of the proposed geometric converging point coincides with the maximum pressure point under different orientation angles. An inward flow on the leakage section observed from the simulation results is responsible for decreasing the leakage rate.

The influencing mechanism of the elliptical dimple on the leakage rate is demonstrated, which can facilitate the design of surface textures.

With the growing scale of power grids, integrated power grids often contain multiple areas. When the control centre of each regional grid conducts an assessment of local voltage stability, the calculation is always based on the local regional power grid model. However, less consideration is given to a detailed model of the entire network, which may lead to a large calculation error. Under the premise of ensuring the data and information security of Supervisory Control and Data Acquisition between different regional power grid operation control centres, the purpose of this paper is to reduce calculation error simply by using the data of a local power network.

According to the calculation methodology of “decomposition and coordination” and the power balance equation of an interconnected power grid, an improved radial equivalent independent (REI) equivalent method, which can reflect the dynamic characteristics of interconnected power grids to a certain extent, is proposed in this paper. A mathematical model of multi-area-grid L indicator synergic computing is derived as well.

With the calculation of Institute of Electrical and Electronics Engineers (IEEE) standard grids and an actual grid model, it is proven that the method proposed in this paper can significantly improve the accuracy of the regional power grid L indicator calculation and achieve the synergic computing of a multi-area power system L indicator, without an increase in data interaction among the regional power grids.

The indicator of voltage stability among multi-area was obtained by using the improved REI equivalent method with the change of the load participation factor. Particularly, the coordinated calculation method can be implemented on a local power grid without knowledge of all the parameters of its interconnection, which can avoid possible leakage of confidential data and information of the system owners.

Noise abatement is one of the key techniques for Partial Discharge (PD) on-line measurement and monitoring. However, how to enhance the efficiency of PD signal noise suppression is a challenging work. Hence, this study aims to improve the efficiency of PD signal noise abatement.

In this approach, the time–frequency characteristics of PD signal had been obtained based on fast kurtogram and S-transform time–frequency spectrum, and these characteristics were used to optimize the parameters for the signal matching over-complete dictionary. Subsequently, a self-adaptive selection of matching atoms was realized when using Matching Pursuit (MP) to analyze PD signals, which leading to seldom noise signal element was represented in sparse decomposition.

The de-noising of PD signals was achieved efficiently. Simulation and experimental results show that the proposed method has good adaptability and significant noise abatement effect compared with Empirical Mode Decomposition, Wavelet Threshold and global signal sparse decomposition of MP.

A self-adaptive noise abatement method was proposed to improve the efficiency of PD signal noise suppression based on the signal sparse representation and its MP algorithm, which is significant to on-line PD measurement.

Paying to view others' answers is a new mode for question and answer (Q&A) platforms. The purpose is to build a model to explore the determinants of the number of listeners and further explore certain meaningful characteristics of the model in the context of different types of questions and answerers.

The authors develop an empirical model and use real panel data to test the hypothesis. Specifically, cues from the answerer and from the question elicit the listener's trust in the answerer (including direct and indirect trust) and perceived value in the question (including intrinsic and extrinsic attributes), respectively.

The authors find that cues from answerers (experience for paid Q&As and popularity for free Q&As) and questions (length, sentence structure, value and number of likes) all have positive effects on the number of listeners. The impact of answerer authentication is more significant than the popularity of free Q&As. Moreover, the length of the question matters only for subjective questions, while sentence structure matters only for objective questions. In addition, the answerer's own attributes and the behavior and feedback of others have greater impacts when the answerer is below average in popularity.

The authors summarize the unique features of the mode of paying to view others' answers in contrast with the traditional mode of paid Q&As. In addition, the authors focus on the characteristics of the question (including the subjectivity and the sentence structure of the question), a topic which has not been studied previously. Our research provides a reference for exploring user behavior patterns. The practical implications for knowledge platforms are also concretely described.

The existing consensus reaching mechanisms ignore the influence of social triangle structure on the decision-makers’ (DMs') weights, and the consensus reaching process (CRP) fails to fully reflect the DMs' subjectivity and can be time consuming and costly. To solve these issues, a novel CRP for multi-criteria group decision-making (MCGDM) problems with intuitionistic grey linguistic numbers (IGLNs) is proposed in this paper.

First, a weight calculation method is proposed by analysing the triangle structure of DMs' social network and scale of adjacent nodes. Then, a consensus degree index based on three-level polygon area is defined and applied to identify the inconsistent DMs. Finally, the feedback mechanism based on particle swarm optimisation (PSO) algorithm under grey linguistic environment is developed, where subjective trust relationships in social network is utilised to determine the adjustment coefficient.

The advantages of the proposed method are highlighted by two practical applications of the evaluation of tunnel construction method and the selection of a hotel for the centralised isolation. Comparision analysis and numerical simulation are performed to reveal the effectiveness and applicability of the method.

The proposed model can not only reflect the effect of triangle structure in social network on DMs' weights, but also reduce the time and cost of decision-making.

The main contribution of this paper is to propose a new MCGDM model based on intuitionistic grey linguistic numbers, which can handle the problem of inconsistency of information more effectively.