Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces

Here, water flow inside large radii semi-infinite carbon nanotubes is investigated. Permeable wall taking into account the molecular interactions between water and a nanotube, and the slip boundary condition will be considered. Furthermore, interactions among molecules are approximated by the continuum approximation. Incompressible and Newtonian fluid is assumed, and the Navier-Stokes equations, after certain assumptions, transformations and derivations, can be reduced into two first integral equations. In conjunction with the asymptotic expansion technique, we are able to derive the radial and axial velocities analytically, capturing the effect of the water leakage, where both mild and exceptionally large leakages will be considered. The radial velocity obeys the prescribed boundary condition at the (im)permeable wall. Through the mean of the radial forces, the sufficiently large leakages will enhance the radial velocity at the center of the tube. On the other hand, unlike the classical laminar flow, the axial velocity attains its maximum at the wall due to the coupling effect with the radial forces as water is being pushed into the proximity of the inner wall. In addition, the axial velocity and the flux with the consideration of the suck-in forces, induced by the tubes’ entry turn out to be one order higher than that without the suck-in forces. All the aforementioned considerations might partially resolve the mysteriously high water penetration through nanotubes. Axial velocity also drops with the tube’s length when the water leakage is permitted and the suck-in forces will ease the decline rate of the axial velocity. The present mathematical framework can be directly employed into the water flow inside other porous nano-materials, where large water leakage is permitted and therefore are of huge practical impact on ultra-filtration and environmental protection

The role of rock joint frictional strength in the containment of fracture propagation

The fracturing phenomenon within the reservoir environment is a complex process that is controlled by several factors and may occur either naturally or by artificial drivers. Even when deliberately induced, the fracturing behaviour is greatly influenced by the subsurface architecture and existing features. The presence of discontinuities such as joints, artificial and naturally occurring faults and interfaces between rock layers and microfractures plays an important role in the fracturing process and has been known to significantly alter the course of fracture growth. In this paper, an important property (joint friction) that governs the shear behaviour of discontinuities is considered. The applied numerical procedure entails the implementation of the discrete element method to enable a more dynamic monitoring of the fracturing process, where the joint frictional property is considered in isolation. Whereas fracture propagation is constrained by joints of low frictional resistance, in non-frictional joints, the unrestricted sliding of the joint plane increases the tendency for reinitiation and proliferation of fractures at other locations. The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, this phenomenon exacerbates the influence of other factors including in situ stresses and overburden conditions. The effect of the joint frictional property is not limited to the strength of rock formations; it also impacts on fracturing processes, which could be particularly evident in jointed rock masses or formations with prominent faults and/or discontinuities

CSR and related terms in SME owner-managers' mental models in six European countries: national context matters

As a contribution to the emerging field of corporate social responsibility (CSR) cognition, this article reports on the findings of an exploratory study that compares SME owner–managers’ mental models with regard to CSR and related concepts across six European countries (Belgium, Italy, Norway, France, UK, Spain). Utilising Repertory Grid Technique, we found that the SME owner–managers’ mental models show a few commonalities as well as a number of differences across the different country samples. We interpret those differences by linking individual cognition to macro-environmental variables, such as language, national traditions and dissemination mechanisms. The results of our exploratory study show that nationality matters but that classifications of countries as found in the comparative capitalism literature do not exactly mirror national differences in CSR cognition and that these classifications need further differentiation. The findings from our study raise questions on the universality of cognition of academic management concepts and warn that promotion of responsible business practice should not rely on the use of unmediated US American management terminology

Synthesising Corporate Responsibility on Organisational and Societal Levels of Analysis: An Integrative Perspective

This article develops an integrative perspective on corporate responsibility by synthesising competing perspectives on the responsibility of the corporation at the organisational and societal levels of analysis. We review three major corporate responsibility perspectives, which we refer to as economic, critical, and politico-ethical. We analyse the major potential uses and pitfalls of the perspectives, and integrate the debate on these two levels. Our synthesis concludes that when a society has a robust division of moral labour in place, the responsibility of a corporation may be economic (as suggested under the economic perspective) without jeopardising democracy and sustainability (as reported under the critical perspective). Moreover, the economic role of corporations neither signifies the absence of deliberative democratic mechanisms nor business practices extending beyond compliance (as called for under the politico-ethical perspective). The study underscores the value of integrating different perspectives and multiple levels of analysis to present comprehensive descriptions and prescriptions of the responsibility phenomenon

Mapping the Relationship Among Political Ideology, CSR Mindset, and CSR Strategy: A Contingency Perspective Applied to Chinese Managers

The literature on antecedents of corporate social responsibility (CSR) strategies of firms has been predominately content driven. Informed by the managerial sense-making process perspective, we develop a contingency theoretical framework explaining how political ideology of managers affects the choice of CSR strategy for their firms through their CSR mindset. We also explain to what extent the outcome of this process is shaped by the firm’s internal institutional arrangements and external factors impacting on the firm. We develop and test several hypotheses using data collected from 129 Chinese managers. The results show that managers with a stronger socialist ideology are likely to develop a mindset favouring CSR, which induces the adoption of a proactive CSR strategy. The CSR mindset mediates the link between socialist ideology and CSR strategy. The strength of the relationship between the CSR mindset and the choice of CSR strategy is moderated by customer response to CSR, industry competition, the role of government, and CSR-related managerial incentives

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit

Sex-Differences in the Pattern of Comorbidities, Functional Independence, and Mortality in Elderly Inpatients: Evidence from the RePoSI Register

Background: The RePoSi study has provided data on comorbidities, polypharmacy, and sex dimorphism in hospitalised elderly patients. Methods: We retrospectively analysed data collected from the 2010, 2012, 2014, and 2016 data sets of the RePoSi register. The aim of this study was to explore the sex-differences and to validate the multivariate model in the entire dataset with an expanded follow-up at 1 year. Results: Among 4714 patients, 51% were women and 49% were men. The disease distribution showed that diabetes, coronary artery disease, chronic obstructive pulmonary disease, chronic kidney disease, and malignancy were more frequent in men but that hypertension, anaemia, osteoarthritis, depression, and diverticulitis disease were more common in women. Severity and comorbidity indexes according to the Cumulative Illness Rating Scale (CIRS-s and CIRS-c) were higher in men, while cognitive impairment, mood disorders, and disability in daily life measured by the Barthel Index (BI) were worse in women. In the multivariate analysis, BI, CIRS, and malignancy significantly increased the risk of death in men at the 1-year follow-up, while age was independently associated with mortality in women. Conclusions: Our study highlighted the relevance and the validity of our previous predictive model in the identification of sex dimorphism in hospitalised elderly patients underscoring the need of sex-personalised health-care

On the Role of Faith in Sustainability Management: A Conceptual Model and Research Agenda

International audienceThe objective of this article is to develop a faith development perspective on corporate sustainability. A firm’s management of sustainability is arguably determined by the way decision-makers relate to the other and the natural environment, and this relationship is fundamentally shaped by faith. This study advances theoretical understanding of the approach managers take on sustainability issues by explaining how four distinct phases of faith development—improvidence, obedience, irreverence and providence—determine a manager’s disposition towards sustainability. Combining insights from intentional and relational faith development theories, the analysis reveals that a manager’s faith disposition can be measured according to four interrelated process criteria: (1) connectivity as a measure of a manager’s actual engagement and activities aimed at relating to sustainability; (2) inclusivity as a measure of who and what is included or excluded in a manager’s moral consideration; (3) emotional affinity as a measure of a manager’s sensitivity and affection towards the well-being of others and ecological welfare; and (4) reciprocity as a measure of the degree to which a manager is rewarded for responding to the needs and concerns of ‘Others’, mainly in the form of a positive emotional (and relational) stimulus. The conceptual model consolidates earlier scholarly works on the psychological drivers of sustainability management by illuminating our search for a process of faith development that connects with an increasingly complex understanding of the role of business in society