This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.

This book paves the way for a more enlarged discussion on religion and migration phenomena in countries of Northern and Southern Europe. From a comparative perspective, these are regions with very different religious traditions and different historical State/Church relations. Although official religion persisted longer in Nordic Protestant countries than in South Mediterranean countries, levels of secularization are higher. In the last decades, both Northern and Southern Europe have received strong flows of newcomers. From this perspective, the book presents through various theoretical lenses and empirical researches the impact mobility and consequent religious transnationalism have on multiple aspects of culture and social life in societies where the religious landscapes are increasingly diverse. The chapters demonstrate that we are dealing with complex scenarios: different contexts of reception, different countries of origin, various ethnicities and religious traditions (Catholics, Orthodox and Evangelical Christians, Muslims, Buddhists). Having become plural spaces, our societies tend to be far more concerned with the issue of social integration rather than with that of social identities reconstruction in society as a whole, often ignoring that today religion manifests itself as a plurality of religions. In short, what are the implications of newcomers for the religious life of Europe and for the redesign of its soul?

This book paves the way for a more enlarged discussion on religion and migration phenomena in countries of Northern and Southern Europe. From a comparative perspective, these are regions with very different religious traditions and different historical State/Church relations. Although official religion persisted longer in Nordic Protestant countries than in South Mediterranean countries, levels of secularization are higher. In the last decades, both Northern and Southern Europe have received strong flows of newcomers. From this perspective, the book presents through various theoretical lenses and empirical researches the impact mobility and consequent religious transnationalism have on multiple aspects of culture and social life in societies where the religious landscapes are increasingly diverse. The chapters demonstrate that we are dealing with complex scenarios: different contexts of reception, different countries of origin, various ethnicities and religious traditions (Catholics, Orthodox and Evangelical Christians, Muslims, Buddhists). Having become plural spaces, our societies tend to be far more concerned with the issue of social integration rather than with that of social identities reconstruction in society as a whole, often ignoring that today religion manifests itself as a plurality of religions. In short, what are the implications of newcomers for the religious life of Europe and for the redesign of its soul?

Historically, European churches have played a large part in the provision of welfare. Responsibility, however, has gradually shifted to the state - a shift that forms an integral part of the process of secularization and one that has been readily accepted by European populations. But what happens when the state itself begins to recede - a process that is occurring in most, if not all, European societies for a wide variety of reasons? The implications for welfare are considerable, not least for the role of the churches which begin to resume the responsibilities previously shed but in new and different ways. This book looks at the connections between religion and welfare in Europe, exploring in detail eight European societies - Finland, Norway, Sweden, England, Germany, France, Italy and Greece. The different theological traditions, different church-state relationships and different welfare regimes are all examined. The analysis is based on first hand empirical research which considers not only the changing situation on the ground, but attitudes towards this within a range of different constituencies - the churches, local government and the general public. Particular attention is paid to the significance of gender in both the process of change and in attitudes towards this. Welfare and Religion in 21st Century Europe: Volume 1 represents comparative research at its best and highlights key policy implications for the future. A companion book, Welfare and Religion in 21st Century Europe: Volume 2 explores thematically the changing nature of religion and welfare and the new relationships that are emerging between the religious and the secular, and between church and state in the 21st century.

Historically, European churches have played a large part in the provision of welfare. Responsibility, however, has gradually shifted to the state - a shift that forms an integral part of the process of secularization and one that has been readily accepted by European populations. But what happens when the state itself begins to recede - a process that is occurring in most, if not all, European societies for a wide variety of reasons? The implications for welfare are considerable, not least for the role of the churches which begin to resume the responsibilities previously shed but in new and different ways. This book looks at the connections between religion and welfare in Europe, exploring in detail eight European societies - Finland, Norway, Sweden, England, Germany, France, Italy and Greece. The different theological traditions, different church-state relationships and different welfare regimes are all examined. The analysis is based on first hand empirical research which considers not only the changing situation on the ground, but attitudes towards this within a range of different constituencies - the churches, local government and the general public. Particular attention is paid to the significance of gender in both the process of change and in attitudes towards this. Welfare and Religion in 21st Century Europe: Volume 1 represents comparative research at its best and highlights key policy implications for the future. A companion book, Welfare and Religion in 21st Century Europe: Volume 2 explores thematically the changing nature of religion and welfare and the new relationships that are emerging between the religious and the secular, and between church and state in the 21st century.

Historically, European churches have played a large part in the provision of welfare. Responsibility, however, has gradually shifted to the state - a shift that forms an integral part of the process of secularization and one that has been readily accepted by European populations. But what happens when the state itself begins to recede - a process that is occurring in most, if not all, European societies for a wide variety of reasons? The implications for welfare are considerable, not least for the role of the churches which begin to resume the responsibilities previously shed but in new and different ways. This book looks at the connections between religion and welfare in Europe, exploring in detail eight European societies - Finland, Norway, Sweden, England, Germany, France, Italy and Greece. The different theological traditions, different church-state relationships and different welfare regimes are all examined. The analysis is based on first hand empirical research which considers not only the changing situation on the ground, but attitudes towards this within a range of different constituencies - the churches, local government and the general public. Particular attention is paid to the significance of gender in both the process of change and in attitudes towards this. Welfare and Religion in 21st Century Europe: Volume 1 represents comparative research at its best and highlights key policy implications for the future. A companion book, Welfare and Religion in 21st Century Europe: Volume 2 explores thematically the changing nature of religion and welfare and the new relationships that are emerging between the religious and the secular, and between church and state in the 21st century.

Historically, European churches have played a large part in the provision of welfare. Responsibility, however, has gradually shifted to the state - a shift that forms an integral part of the process of secularization and one that has been readily accepted by European populations. But what happens when the state itself begins to recede - a process that is occurring in most, if not all, European societies for a wide variety of reasons? The implications for welfare are considerable, not least for the role of the churches which begin to resume the responsibilities previously shed but in new and different ways. This book looks at the connections between religion and welfare in Europe, exploring in detail eight European societies - Finland, Norway, Sweden, England, Germany, France, Italy and Greece. The different theological traditions, different church-state relationships and different welfare regimes are all examined. The analysis is based on first hand empirical research which considers not only the changing situation on the ground, but attitudes towards this within a range of different constituencies - the churches, local government and the general public. Particular attention is paid to the significance of gender in both the process of change and in attitudes towards this. Welfare and Religion in 21st Century Europe: Volume 1 represents comparative research at its best and highlights key policy implications for the future. A companion book, Welfare and Religion in 21st Century Europe: Volume 2 explores thematically the changing nature of religion and welfare and the new relationships that are emerging between the religious and the secular, and between church and state in the 21st century.