Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Numerical studies on quasilinear and linear elliptic equations

We explore here the acceleration of convergence of iterative methods for the solution of a class of quasilinear and linear algebraic equations. The specific systems are the finite difference form of the Navier-Stokes equations and the energy equation for recirculating flows. The acceleration procedures considered are: the successive over relaxation scheme; several implicit methods; and a second-order procedure. A new implicit method—the alternating direction line iterative method—is proposed in this paper. The method combines the advantages of the line successive over relaxation and alternating direction implicit methods. The various methods are tested for their computational economy and accuracy on a typical recirculating flow situation. The numerical experiments show that the alternating direction line iterative method is the most economical method of solving the Navier-Stokes equations for all Reynolds numbers in the laminar regime. The usual ADI method is shown to be not so attractive for large Reynolds numbers because of the loss of diagonal dominance. This loss can however be restored by a suitable choice of the relaxation parameter, but at the cost of accuracy. The accuracy of the new procedure is comparable to that of the well-tested successive overrelaxation method and to the available results in the literature. The second-order procedure turns out to be the most efficient method for the solution of the linear energy equation.

Graduate entrepreneurship: More than child's play

Purpose With the unbridled demand for entrepreneurship in higher education, the purpose of this paper is to identify how pedagogy can inhibit students in making the transition to graduate entrepreneurship. Along the way, the concept of what and who is a graduate entrepreneur is challenged. Design/methodology/approach The paper reports upon the pragmatic development of enterprise programmes in Ireland and Australia. Despite different starting points, a convergence of purpose as to what can be realistically expected of enterprise education has emerged. Findings This study reinforces the shift away from commercialisation strategies associated with entrepreneurial action towards developing essential life skills as core to any university programme and key to developing entrepreneurial capacity among students. Despite similar government intervention, university policy and student demand for practical-based entrepreneurial learning in both cases, graduates tend not to engage in immediate entrepreneurial action due to the lack of fit between their programme of study and individual resource profiles, suggesting that graduate entrepreneurship is more than child's play. Practical implications There are practical implications for educationalists forced to consider the effectiveness of their enterprise teachings, and cautionary evidence for those charged with providing support services for graduates. Originality/value Given the evolutionary approaches used at the University of Tasmania to develop students as "reasonable adventurers" and at the University of Ulster to develop "the enterprising mindset" the paper presents evidence of the need to allow students the opportunity to apply entrepreneurial learning to their individual life experiences in order to reasonably venture into entrepreneurial activity.

Restoration of symmetry by radiative corrections

It is shown using an explicit model that radiative corrections can restore the symmetry of a system which may appear to be broken at the classical level. This is the reverse of the phenomenon demonstrated by Coleman and Weinberg. Our model is different from theirs, but the techniques are the same. The calculations are done up to the two-loop level and it is shown that the two-loop contribution is much smaller than the one-loop contribution, indicating good convergence of the loop expansion.

On the determination of energy eigenvalues and coupling strengths using duality

The Shifman-Vainshtein-Zakharov method of determining the eigenvalues and coupling strengths, from the operator product expansion, for the current correlation functions is studied in the nonrelativistic context, using the semiclassical expansion. The relationship between the low-lying eigenvalues, and the leading corrections to the imaginary-time Green function is elucidated by comparing systems which have almost identical spectra. In the case of an anharmonic oscillator it is found that with the procedure stated in the paper, that inclusion of more terms to the asymptotic expansion does not show any simple trend towards convergence to the exact values. Generalization to higher partial waves is given. In particular for the P-level of the oscillator, the procedure gives poorer results than for the S-level, although the ratio of the two comes out much better.

A probabilistic approach to the problem of electron localization in disordered systems and sharpness of the mobility edge

By applying the theory of the asymptotic distribution of extremes and a certain stability criterion to the question of the domain of convergence in the probability sense, of the renormalized perturbation expansion (RPE) for the site self-energy in a cellularly disordered system, an expression has been obtained in closed form for the probability of nonconvergence of the RPE on the real-energy axis. Hence, the intrinsic mobility mu (E) as a function of the carrier energy E is deduced to be given by mu (E)= mu 0exp(-exp( mod E mod -Ec) Delta ), where Ec is a nominal 'mobility edge' and Delta is the width of the random site-energy distribution. Thus mobility falls off sharply but continuously for mod E mod >Ec, in contradistinction with the notion of an abrupt 'mobility edge' proposed by Cohen et al. and Mott. Also, the calculated electrical conductivity shows a temperature dependence in qualitative agreement with experiments on disordered semiconductors.

Yksilöllisyys ja yhteisöllisyys K. E. Nipkowin uskonnonpedagogisen teorian kehityksessä 1960-1990

Individuality and the Community in the Development of K. E. Nipkow's Theory of Religious Education from 1960 to 1990 The purpose of this study was to describe and analyze the development occurred between 1960 and 1990 of the theory of religious education as proposed by K. E. Nipkow, the German Religious Education specialist, from the point of view of individuality and the community. Nipkow's methodological approach of dialectic convergence theory resulted in a dialogue between theological and educational factors, which supported the thirty-year development of Nipkow's models, theoretical foundations, and theory of religious education. Nipkow's doctoral dissertation, published in 1960, deals with individuality in the thinking of Pestalozzi, Humboldt and Schleiermacher. Nipkow regarded individuality as one of the basic concepts of education, which were to be interpreted anew as social and historical situations changed. In the late 1960s Nipkow developed the so-called experiential hermeneutically oriented context model for the needs of religious education. In this model, individuality is expressed in the attention paid to pupils' life situations and the educational reality. The multi-dimensional theoretical framework of religious education in 1975 emphasized supporting identity as a fundamental task of religious education. The concept of individuality was thus given a new form, in accordance with contemporary theories of developmental psychology. Other fundamental tasks, such as the socio-ethical task, the task of critical religious thinking, and that of ecumenical learning, meant a more specific emphasis on the community. It was an outline of a liberating education, which faced the individualistic-existential and social-ecclesiastical challenges of the time with a critical attitude. The further development of the theoretical outline in 1982 continued to uphold the perspectives of both individuality and the community, as Nipkow combined a historical-social dimension with theories of developmental psychology, especially that of life-span research. According to him, the development of the individual and communal life-reality belonged together. The fundamental task of religious education came to be learning to live and believe together. Nipkow transferred the idea of dialogue into inter-generational learning and developed elementarization as a methodology of Religious Education, which takes into account the point of departure of each age group. His theory of educational responsibility in the church (1990) contained the tasks of walking alongside the individual and the renewal of church communities as prerequisites of communicating the Christian faith in an era characterized by multifaceted Christianity. The "geisteswissenschaftliche" school and its concepts (Ger. Individualität; Bildung) were found to be the explanatory factor of the concepts of individuality and the community in the development of Nipkow's theory of religious education. The concept of education employed by Nipkow (Ger. Bildung) implies, on one hand, the individuality, autonomy, freedom and personal responsibility of people of different ages, and on the other hand, the dialogical nature of education in the community facilitated by this concept. Theologically, Nipkow associates himself in his views on individuality and the community with Schleiermacher's understanding of faith, of which openness towards the world was characteristic. The significance of individuality and the community in Nipkow's thinking was, furthermore, deepened by his participation, as a member of working parties, in the educational discussions of the World Council of Churches.

Small State Cultures of Consensus : State Traditions and Consensus-Seeking in the Neo-Corporatist and Neutrality Policies in Post-1945 Austria and Finland

Austria and Finland are persistently referred to as the “success stories” of post-1945 European history. Notwithstanding their different points of departure, in the course of the Cold War both countries portrayed themselves as small and neutral border-states in the world dictated by superpower politics. By the 1970s, both countries frequently ranked at the top end in various international classifications regarding economic development and well-being in society. This trend continues today. The study takes under scrutiny the concept of consensus which figures centrally in the two national narratives of post-1945 success. Given that the two domestic contexts as such only share few direct links with one another and are more obviously different than similar in terms of their geographical location, historical experiences and politico-cultural traditions, the analogies and variations in the anatomies of the post-1945 “cultures of consensus” provide an interesting topic for a historical comparative and cross-national examination. The main research question concerns the identification and analysis of the conceptual and procedural convergence points of the concepts of the state and consensus. The thesis is divided into six main chapters. After the introduction, the second chapter presents the theoretical framework in more detail by focusing on the key concepts of the study – the state and consensus. Chapter two also introduces the comparative historical and cross-national research angles. Chapter three grounds the key concepts of the state and consensus in the historical contexts of Austria and Finland by discussing the state, the nation and democracy in a longer term comparative perspective. The fourth and fifth chapter present case studies on the two policy fields, the “pillars”, upon which the post-1945 Austrian and Finnish cultures of consensus are argued to have rested. Chapter four deals with neo-corporatist features in the economic policy making and chapter five discusses the building up of domestic consensus regarding the key concepts of neutrality policies in the 1950s and 1960s. The study concludes that it was not consensus as such but the strikingly intense preoccupation with the theme of domestic consensus that cross-cut, in a curiously analogous manner, the policy-making processes studied. The main challenge for the post-1945 architects of Austrian and Finnish cultures of consensus was to find strategies and concepts for consensus-building which would be compatible with the principles of democracy. Discussed at the level of procedures, the most important finding of the study concerns the triangular mechanism of coordination, consultation and cooperation that set into motion and facilitated a new type of search for consensus in both post-war societies. In this triangle, the agency of the state was central, though in varying ways. The new conceptions concerning a small state’s position in the Cold War world also prompted cross-nationally perceivable willingness to reconsider inherited concepts and procedures of the state and the nation. At the same time, the ways of understanding the role of the state and its relation to society remained profoundly different in Austria and Finland and this basic difference was in many ways reflected in the concepts and procedures deployed in the search for consensus and management of domestic conflicts. For more detailed information, please consult the author.

Essays on Illegal Activities, Institutions and Economic Growth

In public economics, two extremist views on the functions of a government compete: one emphasizes government working for the public interest to provide value for the citizens, while another regards government mainly as a workhorse for private interests. Moreover, as the sole legitimate authority, the government has the right to define the rules and laws as well as to enforce them. With respect to regulation, two extremes arise: from too little regulation to too much of it. If the government does not function or ceases to exist, the state falls into anarchy or chaos (Somalia). If it regulates too much, it will completely suffocate private activities, which might be considered extralegal (the former Soviet Union). In this thesis I scrutinize the government s interventionist policies and evaluate the question of how to best promote economic well-being. The first two essays assume that the government s policies promote illegal activity. The first paper evaluates the interaction between the government and the mafia, and pays attention to the law enforcement of underground production. We show that the revenue-maximizing government will always monitor the shadow economy, as monitoring contributes to the government s revenue. In general, both legal and illegal firms are hurt by the entry of the mafia. It is, however, plausible that legal firms might benefit by the entry of the mafia if it competes with the government. The second paper tackles the issue of the measurement of the size of the shadow economy. To formulate policies it is essential to know what drives illegal economic activity; is it the tax burden, excess regulation, corruption or a weak legal environment? In this paper we propose an additional explanation for tax evasion and shadow production, namely cultural factors as manifested by religion as determinants of tax morality. According to our findings, Catholic and Protestant countries do not differ in their tax morale. The third paper contributes to the literature discussing the role of the government in promoting economic and productivity growth. Our main result is that, given the complex relationship between economic growth and economic freedom, marketization has not necessarily been beneficial in terms of growth. The last paper builds on traditional growth literature and revisits the debate on convergence clubs arising from demographic transition. We provide new evidence against the idea that countries within a club would converge over time. Instead, we propose that since the demographic transition is a dynamic process, one can expect countries to enter the last regime of stable, modern growth in stages.

Climate change impact assessment: Uncertainty modeling with imprecise probability

Hydrologic impacts of climate change are usually assessed by downscaling the General Circulation Model (GCM) output of large-scale climate variables to local-scale hydrologic variables. Such an assessment is characterized by uncertainty resulting from the ensembles of projections generated with multiple GCMs, which is known as intermodel or GCM uncertainty. Ensemble averaging with the assignment of weights to GCMs based on model evaluation is one of the methods to address such uncertainty and is used in the present study for regional-scale impact assessment. GCM outputs of large-scale climate variables are downscaled to subdivisional-scale monsoon rainfall. Weights are assigned to the GCMs on the basis of model performance and model convergence, which are evaluated with the Cumulative Distribution Functions (CDFs) generated from the downscaled GCM output (for both 20th Century [20C3M] and future scenarios) and observed data. Ensemble averaging approach, with the assignment of weights to GCMs, is characterized by the uncertainty caused by partial ignorance, which stems from nonavailability of the outputs of some of the GCMs for a few scenarios (in Intergovernmental Panel on Climate Change [IPCC] data distribution center for Assessment Report 4 [AR4]). This uncertainty is modeled with imprecise probability, i.e., the probability being represented as an interval gray number. Furthermore, the CDF generated with one GCM is entirely different from that with another and therefore the use of multiple GCMs results in a band of CDFs. Representing this band of CDFs with a single valued weighted mean CDF may be misleading. Such a band of CDFs can only be represented with an envelope that contains all the CDFs generated with a number of GCMs. Imprecise CDF represents such an envelope, which not only contains the CDFs generated with all the available GCMs but also to an extent accounts for the uncertainty resulting from the missing GCM output. This concept of imprecise probability is also validated in the present study. The imprecise CDFs of monsoon rainfall are derived for three 30-year time slices, 2020s, 2050s and 2080s, with A1B, A2 and B1 scenarios. The model is demonstrated with the prediction of monsoon rainfall in Orissa meteorological subdivision, which shows a possible decreasing trend in the future.