Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Attitudes to community relations in Northern Ireland: signs of optimisim in the post-cease fire period?

This article uses attitudinal data to explore Catholic and Protestant perspectives on community relations and equality since the paramilitary cease fires in 1994. Although attitudes tend to fluctuate with the‘headline grabbing'events of the day, the article argues that there are signs that some fundamental changes have taken place in the post cease fire period. Of particular importance in this regard is the positive response recorded by the Catholic community towards government measures to tackle disadvantage and inequality. Equally significant is the protestant response to many of these measures which is often one of ambivalence rather than derision. In so far as the data appear to challenge the‘zero-sum'game that traditionally underpins relations between the two communities in Northern Ireland, they provide some grounds for optimism. Yet such optimism is tempered somewhat by the seeds of discontent which are manifest within the protestant community, particularly around issues of equality in employment and cultural traditions. Despite the more positive assessment of community relations and equality in 2002, it is argued that further monitoring will be required to determine the long-term effects of policy reform on relationships between the two communit

Professional Educational Psychology and Community Relations Education in Northern Ireland.

This article provides an account of practice-based research of, at least, one-star quality in terms of its contribution to both theory and practice. Aimed at practitioner (as opposed to academic) psychologists, the article addresses a dimension of the practitioner role that has remained silent in the literature. The article makes creative and original connections between school effectiveness, school improvement and education in a divided society. Post 11th September, the article was described as being highly original, significant and relevant to all practising educational psychologists. Concrete evidence for this is gained from, eg: hits on the online electronic version (2002-2003 Annual Report of the Association of Educational Psychologists), citations in reviews of research, and author invitations to present his work at UK and international practitioner psychology conferences. The article is published in the premier journal reporting on quality applied educational research and practice within the United Kingdom and beyond.

A Triumph of Voluntarism? Industrial Relations and Strikes in Northern Ireland During World War Two

Flanders (1974) considered the Second World War to be the great social triumph and vindication of voluntarism in British industrial relations. This paper considers the experience of one region, Northern Ireland, functioning in a unique social and political context and considers the experience of its wartime industrial relations system. The political framework, trade union growth and representation, collective bargaining, strike activity including the major munitions strike of 1944 which may have provoked Defence Regulations Order 1AA, labour management and Joint Production Committees are all examined. The paper gives qualified support to Flanders’ conclusion.