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.

Tools for analysing configuration interaction wavefunctions

The configuration interaction (CI) approach to quantum chemical calculations is a well-established means of calculating accurately the solution to the Schrodinger equation for many-electron systems. It represents the many-body electron wavefunction as a sum of spin-projected Slater determinants of orthogonal one-body spin-orbitals. The CI wavefunction becomes the exact solution of the Schrodinger equation as the length of the expansion becomes infinite, however, it is a difficult quantity to visualise and analyse for many-electron problems. We describe a method for efficiently calculating the spin-averaged one- and two-body reduced density matrices rho(psi)((r) over bar; (r) over bar' ) and Gamma(psi)((r) over bar (1), (r) over bar (2); (r) over bar'(1), (r) over bar'(2)) of an arbitrary CI wavefunction Psi. These low-dimensional functions are helpful tools for analysing many-body wavefunctions; we illustrate this for the case of the electron-electron cusp. From rho and Gamma one can calculate the matrix elements of any one- or two-body spin-free operator (O) over cap. For example, if (O) over cap is an applied electric field, this field can be included into the CI Hamiltonian and polarisation or gating effects may be studied for finite electron systems. (C) 2003 Elsevier B.V. All rights reserved.

Difference, Diversity and Difficulty: Problems in Adult Peace Education in Northern Ireland

The peace process in Northern Ireland has been hailed, variously, as the successful resolution to one of the world's most intractable conflicts, and as a failed attempt to reconcile the conflciting claims of the two main ethnonationalist communities. At both these points, and at every other point along the continuum, recognition is given to the centrality of education. This article looks at the role played by adult learning, and contrasts two fundamentally different apporaoches. In one, Enlightenment assumptions about the power of knowledge to dispel prejudice have run alongside attempts to create a world of shared values; in the other, a postmodern acceptance of different cultures has accompnaied a peace process that builds upon ethnic diistinctions. As with the Dayton Accord and with other peace agreements brokered with international assistance, the consociational model of governance has been chosen for Northern Ireland in order to create a political equilibrium between the unionists and nationalists. Such a political framework reverses the direction of previous integrationist educational policies in favour of a celebration of difference, an approach that is fraught with difficulties.

A panel of single locus minisatellite DNA probes for application to problems in salmonid aquaculture

Eleven minisatellite DNA locus specific probes, isolated from Atlantic salmon (Salmo salar) and brown trout (Salmo trutta) partial genomic DNA libraries, were tested for cross-hybridization to eleven other salmonid species, i.e. sockeye salmon (Oncorhynchus nerka); coho salmon (O. kisutch), chum salmon (O. keta); pink salmon (O. gorbuscha); chinook salmon (O. tshawytscha); rainbow trout (O. mykiss); brook trout (Salvelinus fontinalis); Arctic charr (S. alpinus); grayling (Thymallus thymallus); huchen (Hucho hucho); pollan (Coregonus autumnalis). Simple single locus profiles for each of these species were revealed by, from two to ten SLPs. These markers are likely to be of great value in addressing several problems in aquaculture of these species.

Problems with identifying the '8200-year cold event' in terrestrial records of the Atlantic seaboard: a case study from Dooagh, Achill Island, Ireland.

The Northern Hemisphere cooling event 8200 years ago is believed to represent the last known major freshwater pulse into the North Atlantic as a result of the final collapse of the North American Laurentide ice sheet. This pulse of water is generally believed to have occurred independently of orbital variations and provides an analogue for predicted increases in high-latitude precipitation and ice melt as a result of anthropogenically driven future climate change. The precise timing, duration and magnitude of this event, however, are uncertain, with suggestions that the 100-yr meltwater cooling formed part of a longer-term cold period in the early Holocene. Here we undertook a multiproxy, high-resolution investigation of a peat sequence at Dooagh, Achill Island, on the west coast of Ireland, to determine whether the 8200-year cold event impacted upon the terrestrial vegetation immediately downwind of the proposed changes in the North Atlantic. We find clear evidence for an oscillation in the early Holocene using various measures of pollen, indicating a disruption in the vegetation leading to a grassland-dominated landscape, most probably driven by changes in precipitation rather than temperature. Radiocarbon dating was extremely problematic, however, with bulk peat samples systematically too young for the North Atlantic event, suggesting significant contamination from downward root penetration. The sustained disruption to vegetation over hundreds of years at Dooagh indicates the landscape was impacted by a long-term cooling event in the early Holocene, and not the single century length 8200-year meltwater event proposed in many other records in the North Atlantic region.