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.

Evolution of the nervous system in Paraphanostoma (Acoela)

According to recent molecular studies, the Acoela are the earliest extant bilaterian group. Their nervous system displays a striking variety of patterns. The aim of the present investigation was to study the variability of the nervous system in a monophyletic group of the Acoela. Six species of Paraphanostoma were chosen for the study. Using immunocytochemical methods and confocal scanning laser microscopy, the immunoreactive patterns of serotonin (5-HT) and the neuropeptide GYIRFamide were described in detail. The study has demonstrated that the brains in Paraphanostoma species, although diverse in detail, still follow the same general pattern. 18S rDNA sequences were used to generate a hypothesis of the phylogeny within the group. Characters of the nervous system revealed in this study were coded and analysed together with 18S rDNA data. Several synapomorphies in the nervous system characters were identified. However, numerous parallelisms in the nervous system evolution have occurred. Data obtained demonstrate that the genus Paraphanostoma is closely related to Childia and should belong to the same family, Childiidae.

The evolution of the UK charity Statement of Recommended Practice: The influence of key stakeholders

In the early 1980s, a landmark study identified significant poor reporting practice in UK charities. As a consequence, a journey was commenced with the aim of improving accounting and reporting as a basis for enhancing accountability by charities. Much of this change has been effected through the publication of evolving Statements of Recommended Practice (SORPs) on accounting and reporting by charities. This paper analyses the evolution of the SORP through time using insights from stakeholder theory, and argues that the key stakeholders influencing the evolving SORP have been government and the accounting profession.

Dynamic evolution of the genetic search region through fuzzy coding

A technique for automatic exploration of the genetic search region through fuzzy coding (Sharma and Irwin, 2003) has been proposed. Fuzzy coding (FC) provides the value of a variable on the basis of the optimum number of selected fuzzy sets and their effectiveness in terms of degree-of-membership. It is an indirect encoding method and has been shown to perform better than other conventional binary, Gray and floating-point encoding methods. However, the static range of the membership functions is a major problem in fuzzy coding, resulting in longer times to arrive at an optimum solution in large or complicated search spaces. This paper proposes a new algorithm, called fuzzy coding with a dynamic range (FCDR), which dynamically allocates the range of the variables to evolve an effective search region, thereby achieving faster convergence. Results are presented for two benchmark optimisation problems, and also for a case study involving neural identification of a highly non-linear pH neutralisation process from experimental data. It is shown that dynamic exploration of the genetic search region is effective for parameter optimisation in problems where the search space is complicated.

ON THE PROGENITOR AND EARLY EVOLUTION OF THE TYPE II SUPERNOVA 2009kr

We identify a source coincident with SN 2009kr in Hubble Space Telescope pre-explosion images. The object appears to be a single point source with an intrinsic color V - I = 1.1 +/- 0.25 and M-V = -7.6 +/- 0.6. If this is a single star, it would be a yellow supergiant of log L/L-circle dot similar to 5.1 and a mass of 15(-4)(+5) M-circle dot. The spatial resolution does not allow us yet to definitively determine if the progenitor object is a single star, a binary system, or a compact cluster. We show that the early light curve is similar to a Type IIL SN, but the prominent H alpha P-Cygni profiles and the signature of the end of a recombination phase are reminiscent of a Type IIP. The evolution of the expanding ejecta will play an important role in understanding the progenitor object.

Later Pleistocene evolution of the Exe valley: A chronstratigraphic model of terrace formation and its implications for Palaeolithic archaeology

This paper presents the ?rst systematic chronostratigraphic study of the river terraces of the Exe catchment in South West England and a new conceptual model for terrace formation in unglaciated basins with applicability to terrace staircase sequences elsewhere. The Exe catchment lay beyond the maximum extent of Pleistocene ice sheets and the drainage pattern evolved from the Tertiary to the Middle Pleistocene, by which time the major valley systems were in place and downcutting began to create a staircase of strath terraces. The higher terraces (8-6) typically exhibit altitudinal overlap or appear to be draped over the landscape, whilst the middle terraces show greater altitudinal separation and the lowest terraces are of a cut and ?ll form. The terrace deposits investigated in this study were deposited in cold phases of the glacial-interglacial Milankovitch climatic cycles with the lowest four being deposited in the Devensian Marine Isotope Stages (MIS) 4-2. A new cascade process-response model is proposed of basin terrace evolution in the Exe valley, which emphasises the role of lateral erosion in the creation of strath terraces and the reworking of inherited resistant lithological components down through the staircase. The resultant emergent valley topography and the reworking of artefacts along with gravel clasts, have important implications for the dating of hominin presence and the local landscapes they inhabited. Whilst the terrace chronology suggested here is still not as detailed as that for the Thames or the Solent System it does indicate a Middle Palaeolithic hominin presence in the region, probably prior to the late Wolstonian Complex or MIS 6. This supports existing data from cave sites in South West England.