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.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Measurement of highly transient electrical charging following high-intensity laser-solid interaction

The multi-million-electron-volt proton beams accelerated during high-intensity laser-solid interactions have been used as a particle probe to investigate the electric charging of microscopic targets laser-irradiated at intensity similar to10(19) W cm(2). The charge-up, detected via the proton deflection with high temporal and spatial resolution, is due to the escape of energetic electrons generated during the interaction. The analysis of the data is supported by three- dimensional tracing of the proton trajectories. (C) 2003 American Institute of Physics.

'What say you to [this] book? Is it yours?'::Oral and Collaborative Narrative Trajectories in the Mediated Writings of Anna Trapnel

This article argues that, when a printed page is initially orally generated and then transcribed, either at the time or on a subsequent occasion by a listener or an interlocutor, there are important critical implications for the “I” of the account. It takes as a case study Anna Trapnel's first published works. Appearing within a few weeks of each other in 1654, The Cry of a Stone and Strange and Wonderful News are both mediated texts, large parts of which depend on the agency of a relater. The article begins by examining the textual traces of the relater, arguing for the centrality of his role and other agencies in the shaping of the works which bear Trapnel's name. Situating itself in relation to a current orientation in feminist autobiographical theory that places emphasis on the external requirement to narrate one's life, rather than on the spontaneous production of autobiography by an inner self, the article emphasizes notions of coaxing, witnessing and intersubjectivity to point up an appreciation of women's life writing as a species of cultural production in which various historical actors—male and female—participate. This dialogic process, which persists into the afterlife of transcription, owes part of its genesis to the political vagaries of 1654 and precipitates two contrasting—but equally “authentic”—versions of Trapnel's life and self. Mapping this movement, discussion concentrates on the ways in which a critical confrontation with women's oral narrative is as much an activity of disentangling as it is of reconstructing, an activity which is revealing of the extent to which a spectrum of social and cultural networks participates in and facilitates the female writing act.

Individual differences in trajectories of arithmetical development in typically achieving 5-to 7-year-olds

The arithmetical performance of typically achieving 5- to 7-year-olds (N = 29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear growth over the 18-month period, analysis of individual differences revealed a much more complex picture. Some children exhibited marked variation in performance across the seven tasks, including evidence of difficulty in some cases. Individual growth patterns also showed differences in developmental trajectories between children on each task and within children across tasks. The findings support the idea of the componential nature of arithmetical ability and underscore the need for further longitudinal research on typically achieving children and of careful consideration of individual differences. (C) 2009 Elsevier Inc. All rights reserved.

Restraing Regulatory Capture? Anglo America, Crisis Politics and Trajectories of Change in Global Financial Governance

A growing number of respected commentators now argue that regulatory capture of public agencies and public policy by leading banks was one of the main causal factors behind the financial crisis of 2007–2009, resulting in a permissive regulatory environment. This regulatory environment placed a faith in banks own internal risk models, contributed to pro-cyclical behaviour and turned a blind eye to excessive risk taking. The article argues that a form of ‘multi-level regulatory capture’ characterized the global financial architecture prior to the crisis. Simultaneously, regulatory capture fed off, but also nourished the financial boom, in a fashion that mirrored the life cycle of the boom itself. Minimizing future financial booms and crises will require continuous, conscious and explicit efforts to restrain financial regulatory capture now and into the future. The article assesses the extent to which this has been achieved in current global financial governance reform efforts and highlights some of the persistent difficulties that will continue to hamper efforts to restrain regulatory capture. The evidence concerning the extent to which regulatory capture is being effectively restrained is somewhat mixed, and where it is happening it is largely unintentional and accidental. Recent reforms have overlooked the political causes of the crisis and have failed to focus explicitly or systematically on regulatory capture.