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.

A Maxwell relation for current-induced forces

A Maxwell relation is presented involving current-induced forces. It provides a new physical picture of the origin of current-induced forces and in the small-voltage limit it enables the identification of a simple thermodynamic potential which drives electromigration. The question of whether current-induced forces are conservative or non-conservative is discussed briefly in the light of these insights.

Retrospective assessment of dryland soil stability in relation to grazing and climate change

Accelerated soil erosion is an aspect of dryland degradation that is affected by repeated intense drought events and land management activities such as commercial livestock grazing. A soil stability index (SSI) that detects the erosion status and susceptibility of a landscape at the pixel level, i.e., stable, erosional, or depositional pixels, was derived from the spectral properties of an archived time series (from 1972 to 1997) of Landsat satellite data of a commercial ranch in northeastern Utah. The SSI was retrospectively validated with contemporary field measures of soil organic matter and erosion status that was surveyed by US federal land management agencies. Catastrophe theory provided the conceptual framework for retrospective assessment of the impact of commercial grazing and soil water availability on the SSI. The overall SSI trend was from an eroding landscape in the early drier 1970s towards stable conditions in the wetter mid-1980s and late 1990s. The landscape catastrophically shifted towards an extreme eroding state that was coincident with the “The Great North American Drought of 1988”. Periods of landscape stability and trajectories toward stability were coincident with extremely wet El Niño events. Commercial grazing had less correlation with soil stability than drought conditions. However, the landscape became more susceptible to erosion events under multiple droughts and grazing. Land managers now have nearly a year warning of El Niño and La Niña events and can adjust their management decisions according to predicted landscape erosion conditions.

The Voice as Transcursive Inscriber: The Relation of Body and Instrument Understood through the Workings of a Machine

This article examines the relationship of the body with a musical instrument; specifically it looks at the vital threshold conditions that occur during the interplay of voice and instrument. By examining the work ‘IKAS’ (1982) for solo saxophone by German composer Hans-Joachim Hespos, the unusual timbral relationships created between vocal and instrumental sounds are exposed. I argue that this particular work highlights the performer/instrument relation as one marked by Gilles Deleuze’s notion of the workings of a machine and a machine’s relation to a ‘flow’, in particular a machine’s function with view to the break in the flow. By turning towards Deleuze’s concept of the machine, this article offers a slightly different vocabulary for music analysis, one that more easily encompasses certain works of the twentieth century, specifically those that are more timbre- than pitch-based.