A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Testing solar forcing of pervasive Holocene climate cycles

The temporal and spatial extent of Holocene climate change is an area of considerable uncertainty, with solar forcing recently proposed to be the origin of cycles identified in the North Atlantic region. To address these issues we have developed an annually resolved record of changes in Irish bog tree populations over the last 7468 years which, together with radiocarbon-dated bog and lake-edge populations, extend the dataset back to 9000 yr ago. The Irish trees underpin the internationally accepted radiocarbon calibration curve, used to derive a proxy of solar activity, and allow us to test solar forcing of Holocene climate change. Tree populations and age structures provide unambiguous evidence of major shifts in Holocene surface moisture, with a dominant cyclicity of 800 yr, similar to marine cycles in the North Atlantic, indicating significant changes in the latitude and intensity of zonal atmospheric circulation across the region. The cycles, however, are not coherent with changes in solar activity (both being on the same absolute timescale), indicating that Holocene North Atlantic climate variability at the millennial and centennial scale is not driven by a linear response to changes in solar activity.

An analytic geometry-variant approach to line ratio enhancement above the optically thin limit

We describe a simple theoretical model to investigate the anomalous effects of opacity on spectral line ratios, as previously studied in elements such as Fe XV and Fe XVII. The model developed is general: it is not specific to a particular atomic system, thus giving applicability to a number of coronal and chromospheric plasmas; furthermore, it may be applied to a variety of astrophysically relevant geometries. The analysis is underpinned by geometrical arguments, and we outline a technique for it to be used as a tool for the explicit diagnosis of plasma geometry in distant astrophysical objects.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

High harmonic generation in the relativistic limit

The generation of extremely bright coherent X-ray pulses in the femtosecond and attosecond regime is currently one of the most exciting frontiers of physics - allowing, for the first time, measurements with unprecedented temporal resolution(1-6). Harmonics from laser - solid target interactions have been identified as a means of achieving fields as high as the Schwinger limit(2,7) (E = 1.3 x 10(16) V m(-1)) and as a highly promising route to high-efficiency attosecond (10(-18) s) pulses(8) owing to their intrinsically phase-locked nature. The key steps to attain these goals are achieving high conversion efficiencies and a slow decay of harmonic efficiency to high orders by driving harmonic production to the relativistic limit(1). Here we present the first experimental demonstration of high harmonic generation in the relativistic limit, obtained on the Vulcan Petawatt laser(9). High conversion efficiencies (eta> 10(-6) per harmonic) and bright emission (> 10(22) photons s(-1) mm(-2) mrad(-2) (0.1% bandwidth)) are observed at wavelengths <4 nm ( the 'water-window' region of particular interest for bio-microscopy).

A new method of measuring plastic limit of fine materials

Index properties such as the liquid limit and plastic limit are widely used to evaluate certain geotechnical parameters of fine-grained soils. Measurement of the liquid limit is a mechanical process, and the possibility of errors occurring during measurement is not significant. However, this is not the case for plastic limit testing, despite the fact that the current method of measurement is embraced by many standards around the world. The method in question relies on a fairly crude procedure known widely as the ‘thread rolling' test, though it has been the subject of much criticism in recent years. It is essential that a new, more reliable method of measuring the plastic limit is developed using a mechanical process that is both consistent and easily reproducible. The work reported in this paper concerns the development of a new device to measure the plastic limit, based on the existing falling cone apparatus. The force required for the test is equivalent to the application of a 54 N fast-static load acting on the existing cone used in liquid limit measurements. The test is complete when the relevant water content of the soil specimen allows the cone to achieve a penetration of 20 mm. The new technique was used to measure the plastic limit of 16 different clays from around the world. The plastic limit measured using the new method identified reasonably well the water content at which the soil phase changes from the plastic to the semi-solid state. Further evaluation was undertaken by conducting plastic limit tests using the new method on selected samples and comparing the results with values reported by local site investigation laboratories. Again, reasonable agreement was found.

Media coverage of sustainable development issues – attention cycles or punctuated equilibrium?

Over the last two decades there has been a marked change in the way that the public perceives environmental issues and the concepts associated with sustainable development. Few would argue that this has moved into the mainstream of public consciousness. Coverage of sustainability related concepts within the media, as illustrated by a sample of 112 worldwide newspapers, shows a clear upward trajectory. Taking the example of climate change and sustainable development this paper explores this increasing coverage, and arguably awareness of, sustainability concepts and considers parallels with the concepts of punctuated equilibrium and issue-attention cycles.

Discussion on: Sivakumar, V., Glynn, D., Cairns, P. & Black, J.A. (2009). A new method of measuring plastic limit of fine materials. Géotechnique 59, No. 10, 813-823. by Brendan C. O'Kelly

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