An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

A defect equation approach for the coupling of subdomains in domain decomposition methods

A defect equation for the coupling of nonlinear subproblems defined in nonoverlapped subdomains arise in domain decomposition methods is presented. Numerical solutions of defect equations by means of quasi-Newton methods are considered.

Ghost and self: Jung's paradigm shift and a response to Zinkin

Zinkin's lucid challenge to Jung makes perfect sense. Indeed, it is the implications of this `making sense' that this paper addresses. For Zinkin's characterization of the `self' takes it as a `concept' requiring coherence; a variety of abstract non-contextual knowledge that itself has a mythical heritage. Moreover, Zinkin's refinement of Jung seeks to make his work fit for the scientific paradigm of modernity. In turn, modernity's paradigm owes much to Newton's notion of knowledge via reductionism. Here knowledge or investigation is divided up into the smallest possible units with the aim of eventually putting it all together into `one' picture of scientific truth. Unfortunately, `reductionism' does not do justice to the resonant possibilities of Jung's writing. These look forward to a new scientific paradigm of the twenty-first century, of the interactive `field', emergence and complexity theory. The paper works paradoxically by discovering Zinkin's `intersubjective self' after all, in two undervalued narratives by Jung, his doctoral thesis and a short late ghost story. However, in the ambivalences and radical fictional experimentation of these fascinating texts can be discerned an-Other self, one both created and found. [From the Publisher]

Prehistoric Pinus woodland dynamics in an upland landscape in northern Scotland: the roles of climate change and human impact

Pollen, microscopic charcoal, palaeohydrological and dendrochronological analyses are applied to a radiocarbon and tephrochronologically dated mid Holocene (ca. 8500–3000 cal B.P.) peat sequence with abundant fossil Pinus (pine) wood. The Pinus populations on peat fluctuated considerably over the period in question. Colonisation by Pinus from ca. 7900–7600 cal B.P. appears to have had no specific environmental trigger; it was probably determined by the rate of migration from particular populations. The second phase, at ca. 5000–4400 cal B.P., was facilitated by anthropogenic interference that reduced competition from other trees. The pollen record shows two Pinus declines. The first at ca. 6200–5500 cal B.P. was caused by a series of rapid and frequent climatic shifts. The second, the so-called pine decline, was very gradual (ca. 4200–3300 cal B.P.) at Loch Farlary and may not have been related to climate change as is often supposed. Low intensity but sustained grazing pressures were more important. Throughout the mid Holocene, the frequency and intensity of burning in these open Pinus–Calluna woods were probably highly sensitive to hydrological (climatic) change. Axe marks on several trees are related to the mid to late Bronze Age, i.e., long after the trees had died.

Peat, pine stumps and people: interactions behind climate, vegetation change and human activity in wetland archaeology at Loch Farlary, Northern Scotland

First paragraph: In 1993, a peat-cutter, Bruce Field, working on the blanket peat bank he rented from the Sutherland Estate by Loch Farlary, above Golspie in Sutherland (fig 1), reported to Scottish Natural Heritage and Historic Scotland several pieces of pine wood bearing axe marks. Their depth in the peat suggested the cut marks to be prehistoric. This paper summarizes the work undertaken to understand the age and archaeological significance of this find (see also Tipping et al 2001 in press). The pine trees were initially thought to be part of a population that flourished briefly across northern Scotland in the middle of the Holocene period from c 4800 cal BP (Huntley, Daniell & Allen 1997). The subsequent collapse across northernmost Scotland of this population, the pine decline, at around 4200-4000 cal BP is unexplained: climate change has been widely assumed (Dubois & Ferguson 1985; Bridge, Haggart & Lowe 1990; Gear & Huntley 1991) but anthropogenic activity has not been disproved (Birks 1975; Bennett 1995). It was hypothesized that the Farlary find would allow for the first time the direct link between human woodland clearance and the Early Bronze Age pine decline.