Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices

We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse matrices, each of dimension ~ 3^m, where m is the number of lattice spacings across the strip. As a specific application, we obtain the large-q series of the bulk, surface and corner free energies of the chromatic polynomial. This extends the existing series for the square lattice by 32 terms, to order q^{-79}. On the triangular lattice, we verify Baxter's analytical expression for the bulk free energy (to order q^{-40}), and we are able to conjecture exact product formulae for the surface and corner free energies.Comment: 17 pages. Version 2: added 4 further term to the serie

Foundation and empire : a critique of Hardt and Negri

In this article, Thompson complements recent critiques of Hardt and Negri's Empire (see Finn Bowring in Capital and Class, no. 83) using the tools of labour process theory to critique the political economy of Empire, and to note its unfortunate similarities to conventional theories of the knowledge economy

Series studies of the Potts model. I: The simple cubic Ising model

The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising ($q=2$) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to $u^{26}$ from $u^{20}$. The high-temperature series for the zero-field partition function is extended from $v^{18}$ to $v^{22}$. Subsequent analysis gives critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24 page

Low Temperature Expansions for Potts Models

On simple cubic lattices, we compute low temperature series expansions for the energy, magnetization and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds respectively, and the eight-state Potts model in D=2 to 25 excited bonds. We use a recursive procedure which enumerates states explicitly. We analyze the series using Dlog Pade analysis and inhomogeneous differential approximants.Comment: (17 pages + 8 figures

Kondo Effect in a Metal with Correlated Conduction Electrons: Diagrammatic Approach

We study the low-temperature behavior of a magnetic impurity which is weakly coupled to correlated conduction electrons. To account for conduction electron interactions a diagrammatic approach in the frame of the 1/N expansion is developed. The method allows us to study various consequences of the conduction electron correlations for the ground state and the low-energy excitations. We analyse the characteristic energy scale in the limit of weak conduction electron interactions. Results are reported for static properties (impurity valence, charge susceptibility, magnetic susceptibility, and specific heat) in the low-temperature limit.Comment: 16 pages, 9 figure

Flood magnitude-frequency and lithologic control on bedrock river incision in post-orogenic terrain

Mixed bedrock-alluvial rivers - bedrock channels lined with a discontinuous alluvial cover - are key agents in the shaping of mountain belt topography by bedrock fluvial incision. Whereas much research focuses upon the erosional dynamics of such rivers in the context of rapidly uplifting orogenic landscapes, the present study investigates river incision processes in a post-orogenic (cratonic) landscape undergoing extremely low rates of incision (> 5 m/Ma). River incision processes are examined as a function of substrate lithology and the magnitude and frequency of formative flows along Sandy Creek gorge, a mixed bedrock-alluvial stream in arid SE-central Australia. Incision is focused along a bedrock channel with a partial alluvial cover arranged into riffle-pool macrobedforms that reflect interactions between rock structure and large-flood hydraulics. Variations in channel width and gradient determine longitudinal trends in mean shear stress (τb) and therefore also patterns of sediment transport and deposition. A steep and narrow, non-propagating knickzone (with 5% alluvial cover) coincides with a resistant quartzite unit that subdivides the gorge into three reaches according to different rock erodibility and channel morphology. The three reaches also separate distinct erosional styles: bedrock plucking (i.e. detachment-limited erosion) prevails along the knickzone, whereas along the upper and lower gorge rock incision is dependent upon large formative floods exceeding critical erosion thresholds (τc) for coarse boulder deposits that line 70% of the channel thalweg (i.e. transport-limited erosion). The mobility of coarse bed materials (up to 2 m diameter) during late Holocene palaeofloods of known magnitude and age is evaluated using step-backwater flow modelling in conjunction with two selective entrainment equations. A new approach for quantifying the formative flood magnitude in mixed bedrock-alluvial rivers is described here based on the mobility of a key coarse fraction of the bed materials; in this case the d84 size fraction. A 350 m3/s formative flood fully mobilises the coarse alluvial cover with τb200-300 N/m2 across the upper and lower gorge riffles, peaking over 500 N/m2 in the knickzone. Such floods have an annual exceedance probability much less than 10- 2 and possibly as low as 10- 3. The role of coarse alluvial cover in the gorge is discussed at two scales: (1) modulation of bedrock exposure at the reach-scale, coupled with adjustment to channel width and gradient, accommodates uniform incision across rocks of different erodibility in steady-state fashion; and (2) at the sub-reach scale where coarse boulder deposits (corresponding to <i>τ</i><sub>b</sub> minima) cap topographic convexities in the rock floor, thereby restricting bedrock incision to rare large floods. While recent studies postulate that decreasing uplift rates during post-orogenic topographic decay might drive a shift to transport-limited conditions in river networks, observations here and elsewhere in post-orogenic settings suggest, to the contrary, that extremely low erosion rates are maintained with substantial bedrock channel exposure. Although bed material mobility is known to be rate-limiting for bedrock river incision under low sediment flux conditions, exactly how a partial alluvial cover might be spatially distributed to either optimise or impede the rate of bedrock incision is open to speculation. Observations here suggest that the small volume of very stable bed materials lining Sandy Creek gorge is distributed so as to minimise the rate of bedrock fluvial incision over time

Yours ever (well, maybe): Studies and signposts in letter writing

Electronic mail and other digital communications technologies seemingly threaten to end the era of handwritten and typed letters, now affectionately seen as part of snail mail. In this essay, I analyze a group of popular and scholarly studies about letter writing-including examples of pundits critiquing the use of e-mail, etiquette manuals advising why the handwritten letter still possesses value, historians and literary scholars studying the role of letters in the past and what it tells us about our present attitudes about digital communications technologies, and futurists predicting how we will function as personal archivists maintaining every document including e-mail. These are useful guideposts for archivists, providing both a sense of the present and the past in the role, value and nature of letters and their successors. They also provide insights into how such documents should be studied, expanding our gaze beyond the particular letters, to the tools used to create them and the traditions dictating their form and function. We also can discern a role for archivists, both for contributing to the literature about documents and in using these studies and commentaries, suggesting not a new disciplinary realm but opportunities for new interdisciplinary work. Examining a documentary form makes us more sensitive to both the innovations and traditions as it shifts from the analog to the digital; we can learn not to be caught up in hysteria or nostalgia about one form over another and archivists can learn about what they might expect in their labors to document society and its institutions. At one time, paper was part of an innovative technology, with roles very similar to the Internet and e-mail today. It may be that the shifts are far less revolutionary than is often assumed. Reading such works also suggests, finally, that archivists ought to rethink how they view their own knowledge and how it is constructed and used. © 2010 Springer Science+Business Media B.V

Landscape science: a Russian geographical tradition

The Russian geographical tradition of landscape science (landshaftovedenie) is analyzed with particular reference to its initiator, Lev Semenovich Berg (1876-1950). The differences between prevailing Russian and Western concepts of landscape in geography are discussed, and their common origins in German geographical thought in the late nineteenth and early twentieth centuries are delineated. It is argued that the principal differences are accounted for by a number of factors, of which Russia's own distinctive tradition in environmental science deriving from the work of V. V. Dokuchaev (1846-1903), the activities of certain key individuals (such as Berg and C. O. Sauer), and the very different social and political circumstances in different parts of the world appear to be the most significant. At the same time it is noted that neither in Russia nor in the West have geographers succeeded in specifying an agreed and unproblematic understanding of landscape, or more broadly in promoting a common geographical conception of human-environment relationships. In light of such uncertainties, the latter part of the article argues for closer international links between the variant landscape traditions in geography as an important contribution to the quest for sustainability

The Occupational Wellbeing of People Experiencing Homelessness

This paper reports findings of a study that utilised an occupational perspective to explore how wellbeing was achieved and sustained by the occupations of people experiencing homelessness in Australia. Thirty three in-depth qualitative interviews were conducted with homeless individuals in a regional city in Australia. Data from the interviews were thematically analysed to understand the relationship between wellbeing, as defined by the individual, and the occupations engaged in by people experiencing homelessness. The findings are reported here as three collective narratives that illustrate the experiences of diverse groups within the homelessness population explored in this study. The study demonstrates how occupations go beyond the individual experience and choice; to explore the social and cultural value of occupations as a means to wellbeing. The findings are discussed in relation to three key themes that emerged from the study: survival, self-identity and social connectedness. These three interconnected concepts complement the existing occupational science literature, and offer a preliminary framework for understanding and improving wellbeing for disadvantaged and marginalised people where occupations are restricted by societal forces. The findings support the urgent need to redirect services to support occupational opportunities that are socially and culturally valued and enhance survival, self-identity and connectedness of homeless people