Local availability and long-range trade: the worked stone assemblage

Inter disciplinary study of major excavation assemblage from Norse settlement site in Orkney. Combines methodological and typological developments with scientific discussion

Universal Formulae for Percolation Thresholds

A power law is postulated for both site and bond percolation thresholds. The formula writes $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are found to belong to only three universality classes. For first two classes $b=0$ for site dilution while $b=a$ for bond dilution. The last one associated to high dimensions is characterized by $b=2a-1$ for both sites and bonds. Classes are defined by a set of value for $\{p_0; \ a\}$. Deviations from available numerical estimates at $d \leq 7$ are within $\pm 0.008$ and $\pm 0.0004$ for high dimensional hypercubic expansions at $d \geq 8$. The formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include

Probabilistic Analysis of Power Network Susceptibility to GICs

As reliance on power networks has increased over the last century, the risk of damage from geomagnetically induced currents (GICs) has become a concern to utilities. The current state of the art in GIC modelling requires significant geophysical modelling and a theoretically derived network response, but has limited empirical validation. In this work, we introduce a probabilistic engineering step between the measured geomagnetic field and GICs, without needing data about the power system topology or the ground conductivity profiles. The resulting empirical ensembles are used to analyse the TVA network (south-eastern USA) in terms of peak and cumulative exposure to 5 moderate to intense geomagnetic storms. Multiple nodes are ranked according to susceptibility and the measured response of the total TVA network is further calibrated to existing extreme value models. The probabilistic engineering step presented can complement present approaches, being particularly useful for risk assessment of existing transformers and power systems.Comment: 6 pages, 7 figures, accepted for PMAPS 202

Improvement in the modelling of geomagnetically induced currents in Southern Africa

One of the consequences of the geomagnetic storms resulting from adverse space weather is the induction of geomagnetically induced currents (GICs) in power lines. The GICs that flow in a power transmission network are driven by the induced electric field at the Earth's surface. The electric field, in turn, is affected by the changing magnetic field during a magnetic storm. These GICs can cause extensive and expensive damage to transformers in the power transmission system. Understanding the behaviour of the magnetic field during a magnetic storm is a crucial step in modelling and predicting the electric field and ultimately the GICs in a power transmission network. We present a brief overview of the present status of GIC modelling in southern Africa and then discuss whether it is sufficient to use geomagnetic data from a single magnetic observatory alone to model GICs over the subcontinent. A geomagnetic interpolation method is proposed to improve the modelling of GICs in southern Africa. This improved model is one step closer to our being able to predict GICs accurately in the subcontinent, which will enable power distribution companies to take the necessary precautions to minimize possible transformer damage

Improved Bounds on the Phase Transition for the Hard-Core Model in 2-Dimensions

For the hard-core lattice gas model defined on independent sets weighted by an activity $\lambda$, we study the critical activity $\lambda_c(\mathbb{Z}^2)$ for the uniqueness/non-uniqueness threshold on the 2-dimensional integer lattice $\mathbb{Z}^2$. The conjectured value of the critical activity is approximately $3.796$. Until recently, the best lower bound followed from algorithmic results of Weitz (2006). Weitz presented an FPTAS for approximating the partition function for graphs of constant maximum degree $\Delta$ when $\lambda<\lambda_c(\mathbb{T}_\Delta)$ where $\mathbb{T}_\Delta$ is the infinite, regular tree of degree $\Delta$. His result established a certain decay of correlations property called strong spatial mixing (SSM) on $\mathbb{Z}^2$ by proving that SSM holds on its self-avoiding walk tree $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ where $\sigma=(\sigma_v)_{v\in \mathbb{Z}^2}$ and $\sigma_v$ is an ordering on the neighbors of vertex $v$. As a consequence he obtained that $\lambda_c(\mathbb{Z}^2)\geq\lambda_c( \mathbb{T}_4) = 1.675$. Restrepo et al. (2011) improved Weitz's approach for the particular case of $\mathbb{Z}^2$ and obtained that $\lambda_c(\mathbb{Z}^2)>2.388$. In this paper, we establish an upper bound for this approach, by showing that, for all $\sigma$, SSM does not hold on $T_{\mathrm{saw}}^\sigma(\mathbb{Z}^2)$ when $\lambda>3.4$. We also present a refinement of the approach of Restrepo et al. which improves the lower bound to $\lambda_c(\mathbb{Z}^2)>2.48$.Comment: 19 pages, 1 figure. Polished proofs and examples compared to earlier versio