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

The REBOA window: a cadaveric study delineating the optimum site for austere cannulation of the femoral artery for resuscitative endovascular balloon occlusion of the aorta

Introduction: Haemorrhage is the major cause of early mortality following traumatic injury. Patients suffering from non-compressible torso haemorrhage are more likely to suffer early death. Resuscitative Endovascular Balloon Occlusion of the Aorta (REBOA) can be effective in initial resuscitation; however, establishing swift arterial access is challenging, particularly in a severe shock. This is made more difficult by anatomical variability of the femoral vessels. Methods: The femoral vessels were characterised in 81 cadaveric lower limbs, measuring specifically the distance from the inferior border of the inguinal ligament to the distal part of the origin of the profunda femoris artery (PFA), and from the distal part of the origin of the PFA to where the femoral vein lies posterior to and is completely overlapped by the femoral artery. Results: The femoral vein lay deep to the femoral artery at a mean distance of 105 mm from the inferior border of the inguinal ligament. The PFA arose from the femoral artery at a mean distance of 51.1 mm from the inguinal ligament. From the results, it is predicted that the PFA originates from the common femoral artery approximately 24 mm from the inguinal ligament, and the femoral vein is completely overlapped by the femoral artery by 67.7 mm distal from the inguinal ligament, in 95% of subjects. Conclusions: Based on the results, proposed is an ‘optimal access window’ of up to 24 mm inferior to the inguinal ligament for common femoral arterial catheterisation for pre-hospital REBOA, or more simply within one finger breadth

Bethe approximation for self-interacting lattice trees

In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for instance, in the enumeration of spanning trees. Moreover, the expressions we obtain for the asymptotic number of spanning trees and lattice trees on a graph coincide with analogous expressions derived through different approaches. We study the phase diagram of lattice trees with nearest-neighbour attraction and branching energies. We find a collapse transition at a tricritical theta point, which separates an expanded phase from a compact phase. We compare our results for the theta transition in two and three dimensions with available numerical estimates.Comment: 10 pages, 3 figures, to be published in Europhysics Letter

Double Parton Scattering Singularity in One-Loop Integrals

We present a detailed study of the double parton scattering (DPS) singularity, which is a specific type of Landau singularity that can occur in certain one-loop graphs in theories with massless particles. A simple formula for the DPS singular part of a four-point diagram with arbitrary internal/external particles is derived in terms of the transverse momentum integral of a product of light cone wavefunctions with tree-level matrix elements. This is used to reproduce and explain some results for DPS singularities in box integrals that have been obtained using traditional loop integration techniques. The formula can be straightforwardly generalised to calculate the DPS singularity in loops with an arbitrary number of external particles. We use the generalised version to explain why the specific MHV and NMHV six-photon amplitudes often studied by the NLO multileg community are not divergent at the DPS singular point, and point out that whilst all NMHV amplitudes are always finite, certain MHV amplitudes do contain a DPS divergence. It is shown that our framework for calculating DPS divergences in loop diagrams is entirely consistent with the `two-parton GPD' framework of Diehl and Schafer for calculating proton-proton DPS cross sections, but is inconsistent with the `double PDF' framework of Snigirev.Comment: 29 pages, 8 figures. Minor corrections and clarifications added. Version accepted for publication in JHE

Effective Crystalline Electric Field Potential in a j-j Coupling Scheme

We propose an effective model on the basis of a $j$-$j$ coupling scheme to describe local $f$-electron states for realistic values of Coulomb interaction $U$ and spin-orbit coupling $\lambda$, for future development of microscopic theory of magnetism and superconductivity in $f^n$-electron systems, where $n$ is the number of local $f$ electrons. The effective model is systematically constructed by including the effect of a crystalline electric field (CEF) potential in the perturbation expansion in terms of $1/\lambda$. In this paper, we collect all the terms up to the first order of $1/\lambda$. Solving the effective model, we show the results of the CEF states for each case of $n$=2$\sim$5 with $O_{\rm h}$ symmetry in comparison with those of the Stevens Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF energy levels in an intermediate coupling region with $\lambda/U$ in the order of 0.1 corresponding to actual $f$-electron materials between the $LS$ and $j$-$j$ coupling schemes. Note that the relevant energy scale of $U$ is the Hund's rule interaction. It is found that the CEF energy levels in the intermediate coupling region can be quantitatively reproduced by our modified $j$-$j$ coupling scheme, when we correctly take into account the corrections in the order of $1/\lambda$ in addition to the CEF terms and Coulomb interactions which remain in the limit of $\lambda$=$\infty$. As an application of the modified $j$-$j$ coupling scheme, we discuss the CEF energy levels of filled skutterudites with $T_{\rm h}$ symmetry.Comment: 12 pages, 7 figures. Typeset with jpsj2.cl