Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [M. L. Glasser, J. Math. Phys. 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [M. A. Stremler, J. Math. Phys. 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation

Lattice Green functions in all dimensions

We give a systematic treatment of lattice Green functions (LGF) on the $d$-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality $d \ge 2$ for the first three lattices, and for $2 \le d \le 5$ for the hyper-fcc lattice. We show that there is a close connection between the LGF of the $d$-dimensional hypercubic lattice and that of the $(d-1)$-dimensional diamond lattice. We give constant-term formulations of LGFs for all lattices and dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the s.c., b.c.c. and diamond LGFs and some Ramanujan-type formulae for $1/\pi.$Comment: 30 page

Monitoring RXTE Observations of Markarian 348: the origin of the column density variations

We analyze 37 RXTE observations of the type 2 Seyfert galaxy Mrk348 obtained during a period of 14 months. We confirm the spectral variability previous reported by Smith et al., in the sense that thecolumn density decreases by a factor of ~3 as the count rate increases. Column density variations could possibly originate either due to the random drift of clouds within the absorption screen, or due to photoionization processes. Our modeling of the observed variations implies that the first scenario is more likely. These clouds should lie in a distance of >2 light years from the source, having a diameter of a few light days and a density of >10^7 cm^(-3), hence probably residing outside the Broad Line Region.Comment: 6 pages, 3 figures, to appear in MNRA

Supraglacial lakes on the Larsen B ice shelf, Antarctica, and at Paakitsoq, West Greenland:A Comparative Study

This is the accepted manuscript. The final version is available from Ingenta Connect at http://www.ingentaconnect.com/content/igsoc/agl/2014/00000055/00000066/art00001.Supraglacial meltwater lakes trigger ice-shelf break-up and modulate seasonal ice\ud sheet flow, and are thus agents by which warming is transmitted to the Antarctic\ud and Greenland ice sheets. To characterize supraglacial lake variability we perform a\ud comparative analysis of lake geometry and depth in two distinct regions, one on the\ud pre-collapse (2002) Larsen B Ice Shelf, and the other in the ablation zone of\ud Paakitsoq, a land-terminating region of the Greenland Ice Sheet. Compared to\ud Paakitsoq, lakes on the Larsen B Ice Shelf cover a greater proportion of surface area\ud (5.3% vs. 1%), but are shallower and more uniform in area. Other aspects of lake\ud geometry, such as eccentricity, degree of convexity (solidity) and orientation, are\ud relatively similar between the two regions. We attribute the notable difference in\ud lake density and depth between ice-shelf and grounded ice to the fact that ice shelves\ud have flatter surfaces and less distinct drainage basins. Ice shelves also possess more\ud stimuli to small-scale, localized surface elevation variability due to the various\ud structural features that yield small variations in thickness and which float at\ud different levels by Archimedes? principle.We acknowledge the support of the U.S. National Science Foundation under grant ANT-0944248

RXTE monitoring observations of Markarian 3

We present Rossi X-ray Timing Explorer, monitoring observations of the Seyfert 2 galaxy Markarian 3 spanning a 200 day period during which time the source flux varied by a factor $\sim 2$ in the 4-20 keV bandpass. In broad agreement with earlier Ginga results, the average spectrum can be represented in terms of a simple spectral model consisting of a very hard power-law continuum ($\Gamma \approx 1.1$) modified below $\sim 6$ keV by a high absorbing column ($N_H\sim 6\times 10^{23}$ \cunits) together with a high equivalent width Fe-K emission feature at 6.4 keV. The abnormally flat spectral index is probably the signature of a strong reflection component and we consider two models incorporating such emission. In the first the reflected signal suffers the same absorption as the intrinsic continuum, whereas in the second the reflection is treated as an unabsorbed spectral component. In the former case, we require a very strong reflection signal ($R ~< 3$) in order to match the data; in addition variability of both the intrinsic power-law and the reflection component is required. The unabsorbed reflection model requires a somewhat higher line-of-sight column density to the nuclear source ($\sim 10^{24}$ \cunits), but in this case the reflected signal remains constant whilst the level of the intrinsic continuum varies. The latter description is consistent with the reflection originating from the illuminated far inner wall of a molecular torus, the nearside of which screens our direct view of the central continuum source.Comment: 7 pages, submitted to the MNRA

Exact results for some Madelung type constants in the finite-size scaling theory

A general formula is obtained from which the madelung type constant: $$C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}]$$ extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters $d$ and $\nu$. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added

Non-negative data-driven mapping of structural connections with application to the neonatal brain

Mapping connections in the neonatal brain can provide insight into the crucial early stages of neurodevelopment that shape brain organisation and lay the foundations for cognition and behaviour. Diffusion MRI and tractography provide unique opportunities for such explorations, through estimation of white matter bundles and brain connectivity. Atlas-based tractography protocols, i.e. a priori defined sets of masks and logical operations in a template space, have been commonly used in the adult brain to drive such explorations. However, rapid growth and maturation of the brain during early development make it challenging to ensure correspondence and validity of such atlas-based tractography approaches in the developing brain. An alternative can be provided by data-driven methods, which do not depend on predefined regions of interest. Here, we develop a novel data-driven framework to extract white matter bundles and their associated grey matter networks from neonatal tractography data, based on non-negative matrix factorisation that is inherently suited to the non-negative nature of structural connectivity data. We also develop a non-negative dual regression framework to map group-level components to individual subjects. Using in-silico simulations, we evaluate the accuracy of our approach in extracting connectivity components and compare with an alternative data-driven method, independent component analysis. We apply non-negative matrix factorisation to whole-brain connectivity obtained from publicly available datasets from the Developing Human Connectome Project, yielding grey matter components and their corresponding white matter bundles. We assess the validity and interpretability of these components against traditional tractography results and grey matter networks obtained from resting-state fMRI in the same subjects. We subsequently use them to generate a parcellation of the neonatal cortex using data from 323 new-born babies and we assess the robustness and reproducibility of this connectivity-driven parcellation

The 2015 Chileno Valley glacial lake outburst flood, Patagonia

Glacial Lake Outburst Floods (GLOFs) have become increasingly common over the past century in response to climate change, posing risks for human activities in many mountain regions. In this paper we document and reconstruct the sequence of events and impact of a large GLOF that took place in December 2015 in the Chileno Valley, Patagonia. Hydrograph data suggests that the flood continued for around eight days with an estimated total discharge of 105.6 × 106 m3 of water. The sequence of events was as follows: (1) A large debris flow entered the lake from two steep and largely non-vegetated mountain gullies located northeast of the Chileno Glacier terminus. (2) Water displaced in the lake by the debris flow increased the discharge through the Chileno Lake outflow. (3) Lake and moraine sediments were eroded by the flood. (4) Eroded sediments were redistributed downstream by the GLOF. The post-GLOF channel at the lake outlet widened in some places by >130 m and the surface elevation of the terrain lowered by a maximum of 38.8 ± 1.5 m. Farther downstream, large amounts of entrained sediment were deposited at the head of an alluvial plain and these sediments produced an ~340 m wide fan with an average increase in surface elevation over the pre-GLOF surface of 4.6 ± 1.5 m. We estimate that around 3.5 million m3 of material was eroded from the flood-affected area whilst over 0.5 million m3 of material was deposited in the downstream GLOF fan. The large debris flow that triggered the GLOF was probably a paraglacial response to glacier recession from its Little Ice Age limits. We suggest that GLOFs will continue to occur in these settings in the future as glaciers further recede in response to global warming and produce potentially unstable lakes. Detailed studies of GLOF events are currently limited in Patagonia and the information presented here will therefore help to inform future glacial hazard assessments in this region

Smooth Paths on Three Dimensional Lattice

A particular class of random walks with a spin factor on a three dimensional cubic lattice is studied. This three dimensional random walk model is a simple generalization of random walk for the two dimensional Ising model. All critical diffusion constants and associated critical exponents are calculated. Continuum field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories are constructed near several critical points.Comment: 7 pages,NUP-A-94-