Allometry and growth of eight tree taxa in United Kingdom woodlands.

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0As part of a project to develop predictive ecosystem models of United Kingdom woodlands we have collated data from two United Kingdom woodlands - Wytham Woods and Alice Holt. Here we present data from 582 individual trees of eight taxa in the form of summary variables relating to the allometric relationships between trunk diameter, height, crown height, crown radius and trunk radial growth rate to the tree's light environment and diameter at breast height. In addition the raw data files containing the variables from which the summary data were obtained. Large sample sizes with longitudinal data spanning 22 years make these datasets useful for future studies concerned with the way trees change in size and shape over their life-span

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrodinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, asymptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt & Wattis, J Phys A, 39, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.Comment: 29 pages, 14 Figure

Leading quantum gravitational corrections to QED

We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged spin-1/2 fermions in the combined theory of general relativity and QED. The coupled Dirac-Einstein system is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the non-analytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two massive fermions with electric charge.Comment: 14 pages, 29 figures, format RevTex

Spontaneous jumping, bouncing and trampolining of hydrogel drops on a heated plate

Drops of liquid on a hot surface can exhibit fascinating behaviour such as the Leidenfrost effect in which drops hover on a vapour layer. Here Pham et al. show that when hydrogel drops are placed on a rapidly heated plate they bounce to increasing heights even if they were initially at rest

SciKit-SurgeryGlenoid, an Open Source Toolkit for Glenoid Version Measurement

Correct understanding of the geometry of the glenoid (the socket of the shoulder joint) is key to successful planning of shoulder replacement surgery. This surgery typically involves placing an implant in the shoulder joint to restore joint function. The most relevant geometry is the glenoid version, which is the angular orientation of the glenoid surface relative to the long axis of the scapula in the axial plane. However, measuring the glenoid version is not straightforward and there are multiple measurement methods in the literature and used in commercial planning software. In this paper we introduce SciKit-SurgeryGlenoid, an open source toolkit for the measurement of glenoid version. SciKit-SurgeryGlenoid contains implementations of the 4 most frequently used glenoid version measurement algorithms enabling easy and unbiased comparison of the different techniques. We present the results of using the software on 10 sets of pre-operative CT scans taken from patients who have subsequently undergone shoulder replacement surgery. We further compare these results with those obtained from a commercial implant planning software. SciKit-SurgeryGlenoid currently requires manual segmentation of the relevant anatomical features for each method. Future work will look at automating the segmentation process to build an automatic and repeatable pipeline from CT or radiograph to quantitative glenoid version measurement

Cylindrical chains of water drops condensing on microstructured lubricant-infused surfaces

We studied the condensation of water drops on a micro-structured lubricant-infused surfaces. Hierarchical micro-prism surfaces were fabricated by soft imprinting with wet TiO2 nanoparticle paste. After hydrophobization, the patterned surfaces were infused with silicone oil as a lubricant. When cooling at high humidity (over 80%), water drops nucleate and start growing on the surface. Once they have reached a certain size, the drops at neighboring channels of the micro-prisms attract each other and spontaneously form cylindrical chains. These chains of drops align perpendicular to the prism array. The morphology and the length-to-width ratio of the chains of drops depend on the thickness of the lubricant layer. This new concept of water drop alignment on lubricant-infused surfaces offers a new route for pattern formation with condensed drops.N