∗\ast-SDYM fields and heavenly spaces: II. Reductions of the ∗\ast-SDYM system

Reductions of self-dual Yang-Mills (SDYM) system for $\ast$-bracket Lie algebra to the Husain-Park (HP) heavenly equation and to sl(N,{\boldmath{C}) SDYM equation are given. An example of a sequence of $su(N)$ chiral fields ($N\geq 2$) tending for $N\to\infty$ to a curved heavenly space is found.Comment: 18 page

On a low energy bound in a class of chiral field theories with solitons

A low energy bound in a class of chiral solitonic field theories related the infrared physics of the SU(N) Yang-Mills theory is established.Comment: Plain Latex, 8 pages, no figure

Stripe to spot transition in a plant root hair initiation model

A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytically in two spatial dimensions. The system has been proposed as a model of hair initiation in the epidermal cells of plant roots. Specifically the model captures the kinetics of a small G-protein ROP, which can occur in active and inactive forms, and whose activation is believed to be mediated by a gradient of the plant hormone auxin. Here the model is made more realistic with the inclusion of a transverse co-ordinate. Localised stripe-like solutions of active ROP occur for high enough total auxin concentration and lie on a complex bifurcation diagram of single and multi-pulse solutions. Transverse stability computations, confirmed by numerical simulation show that, apart from a boundary stripe, these 1D solutions typically undergo a transverse instability into spots. The spots so formed typically drift and undergo secondary instabilities such as spot replication. A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. The parameter values studied lead to a natural singularly perturbed, so-called semi-strong interaction regime. This scaling enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem. The analytical results are found to agree favourably with the numerics. Possible biological implications of the results are discussed.Comment: 28 pages, 44 figure

Type I singularities and the Phantom Menace

We consider the future dynamics of a transient phantom dominated phase of the universe in LQC and in the RS braneworld, which both have a non-standard Friedmann equation. We find that for a certain class of potentials, the Hubble parameter oscillates with simple harmonic motion in the LQC case and therefore avoids any future singularity. For more general potentials we find that damping effects eventually lead to the Hubble parameter becoming constant. On the other hand in the braneworld case we find that although the type I singularity can be avoided, the scale factor still diverges at late times.Comment: More references added. Final PRD versio

Resummed Quantum Gravity

We present the current status of the a new approach to quantum general relativity based on the exact resummation of its perturbative series as that series was formulated by Feynman. We show that the resummed theory is UV finite and we present some phenomenological applications as well.Comment: 4 pages, 1 figure; presented at ICHEP0

Electromagnetic analysis of arbitrarily shaped pinched carpets

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map a non convex region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components, and this may lead to some broadband cloaking.Comment: 6 pages, 6 figures, Current Status of Manuscript: 19Apr10 26May10-Sent on appeal;report rcvd 29Dec09 13Apr10-Ed. decision and/or ref. comments to author;response rcvd 04Dec09 21Dec09-Ed. decision and/or ref. comments to author;response rcvd 01Dec09-Transferred from PRL to PRA 18Aug09 30Nov09-Ed.decision and/or ref. comments to author;response rcvd 14Aug09 - Correspondence sent to autho

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

The development and application of audit criteria for assessing knowledge exchange plans in health research grant applications.

Background: Research funders expect evidence of end user engagement and impact plans in research proposals. Drawing upon existing frameworks, we developed audit criteria to help researchers and their institutions assess the knowledge exchange plans of health research proposals. Findings: Criteria clustered around five themes: problem definition; involvement of research users; public and patient engagement; dissemination and implementation; and planning, management and evaluation of knowledge exchange. We applied these to a sample of grant applications from one research institution in the United Kingdom to demonstrate feasibility. Conclusion: Our criteria may be useful as a tool for researcher self-assessment and for research institutions to assess the quality of knowledge exchange plans and identify areas for systematic improvement

Infall models of Class 0 protostars

We have carried out radiative transfer calculations of infalling, dusty envelopes surrounding embedded protostars to understand the observed properties of the recently identified ``Class 0'' sources. To match the far-infrared peaks in the spectral energy distributions of objects such as the prototype Class 0 source VLA 1623, pure collapse models require mass infall rates \sim10^{-4}\msunyr$^{-1}$. The radial intensity distributions predicted by such infall models are inconsistent with observations of VLA 1623 at sub-mm wavelengths, in agreement with the results of Andre et al. (1993) who found a density profile of $\rho \propto r^{-1/2}$ rather than the expected $\rho \propto r^{-3/2}$ gradient. To resolve this conflict, while still invoking infall to produce the outflow source at the center of VLA 1623, we suggest that the observed sub-mm intensity distribution is the sum of two components: an inner infall zone, plus an outer, more nearly constant-density region. This explanation of the observations requires that roughly half the total mass observed within 2000 AU radius of the source lies in a region external to the infall zone. The column densities for this external region are comparable to those found in the larger Oph A cloud within which VLA 1623 is embedded. The extreme environments of Class 0 sources lead us to suggest an alternative or additional interpretation of these objects: rather than simply concluding with Andre et al. that Class 0 objects only represent the earliest phases of protostellar collapse, and ultimately evolve into older ``Class I'' protostars, we suggest that many Class 0 sources could be the protostars of very dense regions. (Shortened)Comment: 22 pages, including 3 PostScript figures, accepted for publication in The Astrophysical Journa

Scotland's aquifers and groundwater bodies

Scotland’s groundwater is a highly valuable resource. The volume of groundwater is greater than the water found in our rivers and lochs, but is hidden from sight beneath our feet. Groundwater underpins Scotland’s private drinking water supplies and provides reliable strategic public water supply to many rural towns; it also sustains the bottled water and whisky industries and is relied upon for irrigation by many farmers. Groundwater also provides many important environmental functions, providing at least 30% of the flow in most Scottish rivers, and maintaining many precious ecosystems. Groundwater management in Scotland is delivered primarily through the River Basin Management framework. Groundwater bodies are a key component of this, defining areas of groundwater that behave in a similar way, both naturally and in response to pressures from human activity. Groundwater bodies provide a risk-based framework for prioritising action to remediate problems, and preventing new problems. Scottish groundwater bodies have undergone a major review for the second River Basin Management cycle, using the latest geological information from the British Geological Survey (BGS), and improved experience of groundwater management from the Scottish Environment Protection Agency (SEPA). A key new development is the separation of groundwater bodies into two layers: a shallow layer of superficial groundwater bodies, and a deep layer of bedrock groundwater bodies. This is important in order to help target action. Shallow groundwater bodies are more at risk from activities such as agriculture, whilst deeper bodies are more at risk from activities such as mining. This report provides a summary of the results of the review, which has been a collaborative project by BGS and SEPA. It documents the process of how the groundwater bodies and aquifers of Scotland were defined, and describes the hydrogeology of each of the main aquifers. The report can therefore be used as a technical introduction to the hydrogeology of Scotland. The two maps overleaf illustrate Scotland’s aquifers and the latest iteration of groundwater bodies as developed during this project