Positivity in Lorentzian Barrett-Crane Models of Quantum Gravity

The Barrett-Crane models of Lorentzian quantum gravity are a family of spin foam models based on the Lorentz group. We show that for various choices of edge and face amplitudes, including the Perez-Rovelli normalization, the amplitude for every triangulated closed 4-manifold is a non-negative real number. Roughly speaking, this means that if one sums over triangulations, there is no interference between the different triangulations. We prove non-negativity by transforming the model into a ``dual variables'' formulation in which the amplitude for a given triangulation is expressed as an integral over three copies of hyperbolic space for each tetrahedron. Then we prove that, expressed in this way, the integrand is non-negative. In addition to implying that the amplitude is non-negative, the non-negativity of the integrand is highly significant from the point of view of numerical computations, as it allows statistical methods such as the Metropolis algorithm to be used for efficient computation of expectation values of observables.Comment: 13 page

Finiteness and Dual Variables for Lorentzian Spin Foam Models

We describe here some new results concerning the Lorentzian Barrett-Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated to all non-degenerate triangulations of 4-manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable re-factoring and re-ordering of integration, through which a large set of variables can be eliminated. The resulting formulation can be interpreted as a ``dual variables'' model that uses hyperboloid variables associated to spin foam edges in place of representation variables associated to faces. We outline how this method may also be useful for numerical computations, which have so far proven to be very challenging for Lorentzian spin foam models.Comment: 15 pages, 1 figur

Printing technologies for current collectors for dye-sensitized solar cells.

This project was in collaboration with TATA Steel Colors to investigate printing technologies for current collection grids in dye-sensitized solar cells (DSCs) for high volume, large area production. Current collecting grids are important to reduce resistive losses and maintain performance. The aims of the thesis were to; investigate different high volume printing technologies as an alternative to screen printing for depositing current collector grids, develop a fast drying and sintering method for improved manufacturing speed, and to develop monitoring technology for quality control to optimize production. Flexographic printing was identified as an alternative to screen printing. Flexible DSCs produced with a flexographic printed current collecting grid were found to have an efficiency drop of -33%, when compared cells built with screen printed current collecting grids. However, the amount of silver printed using flexography saw a reduction of -95% offering a significant reduction in materials cost. A barrier to high volume roll-to-roll printing of conducting inks is the time required for drying and for nanoparticle inks sintering. Nanoparticle inks require a secondary sintering phase to form a highly conductive metallic film. Near infrared (NIR) radiation has been shown to be a rapid method for drying and sintering a silver nanoparticle ink in just 1 second, compared to 10 minutes in an oven, offering a significant reduction in process time. Polymer thick-film inks with microparticles require thermal treatment to remove the solvent to facilitate particle contact which allows the ink to become conductive and NIR drying was found not to be effective. Quality control of the sintering process of silver nanoparticle inks is carried out offline. A method which could be implemented inline has been developed using colorimetry to correlate the colour of a silver nanoparticle ink film to its electrical performance using CIELAB colour coordinates. It is a fast, non-contact method. The technique works on the principle of light scattering through nanoparticles

Genetics, Geography, and Satellites: From Genes to Space

No abstract availabl

3-D seismic exploration for the Victorio Peak treasure

In January of 1994, we conducted an extensive seismic experiment to find caverns under Victorio Peak, a bioherm reef structure located approximately 80 miles northeast of Las Cruces, New Mexico. Within Victorio Peak there is reputed to be an extensive network of caverns, tunnels and fissures that contain a large and varied treasure consisting of gold bars, Spanish armor, jewels, coins, and human skeletons. We used an array of seismic sources that included a sledgehammer on the surface of the mountain, a sledgehammer impacting on the walls of two deep fissures within the mountain, as well as blasting caps located in boreholes drilled into the mountain. Approximately 2,000 source positions were recorded by 120 receiver channels consisting of geophones cemented into fissure walls and hydrophones deployed in a deep horizontal borehole drilled at the base of the mountain. The data analysis consisted of measuring reduced traveltime and amplitude of the direct arrival and isolating those source/receiver pairs that exhibited anomalously large direct arrival traveltimes and/or low amplitudes. We have currently identified and located a major amplitude anomaly under the peak that will be drilled and explored during the summer of 1994

Coupling of spacetime atoms and spin foam renormalisation from group field theory

We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an additional coupling between the normals to tetrahedra, as defined in different 4-simplices that share them, is present. This is realised through an extension of the usual field over the group manifold to a five argument one. We define a specific model in which this coupling is parametrised by an additional real parameter that allows to tune the degree of locality of the resulting model, interpolating between the usual Barrett-Crane model and a flat BF-type one. Moreover, we define a further extension of the group field theory formalism in which the coupling parameter enters as a new variable of the field, and the action presents derivative terms that lead to modified classical equations of motion. Finally, we discuss the issue of renormalisation of spin foam models, and how the new coupled model can be of help regarding this.Comment: RevTeX, 18 pages, no figure

Dual Computations of Non-abelian Yang-Mills on the Lattice

In the past several decades there have been a number of proposals for computing with dual forms of non-abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet non-trivial case in which the gauge group is non-abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.Comment: v1: 18 pages, 7 figures, v2: Many changes to appendix, minor changes throughout, references and figures added, v3: minor corrections, 22 page

A perspective on circular innovation: Dynamics, strategies, and implications

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this record This Letter considers the multifaceted realm of circular innovation, shedding light on its dynamics, strategic implications, and broader significance for sustainable development. By evaluating existing research and exploring examples across sectors, this work contributes to a deeper understanding of the role of circular innovation in transforming industries, economies, and societies. Although the topic has received increased interest in recent years, we find that there are notable gaps. While significant attention has been given to initial adoption and expansion, there is a lack of understanding regarding the enduring impacts on businesses and society. Further research addressing these gaps can enrich our understanding of the challenges and opportunities in this evolving field.University of Exete

Exploring the circular economy through coatings in transport

This is the final version. Available on open access from Elsevier via the DOI in this recordCoatings are widely used in a range of aesthetic, protective and durable applications, often leading to extension of the in-service period of many components. There is sizable demand for coatings in the transport sector across road, rail, marine and air. However, the issue of materials circularity with consideration of their surface treatment is an under researched and often overlooked area. The aim of this paper is to explore challenges and enabling factors that can catalyse industrial growth of a new material, technology, or process by investigating coatings within the transport sector. We do this by studying six new or novel approaches that have garnered significant research interest in the last decade, set against system-level drivers and enablers of circularity. Our findings highlight the complications, assumptions and benefits of a circular transition. We conclude that policy and regulation play a key role in supporting or hindering the transition, and further consideration of material ‘lock-in’ is required to understand how materials can be phased out from a design standpoint.Engineering and Physical Sciences Research Council (EPSRC