Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation

Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It is the purpose of this paper to develop these issues and find applications in GR. The applications center around the problem of extracting interior physical properties of an asymptotically flat space-time directly from the asymptotic gravitational (and Maxwell) field itself in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center of mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular momentum conservation law with well-defined flux terms. When a Maxwell field is present the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world-line and intrinsic magnetic dipole moment.Comment: 98 pages, 6 appendices. v2: typos corrected; v3: significant changes made to results section using simpler arguments, added discussion of real structures, additional references, 2 new appendice

Which SMEs seek external support? Business characteristics, management behaviour and external influences in a contingency approach

To improve SME growth and competitiveness, governments often encourage business owner-managers to make use of external sources of support. Whether they seek this depends on the degree to which they perceive themselves to need assistance. Additionally its use can be constrained by market failures. In this paper, we model whether SME owner-managers seek information and advice from formal sources, including public and private providers. In 2011, the researchers conducted a telephone survey of 1202 SMEs (1-249 employees) in England to assess the use and non-use of external support between 2008 and 2011. Using a contingency approach, we model various influences on the use and non-use of formal support and identify those owner-managers who face more concerns but have less confidence in their capabilities. We find the demand for support, especially from private providers, is fuelled by a firm’s objective to grow and a size threshold, although this is moderated by various concerns which increase the likelihood of using public sources. The willingness to take informal advice can act as a stepping stone to using formal sources. Whilst market failures affected less than a fifth of firms, those with women directors were particularly affected as were newly founded firms

A Snapshot of J. L. Synge

A brief description is given of the life and influence on relativity theory of Professor J. L. Synge accompanied by some technical examples to illustrate his style of work

A window to quantum gravity phenomena in the emergence of the seeds of cosmic structure

Inflationary cosmology has, in the last few years,received a strong dose of support from observations. The fact that the fluctuation spectrum can be extracted from the inflationary scenario through an analysis that involves quantum field theory in curved space-time, and that it coincides with the observational data has lead to a certain complacency in the community, which prevents the critical analysis of the obscure spots in the derivation. We argue here briefly, as we have discussed in more detail elsewhere, that there is something important missing in our understanding of the origin of the seeds of Cosmic Structure, as is evidenced by the fact that in the standard accounts the inhomogeneity and anisotropy of our universe seems to emerge from an exactly homogeneous andisotropic initial state through processes that do not break those symmetries. This article gives a very brief recount of the problems faced by the arguments based on established physics. The conclusion is that we need some new physics to be able to fully address the problem. The article then exposes one avenue that has been used to address the central issue and elaborates on the degree to which, the new approach makes different predictions from the standard analyses. The approach is inspired on Penrose's proposals that Quantum Gravity might lead to a real, dynamical collapse of the wave function, a process that we argued has the properties needed to extract us from the theoretical impasse described above.Comment: 13 pages, 3 figures. To appear in DICE 2008 conference proceeding

A practical approach to achieving agility : a theory of constraints perspective

This article documents an action research (AR) project aimed at identifying the practical steps needed to become an agile manufacturer through a combination of the theory of constraints (TOC) and resource- based view (RBV) approaches in a small to medium enterprise (SME) in the Australian manufacturing sector. To date, lean production has been highlighted as a possible catalyst for creating an agile manufacturer, despite the evidence suggesting that lean manufacturing lacks the responsiveness and adaptability to effectively handle a rapidly changing market place and only works well in a stable environment. A more flexible system of production is required to fully encompass the agile characteristics needed to attain a competitive advantage. This research provides empirical evidence that the TOC perspective can be used as a practical approach for becoming an agile manufacturer. The study provides a workable approach for small firms to achieve ‘Agility’ in practice

Direct entropy determination and application to artificial spin ice

From thermodynamic origins, the concept of entropy has expanded to a range of statistical measures of uncertainty, which may still be thermodynamically significant. However, laboratory measurements of entropy continue to rely on direct measurements of heat. New technologies that can map out myriads of microscopic degrees of freedom suggest direct determination of configurational entropy by counting in systems where it is thermodynamically inaccessible, such as granular and colloidal materials, proteins and lithographically fabricated nanometre-scale arrays. Here, we demonstrate a conditional-probability technique to calculate entropy densities of translation-invariant states on lattices using limited configuration data on small clusters, and apply it to arrays of interacting nanometre-scale magnetic islands (artificial spin ice). Models for statistically disordered systems can be assessed by applying the method to relative entropy densities. For artificial spin ice, this analysis shows that nearest-neighbour correlations drive longer-range ones.Comment: 10 page

Scattering Amplitudes and BCFW Recursion in Twistor Space

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for $n$-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N^2MHV super-amplitude. We also give simple closed form formulae for the N=8 supergravity recursion and the MHV and conjugate MHV amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N^kMHV, the amplitudes are given by 2n-4 integrals in the form of Hilbert transforms of a product of $n-k-2$ purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in N=4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.Comment: v2: minor corrections + extra refs. v3: further minor corrections, extra discussion of signature issues + more ref

Value Creation from Big Data: Looking Inside the Black Box

The advent of big data is fundamentally changing the business landscape. We open the ‘black box’ of the firm to explore how firms transform big data in order to create value and why firms differ in their abilities to create value from big data. Grounded in detailed evidence from China, the world’s largest digital market, where many firms actively engage in value creation activities from big data, we identify several novel features. We find that it is not the data itself, or individual data scientists, that generate value creation opportunities. Rather, value creation occurs through the process of data management, where managers are able to democratize, contextualize, experiment and execute data insights in a timely manner. We add richness to current theory by developing a conceptual framework of value creation from big data. We also identify avenues for future research and implications for practicing managers

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

The EROS2 search for microlensing events towards the spiral arms: the complete seven season results

The EROS-2 project has been designed to search for microlensing events towards any dense stellar field. The densest parts of the Galactic spiral arms have been monitored to maximize the microlensing signal expected from the stars of the Galactic disk and bulge. 12.9 million stars have been monitored during 7 seasons towards 4 directions in the Galactic plane, away from the Galactic center. A total of 27 microlensing event candidates have been found. Estimates of the optical depths from the 22 best events are provided. A first order interpretation shows that simple Galactic models with a standard disk and an elongated bulge are in agreement with our observations. We find that the average microlensing optical depth towards the complete EROS-cataloged stars of the spiral arms is $\bar{\tau} =0.51\pm .13\times 10^{-6}$, a number that is stable when the selection criteria are moderately varied. As the EROS catalog is almost complete up to $I_C=18.5$, the optical depth estimated for the sub-sample of bright target stars with $I_C<18.5$ ($\bar{\tau}=0.39\pm >.11\times 10^{-6}$) is easier to interpret. The set of microlensing events that we have observed is consistent with a simple Galactic model. A more precise interpretation would require either a better knowledge of the distance distribution of the target stars, or a simulation based on a Galactic model. For this purpose, we define and discuss the concept of optical depth for a given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic