Classical and quantum properties of a 2-sphere singularity

Recently Boehmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein-Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.Comment: 10 pages, 1 figure, minor corrections, final versio

Birds, bogs and forestry: the peatlands of Caithness and Sutherland

NCC’s Upland Bird Survey had surveyed a significant area of the Flow Country between 1979 and 1986, and the 1987 report analysed and published the data from those surveys, together with those obtained from eight sites in Caithness surveyed by RSPB in 1985 using NCC methods. The results highlighted losses of up to 19% of the populations of Golden Plover, Greenshank and Dunlin in the Flow Country area as a result of then widespread and rapidly occurring afforestation of the peatlands. NCC considered that this land-use change represented “perhaps the most massive single loss of important wildlife habitat in Britain since the Second World War.” Although Birds, bogs and forestry also included summary results from other NCC surveys in Caithness and Sutherland, these studies of peatland vegetation were reported in more detail in the complementary report The Flow Country, published by NCC the following year. As a result of the case made by Birds, bogs and forestry and The Flow Country, a substantial proportion of the extent of these peatlands was designated as a Ramsar site and also classified under European nature Directives as a Special Protection Area and Special Area of Conservation

Spectral simplicity and asymptotic separation of variables

We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not. With certain additional assumptions, we show that if the families are asymptotic at first order as t tends to 0, then the generic spectral simplicity of the separable family implies that the eigenbranches of the second family are also generically one-dimensional. As an application, we prove that for the generic triangle (simplex) in Euclidean space (constant curvature space form) each eigenspace of the Laplacian is one-dimensional. We also show that for all but countably many t, the geodesic triangle in the hyperbolic plane with interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure

Engineering Analysis of Intermediate Loop and Process Heat Exchanger Requirements to Include Configuration Analysis and Materials Needs

The need to locate advanced hydrogen production facilities a finite distance away from a nuclear power source necessitates the need for an intermediate heat transport loop (IHTL). This IHTL must not only efficiently transport energy over distances up to 500 meters but must also be capable of operating at high temperatures (>850oC) for many years. High temperature, long term operation raises concerns of material strength, creep resistance and general material stability (corrosion resistance). IHTL design is currently in the initial stages. Many questions remain to be answered before intelligent design can begin. The report begins to look at some of the issues surrounding the main components of an IHTL. Specifically, a stress analysis of a compact heat exchanger design under expected operating conditions is reported. Also the results of a thermal analysis performed on two ITHL pipe configurations for different heat transport fluids are presented. The configurations consist of separate hot supply and cold return legs as well as annular design in which the hot fluid is carried in an inner pipe and the cold return fluids travels in the opposite direction in the annular space around the hot pipe. The effects of insulation configurations on pipe configuration performance are also reported. Finally, a simple analysis of two different process heat exchanger designs, one a tube in shell type and the other a compact or microchannel reactor are evaluated in light of catalyst requirements. Important insights into the critical areas of research and development are gained from these analyses, guiding the direction of future areas of research

Exact Synchronization for Finite-State Sources

We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult case of strictly asymptotic synchronization is treated in a sequel. In both cases, we find that an observer, on average, will synchronize to the source state exponentially fast and that, as a result, the average accuracy in an observer's predictions of the source output approaches its optimal level exponentially fast as well. Additionally, we show here how to analytically calculate the synchronization rate for exact epsilon-machines and provide an efficient polynomial-time algorithm to test epsilon-machines for exactness.Comment: 9 pages, 6 figures; now includes analytical calculation of the synchronization rate; updates and corrections adde

Quantum singularities in a model of f(R) Gravity

The formation of a naked singularity in a model of f(R) gravity having as source a linear electromagnetic field is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used to probe the classical timelike naked singularity developed at r=0. We prove that the spatial derivative operator of the fields fails to be essentially self-adjoint. As a result, the classical timelike naked singularity remains quantum mechanically singular when it is probed with quantum fields having different spin structures.Comment: 12 pages, final version. Accepted for publication in EPJ

Mining metrics for buried treasure

The same but different: That might describe two metrics. On the surface CLASSI may show two metrics are locally equivalent, but buried beneath one may be a wealth of further structure. This was beautifully described in a paper by M.A.H. MacCallum in 1998. Here I will illustrate the effect with two flat metrics -- one describing ordinary Minkowski spacetime and the other describing a three-parameter family of Gal'tsov-Letelier-Tod spacetimes. I will dig out the beautiful hidden classical singularity structure of the latter (a structure first noticed by Tod in 1994) and then show how quantum considerations can illuminate the riches. I will then discuss how quantum structure can help us understand classical singularities and metric parameters in a variety of exact solutions mined from the Exact Solutions book.Comment: 16 pages, no figures, minor grammatical changes, submitted to Proceedings of the Malcolm@60 Conference (London, July 2004

Transport by molecular motors in the presence of static defects

The transport by molecular motors along cytoskeletal filaments is studied theoretically in the presence of static defects. The movements of single motors are described as biased random walks along the filament as well as binding to and unbinding from the filament. Three basic types of defects are distinguished, which differ from normal filament sites only in one of the motors' transition probabilities. Both stepping defects with a reduced probability for forward steps and unbinding defects with an increased probability for motor unbinding strongly reduce the velocities and the run lengths of the motors with increasing defect density. For transport by single motors, binding defects with a reduced probability for motor binding have a relatively small effect on the transport properties. For cargo transport by motors teams, binding defects also change the effective unbinding rate of the cargo particles and are expected to have a stronger effect.Comment: 20 pages, latex, 7 figures, 1 tabl