A new result on the Klein-Gordon equation in the background of a rotating black hole

This short paper should serve as basis for further analysis of a previously found new symmetry of the solutions of the wave equation in the gravitational field of a Kerr black hole. Its main new result is the proof of essential self-adjointness of the spatial part of a reduced normalized wave operator of the Kerr metric in a weighted L^2-space. As a consequence, it leads to a purely operator theoretic proof of the well-posedness of the initial value problem of the reduced Klein-Gordon equation in that field in that L^2-space and in this way generalizes a corresponding result of Kay (1985) in the case of the Schwarzschild black hole. It is believed that the employed methods are applicable to other separable wave equations

Approach to equilibrium in adiabatically evolving potentials

For a potential function (in one dimension) which evolves from a specified initial form $V_{i}(x)$ to a different $V_{f}(x)$ asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibeium.There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form $V(x,t)=V_{f}(x)+(V_{i}-V_{f})e^{-\lambda t}$. For a $V_{f}(x)$, which is double welled and a $V_{i}(x)$ which is simple harmonic, we show that, in particular, if the evolution is adiabatic, the results in a decrease in the Kramers time characteristics of $V_{f}(x)$. Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when $V_{i}(x)$ and $V_{f}(x)$ are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterising the potential variation and the Kramers time.Comment: This paper contains 5 page

Design and implementation of an electro-optical backplane with pluggable in-plane connectors

The design, implementation and characterisation of an electro-optical backplane and an active pluggable in-plane optical connector technology is presented. The connection architecture adopted allows line cards to be mated to and unmated from a passive electro-optical backplane with embedded polymeric waveguides. The active connectors incorporate a photonics interface operating at 850 nm and a mechanism to passively align the interface to the optical waveguides embedded in the backplane. A demonstration platform has been constructed to assess the viability of embedded electro-optical backplane technology in dense data storage systems. The demonstration platform includes four switch cards, which connect both optically and electronically to the electro-optical backplane in a chassis. These switch cards are controlled by a single board computer across a Compact PCI bus on the backplane. The electrooptical backplane is comprised of copper layers for power and low speed bus communication and one polymeric optical layer, wherein waveguides have been patterned by a direct laser writing scheme. The optical waveguide design includes densely arrayed multimode waveguides with a centre to centre pitch of 250μm between adjacent channels, multiple cascaded waveguide bends, non-orthogonal crossovers and in-plane connector interfaces. In addition, a novel passive alignment method has been employed to simplify high precision assembly of the optical receptacles on the backplane. The in-plane connector interface is based on a two lens free space coupling solution, which reduces susceptibility to contamination. Successful transfer of 10.3 Gb/s data along multiple waveguides in the electro-optical backplane has been demonstrated and characterised

Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #

Fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage

We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the non-equilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons via the Cooper-Frye equation and the subsequent hadronic cascade calculation within UrQMD proceeds to incorporate the important final state effects for a realistic freeze-out. This implementation allows to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics - ideal fluid dynamics vs. non-equilibrium transport theory - will be explored. The freeze-out and initial state parameter dependences are investigated for different observables. Furthermore, the time evolution of the baryon density and particle yields are discussed. We find that the final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The results of the different calculations for the mean transverse mass excitation function, rapidity and transverse mass spectra for different particle species at three different beam energies are discussed in the context of the available data.Comment: 20 pages, 21 figures, 1 additional figure, minor corrections and revised figures for clarity, version published in PR

Rigid thinking about deformables: do children sometimes overgeneralize the shape bias?

Young children learning English are biased to attend to the shape of solid rigid objects when learning novel names. This study seeks further understanding of the processes that support this behavior by examining a previous finding that three-year-old children are also biased to generalize novel names for objects made from deformable materials by shape, even after the materials are made salient. In two experiments, we examined the noun generalizations of 72 two-, three- and four-year- old children with rigid and deformable stimuli. Data reveal that three-year-old, but not two- or four-year-old, children generalize names for deformable things by shape, and that this behavior is not due to the syntactic context of the task. We suggest this behavior is an overgeneralization of three-year-old children’s knowledge of how rigid things are named and discuss the implications of this finding for a developmental account of the origins of the shape bias

Using sonic anemometer temperature to measure sensible heat flux in strong winds

Sonic anemometers simultaneously measure the turbulent fluctuations of vertical wind (<i>w</i>') and sonic temperature (<i>T</i><sub>s</sub>'), and are commonly used to measure sensible heat flux (<i>H</i>). Our study examines 30-min heat fluxes measured with a Campbell Scientific CSAT3 sonic anemometer above a subalpine forest. We compared <i>H</i> calculated with <i>T</i><sub>s</sub> to <i>H</i> calculated with a co-located thermocouple and found that, for horizontal wind speed (<i>U</i>) less than 8 m s<sup>−1</sup>, the agreement was around ±30 W m<sup>−2</sup>. However, for <i>U</i> ≈ 8 m s<sup>−1</sup>, the CSAT <i>H</i> had a generally positive deviation from <i>H</i> calculated with the thermocouple, reaching a maximum difference of ≈250 W m<sup>−2</sup> at <i>U</i> ≈ 18 m s<sup>−1</sup>. With version 4 of the CSAT firmware, we found significant underestimation of the speed of sound and thus <i>T</i><sub>s</sub> in high winds (due to a delayed detection of the sonic pulse), which resulted in the large CSAT heat flux errors. Although this <i>T</i><sub>s</sub> error is qualitatively similar to the well-known fundamental correction for the crosswind component, it is quantitatively different and directly related to the firmware estimation of the pulse arrival time. For a CSAT running version 3 of the firmware, there does not appear to be a significant underestimation of <i>T</i><sub>s</sub>; however, a <i>T</i><sub>s</sub> error similar to that of version 4 may occur if the CSAT is sufficiently out of calibration. An empirical correction to the CSAT heat flux that is consistent with our conceptual understanding of the <i>T</i><sub>s</sub> error is presented. Within a broader context, the surface energy balance is used to evaluate the heat flux measurements, and the usefulness of side-by-side instrument comparisons is discussed