Reduction of Second-Order Network Systems with Structure Preservation

This paper proposes a general framework for structure-preserving model reduction of a secondorder network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual states, and the dissimilarities of vertices are quantified by the H2-norms of the transfer function discrepancies. A greedy hierarchical clustering algorithm is proposed to place those vertices with similar dynamics into same clusters. Then, the reduced-order model is generated by the Petrov-Galerkin method, where the projection is formed by the characteristic matrix of the resulting network clustering. It is shown that the simplified system preserves an interconnection structure, i.e., it can be again interpreted as a second-order system evolving over a reduced graph. Furthermore, this paper generalizes the definition of network controllability Gramian to second-order network systems. Based on it, we develop an efficient method to compute H2-norms and derive the approximation error between the full-order and reduced-order models. Finally, the approach is illustrated by the example of a small-world network

Optimization of a Langmuir-Taylor detector for lithium

This paper describes the construction and optimization of a Langmuir-Taylor detector for lithium, using a rhenium ribbon. The absolute detection probability of this very sensitive detector is measured and the dependence of this probability with oxygen pressure and surface temperature is studied. Sources of background signal and their minimization are also discussed in details. And a comparison between our data concerning the response time of the detector and literature values is given. A theoretical analysis has been made: this analysis supports the validity of the Saha-Langmuir law to relate the ionization probability to the work function. Finally, the rapid variations of the work function with oxygen pressure and temperature are explained by a chemical equilibrium model.Comment: 11 pages, 7 figures, to appear in Rev. Sci. Instru

Krasovskii's Passivity

In this paper we introduce a new notion of passivity which we call Krasovskii's passivity and provide a sufficient condition for a system to be Krasovskii's passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii's passive. Moreover, we provide a new interconnection based control technique based on Krasovskii's passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit

Heterodyne interferometer with unequal path lengths

Laser interferometry is an extensively used diagnostic for plasma experiments. Existing plasma interferometers are designed on the presumption that the scene and reference beam path lengths have to be equal, a requirement that is costly in both the number of optical components and the alignment complexity. It is shown here that having equal path lengths is not necessary - instead what is required is that the path length difference be an even multiple of the laser cavity length. This assertion has been verified in a heterodyne laser interferometer that measures typical line-average densities of $\sim 10^{21}/\textrm{m}^2$ with an error of $\sim 10^{19}/\textrm{m}^2$.Comment: 15 pages, 9 figures, to be published in Rev. Sci. Instrum. 77 (2006

C.S. Lewis: The Public Poet

Contends that Lewis’s distinction between Milton the private man and epic, or public, poet can be applied to Lewis himself. “The public character and convention of poetry interested [Lewis] most of all,” which put him out of step with the poetry of his time, with its focus on private imagery

Dispersive Gap Mode of Phonons in Anisotropic Superconductors

We estimate the effect of the superconducting gap anisotropy in the dispersive gap mode of phonons, which is observed by the neutron scattering on borocarbide superconductors. We numerically analyze the phonon spectrum considering the electron-phonon coupling, and examine contributions coming from the gap suppression and the sign change of the pairing function on the Fermi surface. When the sign of the pairing function is changed by the nesting translation, the gap mode does not appear. We also discuss the suppression of the phonon softening of the Kohn anomaly due to the onset of superconductivity. We demonstrate that observation of the gap dispersive mode is useful for sorting out the underlying superconducting pairing function.Comment: 7 pages, 12 figures, to be published in J. Phys. Soc. Jp

The Impact of Charles Williams\u27 Death on C.S. Lewis

Recounts the beginnings of the friendship of Lewis and Williams and Williams’s later association with the Inklings until his death following complications from surgery in May 1945. Discusses the effect of his death on C.S. Lewis’s thoughts about mortality and reprints his poem “On the Death of Charles Williams.

Microstructure and superconducting properties of hot isostatically pressed MgB2

Bulk samples of MgB2 have been formed by hot isostatic pressing (HIPping) of commercial powder at 100MPa and 950=B0C. The resulting material is 100% dense with a sharp superconducting transition at 37.5K. Microstructural studies have indicated the presence of small amounts of second phases within the material, namely MgO and B rich compositions, probably MgB4. Magnetisation measurements performed at 20K have revealed values of Jc=1.3 x 106A/cm2 at zero field, and 9.3 x 105A/cm2 at 1T. Magneto optical (MO) studies have shown direct evidence for the superconducting homogeneity and strong intergranular current flow in the material.Comment: 3 pages, 6 figures, text updated, new references included and discussed. Submitted to Superconductor Science and Technolog