Standing Waves in a Non-linear 1D Lattice : Floquet Multipliers, Krein Signatures, and Stability

We construct a class of exact commensurate and incommensurate standing wave (SW) solutions in a piecewise smooth analogue of the discrete non-linear Schr\"{o}dinger (DNLS) model and present their linear stability analysis. In the case of the commensurate SW solutions the analysis reduces to the eigenvalue problem of a transfer matrix depending parametrically on the eigenfrequency. The spectrum of eigenfrequencies and the corresponding eigenmodes can thereby be determined exactly. The spatial periodicity of a commensurate SW implies that the eigenmodes are of the Bloch form, characterised by an even number of Floquet multipliers. The spectrum is made up of bands that, in general, include a number of transition points corresponding to changes in the disposition of the Floquet multipliers. The latter characterise the different band segments. An alternative characterisation of the segments is in terms of the Krein signatures associated with the eigenfrequencies. When one or more parameters characterising the SW solution is made to vary, one occasionally encounters collisions between the band-edges or the intra-band transition points and, depending on the the Krein signatures of the colliding bands or segments, the spectrum may stretch out in the complex plane, leading to the onset of instability. We elucidate the correlation between the disposition of Floquet multipliers and the Krein signatures, presenting two specific examples where the SW possesses a definite window of stability, as distinct from the SW's obtained close to the anticontinuous and linear limits of the DNLS model.Comment: 31 pages, 11 figure

Predicate Abstraction with Indexed Predicates

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International Conference on Verification, Model Checking and Abstract Interpretation (VMCAI'04), LNCS 2937, pages = 267--28

Probing the indefinite CP nature of the Higgs Boson through decay distributions in the process e+e−→ttˉΦe^+e^-\to t\bar{t}\Phi

The recently discovered scalar resonance at the LHC is now almost confirmed to be a Higgs Boson, whose CP properties are yet to be established. At the ILC with and without polarized beams, it may be possible to probe these properties at high precision. In this work, we study the possibility of probing departures from the pure CP-even case, by using the decay distributions in the process $e^+ e^- \to t \bar{t} \Phi$, with $\Phi$ mainly decaying into a $b\bar b$ pair. We have compared the case of a minimal extension of the SM case (Model I) with an additional pseudoscalar degree of freedom, with a more realistic case namely the CP-violating Two-Higgs Doublet Model (Model II) that permits a more general description of the couplings. We have considered the ILC with $\sqrt{s}=800$\,GeV and integrated luminosity of $300\, {\rm fb}^{-1}$. Our main findings are that even in the case of small departures from the CP-even case, the decay distributions are sensitive to the presence of a CP-odd component in Model II, while it is difficult to probe these departures in Model I unless the pseudoscalar component is very large. Noting that the proposed degrees of beam polarization increases the statistics, the process demonstrates the effective role of beam polarization in studies beyond the Standard Model. Further, our study shows that an indefinite CP Higgs would be a sensitive laboratory to physics beyond the SM.Comment: 14 pages using revtex, 10 figures, corresponds to version accepted for publication in Phys. Rev. D.; compared to v1, discussion extended, figure added, table added, section reorganize

Metadata & Cataloging Unit Statistics 2014-2015

Annual productivity statistics from the Metadata & Cataloging Unit of the University of Rhode Island Library for 2014-2015. Includes total number of copy-cataloged records and original catalog records created. Also includes bibliographic and item records created, modified, and deleted in the local Innovative Interfaces library system

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Annual productivity statistics from the Cataloging Unit of the University of Rhode Island Library for 1997-1998. Includes total number of copy-cataloged records and original catalog records created. Also includes bibliographic and item records created, modified, and deleted in the local Innovative Interfaces library system