3,304 research outputs found
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
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
, with mainly decaying into a
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
\,GeV and integrated luminosity of . 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
Cataloging Unit Statistics 2011-2012
Annual productivity statistics from the Cataloging Unit of the University of Rhode Island Library for 2011-2012. 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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