414 research outputs found
Graphene as an electronic membrane
Experiments are finally revealing intricate facts about graphene which go
beyond the ideal picture of relativistic Dirac fermions in pristine two
dimensional (2D) space, two years after its first isolation. While observations
of rippling added another dimension to the richness of the physics of graphene,
scanning single electron transistor images displayed prevalent charge
inhomogeneity. The importance of understanding these non-ideal aspects cannot
be overstated both from the fundamental research interest since graphene is a
unique arena for their interplay, and from the device applications interest
since the quality control is a key to applications. We investigate the membrane
aspect of graphene and its impact on the electronic properties. We show that
curvature generates spatially varying electrochemical potential. Further we
show that the charge inhomogeneity in turn stabilizes ripple formation.Comment: 6 pages, 11 figures. Updated version with new results about the
re-hybridization of the electronic orbitals due to rippling of the graphene
sheet. The re-hybridization adds the next-to-nearest neighbor hopping effect
discussed in the previous version. New reference to recent STM experiments
that give support to our theor
Interpolatory methods for model reduction of multi-input/multi-output systems
We develop here a computationally effective approach for producing
high-quality -approximations to large scale linear
dynamical systems having multiple inputs and multiple outputs (MIMO). We extend
an approach for model reduction introduced by Flagg,
Beattie, and Gugercin for the single-input/single-output (SISO) setting, which
combined ideas originating in interpolatory -optimal model
reduction with complex Chebyshev approximation. Retaining this framework, our
approach to the MIMO problem has its principal computational cost dominated by
(sparse) linear solves, and so it can remain an effective strategy in many
large-scale settings. We are able to avoid computationally demanding
norm calculations that are normally required to monitor
progress within each optimization cycle through the use of "data-driven"
rational approximations that are built upon previously computed function
samples. Numerical examples are included that illustrate our approach. We
produce high fidelity reduced models having consistently better
performance than models produced via balanced truncation;
these models often are as good as (and occasionally better than) models
produced using optimal Hankel norm approximation as well. In all cases
considered, the method described here produces reduced models at far lower cost
than is possible with either balanced truncation or optimal Hankel norm
approximation
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