11,881 research outputs found
Symplectic-energy-momentum preserving variational integrators
The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space–time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given
Electron Interactions and Scaling Relations for Optical Excitations in Carbon Nanotubes
Recent fluorescence spectroscopy experiments on single wall carbon nanotubes
reveal substantial deviations of observed absorption and emission energies from
predictions of noninteracting models of the electronic structure. Nonetheless,
the data for nearly armchair nanotubes obey a nonlinear scaling relation as a
function the tube radius . We show that these effects can be understood in a
theory of large radius tubes, derived from the theory of two dimensional
graphene where the coulomb interaction leads to a logarithmic correction to the
electronic self energy and marginal Fermi liquid behavior. Interactions on
length scales larger than the tube circumference lead to strong self energy and
excitonic effects that compete and nearly cancel so that the observed optical
transitions are dominated by the graphene self energy effects.Comment: 4 page
Analysis of sonic boom measurements near shock wave extremities for flight near Mach 1.0 and for airplane accelerations
The analysis of the 14 low-altitude transonic flights showed that the prevailing meteorological consideration of the acoustic disturbances below the cutoff altitude during threshold Mach number flight has shown that a theoretical safe altitude appears to be valid over a wide range of meteorological conditions and provides a reasonable estimate of the airplane ground speed reduction to avoid sonic boom noise during threshold Mach number flight. Recent theoretical results for the acoustic pressure waves below the threshold Mach number caustic showed excellent agreement with observations near the caustic, but the predicted overpressure levels were significantly lower than those observed far from the caustic. The analysis of caustics produced by inadvertent low-magnitude accelerations during flight at Mach numbers slightly greater than the threshold Mach number showed that folds and associated caustics were produced by slight changes in the airplane ground speed. These caustic intensities ranged from 1 to 3 time the nominal steady, level flight intensity
Surface States of Topological Insulators
We develop an effective bulk model with a topological boundary condition to
study the surface states of topological insulators. We find that the Dirac
point energy, the band curvature and the spin texture of surface states are
crystal face-dependent. For a given face on a sphere, the Dirac point energy is
determined by the bulk physics that breaks p-h symmetry in the surface normal
direction and is tunable by surface potentials that preserve T symmetry.
Constant energy contours near the Dirac point are ellipses with spin textures
that are helical on the S/N pole, collapsed to one dimension on any side face,
and tilted out-of-plane otherwise. Our findings identify a route to engineering
the Dirac point physics on the surfaces of real materials.Comment: 4.1 pages, 2 figures and 1 tabl
Frictional Collisions Off Sharp Objects
This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact
geometries for which neither normals nor gap functions can be defined. Such situations arise
in the early stage of fragmentation when a number of angular fragments undergo complex collision
sequences before eventually scattering. Such situations precludes the application of most contact
algorithms proposed to date
Variational integrators, the Newmark scheme, and dissipative systems
Variational methods are a class of symplectic-momentum integrators for ODEs. Using
these schemes, it is shown that the classical Newmark algorithm is structure preserving in a
non-obvious way, thus explaining the observed numerical behavior. Modifications to variational
methods to include forcing and dissipation are also proposed, extending the advantages
of structure preserving integrators to non-conservative systems
Quantum Spin Hall Effect in Graphene
We study the effects of spin orbit interactions on the low energy electronic
structure of a single plane of graphene. We find that in an experimentally
accessible low temperature regime the symmetry allowed spin orbit potential
converts graphene from an ideal two dimensional semimetallic state to a quantum
spin Hall insulator. This novel electronic state of matter is gapped in the
bulk and supports the quantized transport of spin and charge in gapless edge
states that propagate at the sample boundaries. The edge states are non chiral,
but they are insensitive to disorder because their directionality is correlated
with spin. The spin and charge conductances in these edge states are calculated
and the effects of temperature, chemical potential, Rashba coupling, disorder
and symmetry breaking fields are discussed.Comment: 4 pages, published versio
Hydrogenic Spin Quantum Computing in Silicon: A Digital Approach
We suggest an architecture for quantum computing with spin-pair encoded
qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic
field and electrode-switched on and off hyperfine interaction. This digital
processing is insensitive to tuning errors and easy to model. Electron
shuttling between donors enables multi-qubit logic. These hydrogenic spin
qubits are transferable to nuclear spin-pairs, which have long coherence times,
and electron spin-pairs, which are ideally suited for measurement and
initialization. The architecture is scalable to highly parallel operation.Comment: 4 pages, 5 figures; refereed and published version with improved
introductio
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