14,748 research outputs found
Convex Hulls, Oracles, and Homology
This paper presents a new algorithm for the convex hull problem, which is
based on a reduction to a combinatorial decision problem
POLYTOPE-COMPLETENESS-COMBINATORIAL, which in turn can be solved by a
simplicial homology computation. Like other convex hull algorithms, our
algorithm is polynomial (in the size of input plus output) for simplicial or
simple input. We show that the ``no''-case of
POLYTOPE-COMPLETENESS-COMBINATORIAL has a certificate that can be checked in
polynomial time (if integrity of the input is guaranteed).Comment: 11 pages, 2 figure
Two-component Bose gas in an optical lattice at single-particle filling
The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an
optical lattice with one particle per site and virtual tunneling to empty and
doubly-occupied sites. An effective Hamiltonian for this system is derived
within a continued-fraction approach. The ground state of the effective model
is studied in mean-field approximation for a modulated optical lattice. A
dimerized mean-field state gives a Mott insulator whereas the lattice without
modulations develops long-range correlated phase fluctuations due to a
Goldstone mode. This result is discussed in comparison with the superfluid and
the Mott-insulating state of a single-component hard-core Bose.Comment: 11 page
Polytopality and Cartesian products of graphs
We study the question of polytopality of graphs: when is a given graph the
graph of a polytope? We first review the known necessary conditions for a graph
to be polytopal, and we provide several families of graphs which satisfy all
these conditions, but which nonetheless are not graphs of polytopes. Our main
contribution concerns the polytopality of Cartesian products of non-polytopal
graphs. On the one hand, we show that products of simple polytopes are the only
simple polytopes whose graph is a product. On the other hand, we provide a
general method to construct (non-simple) polytopal products whose factors are
not polytopal.Comment: 21 pages, 10 figure
Integer Quantum Hall Effect for Lattice Fermions
A two-dimensional lattice model for non-interacting fermions in a magnetic
field with half a flux quantum per plaquette and levels per site is
considered. This is a model which exhibits the Integer Quantum Hall Effect
(IQHE) in the presence of disorder. It presents an alternative to the
continuous picture for the IQHE with Landau levels. The large limit can be
solved: two Hall transitions appear and there is an interpolating behavior
between the two Hall plateaux. Although this approach to the IQHE is different
from the traditional one with Landau levels because of different symmetries
(continuous for Landau levels and discrete here), some characteristic features
are reproduced. For instance, the slope of the Hall conductivity is infinite at
the transition points and the electronic states are delocalized only at the
transitions.Comment: 9 pages, Plain-Te
Several examples of neigbourly polyhedra in co-dimension 4
In the article, a series of neigbourly polyhedra is constructed. They have
vertices and are embedded in . Their (affine) Gale
diagrams in have black points that form a convex polygon.
These Gale diagams can be enumerated using 3-trees (trees with some
additional structure).
Given and , each of the constructed polyhedra in has
a fixed number of faces of dimension that contain a vertex . (This
number depends on and does not depend on the polyhedron and the vertex
).Comment: In russian, 25 pages, 16 figure
The cross helicity at the solar surface by simulations and observations
The quasilinear mean-field theory for driven MHD turbulence leads to the
result that the observed cross helicity may directly yield the
magnetic eddy diffusivity \eta_{T} of the quiet Sun. In order to model the
cross helicity at the solar surface, magnetoconvection under the presence of a
vertical large-scale magnetic field is simulated with the nonlinear MHD code
NIRVANA. The very robust result of the calculations is that \simeq 2
independent of the applied magnetic field amplitude. The
correlation coefficient for the cross helicity is about 10%. Of similar
robustness is the finding that the rms value of the magnetic perturbations
exceeds the mean-field amplitude (only) by a factor of five. The characteristic
helicity speed u_{\eta} as the ratio of the eddy diffusivity and the density
scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s
for weak fields. This value well coincides with empirical results obtained from
the data of the HINODE satellite and the Swedish 1-m Solar Telescope (SST)
providing the cross helicity component . Both simulations and
observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as
characteristic for the surface of the quiet Sun.Comment: 6 pages, 6 figure
Scanning tunneling microscopy and kinetic Monte Carlo investigation of Cesium superlattices on Ag(111)
Cesium adsorption structures on Ag(111) were characterized in a
low-temperature scanning tunneling microscopy experiment. At low coverages,
atomic resolution of individual Cs atoms is occasionally suppressed in regions
of an otherwise hexagonally ordered adsorbate film on terraces. Close to step
edges Cs atoms appear as elongated protrusions along the step edge direction.
At higher coverages, Cs superstructures with atomically resolved hexagonal
lattices are observed. Kinetic Monte Carlo simulations model the observed
adsorbate structures on a qualitative level.Comment: 8 pages, 7 figure
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