18,656 research outputs found
Many projectively unique polytopes
We construct an infinite family of 4-polytopes whose realization spaces have
dimension smaller or equal to 96. This in particular settles a problem going
back to Legendre and Steinitz: whether and how the dimension of the realization
space of a polytope is determined/bounded by its f-vector.
From this, we derive an infinite family of combinatorially distinct
69-dimensional polytopes whose realization is unique up to projective
transformation. This answers a problem posed by Perles and Shephard in the
sixties. Moreover, our methods naturally lead to several interesting classes of
projectively unique polytopes, among them projectively unique polytopes
inscribed to the sphere.
The proofs rely on a novel construction technique for polytopes based on
solving Cauchy problems for discrete conjugate nets in S^d, a new
Alexandrov--van Heijenoort Theorem for manifolds with boundary and a
generalization of Lawrence's extension technique for point configurations.Comment: 44 pages, 18 figures; to appear in Invent. mat
Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length
Electrons on a square lattice with half a flux quantum per plaquette are
considered. An effective description for the current loops is given by a
two-dimensional Dirac theory with random mass. It is shown that the
conductivity and the localization length can be calculated from a product of
Dirac Green's functions with the {\it same} frequency. This implies that the
delocalization of electrons in a magnetic field is due to a critical point in a
phase with a spontaneously broken discrete symmetry. The estimation of the
localization length is performed for a generalized model with fermion
levels using a --expansion and the Schwarz inequality. An argument for the
existence of two Hall transition points is given in terms of percolation
theory.Comment: 10 pages, RevTeX, no figure
Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions
We consider a disordered d--wave superconductor in two dimensions. Recently,
we have shown in an exact calculation that for a lattice model with a
Lorentzian distributed random chemical potential the quasiparticle density of
states at the Fermi level is nonzero. As the exact result holds only for the
special choice of the Lorentzian, we employ different methods to show that for
a large class of distributions, including the Gaussian distribution, one can
establish a nonzero lower bound for the Fermi level density of states. The fact
that the tails of the distributions are unimportant in deriving the lower bound
shows that the exact result obtained before is generic.Comment: 15 preprint pages, no figures, submitted to PR
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
Piloting Mobile Mixed Reality to Enhance Building Information Modelling Delivery in Construction Education
Laser-only adaptive optics achieves significant image quality gains compared to seeing-limited observations over the entire sky
Adaptive optics laser guide star systems perform atmospheric correction of
stellar wavefronts in two parts: stellar tip-tilt and high-spatial-order
laser-correction. The requirement of a sufficiently bright guide star in the
field-of-view to correct tip-tilt limits sky coverage. Here we show an
improvement to effective seeing without the need for nearby bright stars,
enabling full sky coverage by performing only laser-assisted wavefront
correction. We used Robo-AO, the first robotic AO system, to comprehensively
demonstrate this laser-only correction. We analyze observations from four years
of efficient robotic operation covering 15,000 targets and 42,000 observations,
each realizing different seeing conditions. Using an autoguider (or a
post-processing software equivalent) and the laser to improve effective seeing
independent of the brightness of a target, Robo-AO observations show a 39+/-19%
improvement to effective FWHM, without any tip-tilt correction. We also
demonstrate that 50% encircled-energy performance without tip-tilt correction
remains comparable to diffraction-limited, standard Robo-AO performance.
Faint-target science programs primarily limited by 50% encircled-energy (e.g.
those employing integral field spectrographs placed behind the AO system) may
see significant benefits to sky coverage from employing laser-only AO.Comment: Accepted for publication in The Astronomical Journal. 7 pages, 6
figure
Investigation into the redox behavior of bis(pentamethylcyclopentadienyl)(.mu.-.eta.1-disulfide)(.mu.-.eta.2-disulfide)diiron: an unexpected reversible .eta.1 .dblharw. .eta.2 rearrangement of a disulfur bridge
Equivalence of domains for hyperbolic Hubbard-Stratonovich transformations
We settle a long standing issue concerning the traditional derivation of
non-compact non-linear sigma models in the theory of disordered electron
systems: the hyperbolic Hubbard-Stratonovich (HS) transformation of
Pruisken-Schaefer type. Only recently the validity of such transformations was
proved in the case of U(p,q) (non-compact unitary) and O(p,q) (non-compact
orthogonal) symmetry. In this article we give a proof for general non-compact
symmetry groups. Moreover we show that the Pruisken-Schaefer type
transformations are related to other variants of the HS transformation by
deformation of the domain of integration. In particular we clarify the origin
of surprising sign factors which were recently discovered in the case of
orthogonal symmetry.Comment: 30 pages, 3 figure
A new electromagnetic mode in graphene
A new, weakly damped, {\em transverse} electromagnetic mode is predicted in
graphene. The mode frequency lies in the window
, where is the chemical potential, and can be
tuned from radiowaves to the infrared by changing the density of charge
carriers through a gate voltage.Comment: 5 pages, 4 figure
- …