23,907 research outputs found
A chain theorem for internally 4-connected binary matroids
This is the post-print version of the Article - Copyright @ 2011 ElsevierLet M be a matroid. When M is 3-connected, Tutte’s Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M) − E(N)| = 1 unless M is a wheel or a whirl. This paper establishes a corresponding result for internally 4-connected binary matroids. In particular, we prove that if M is such a matroid, then M has an internally 4-connected proper minor N with |E(M) − E(N)| at most 3 unless M or its dual is the cycle matroid of a planar or Möbius quartic ladder, or a 16-element variant of such a planar ladder.This study was partially supported by the National Security Agency
Towards a splitter theorem for internally 4-connected binary matroids
This is the post-print version of the Article - Copyright @ 2012 ElsevierWe prove that if M is a 4-connected binary matroid and N is an internally 4-connected proper minor of M with at least 7 elements, then, unless M is a certain 16-element matroid, there is an element e of E(M) such that either M\e or M/e is internally 4-connected having an N-minor. This strengthens a result of Zhou and is a first step towards obtaining a splitter theorem for internally 4-connected binary matroids.This study is partially funded by Marsden Fund of New Zealand and the National Security Agency
Probing dipole-forbidden autoionizing states by isolated attosecond pulses
We propose a general technique to retrieve the information of
dipole-forbidden resonances in the autoionizing region. In the simulation, a
helium atom is pumped by an isolated attosecond pulse in the extreme
ultraviolet (EUV) combined with a few-femtosecond laser pulse. The excited wave
packet consists of the , , and states, including the background
continua, near the doubly excited state. The resultant electron
spectra with various laser intensities and time delays between the EUV and
laser pulses are obtained by a multilevel model and an ab initio time-dependent
Schr\"odinger equation calculation. By taking the ab initio calculation as a
"virtual measurement", the dipole-forbidden resonances are characterized by the
multilevel model. We found that in contrast to the common assumption, the
nonresonant coupling between the continua plays a significant role in the
time-delayed electron spectra, which shows the correlation effect between
photoelectrons before they leave the core. This technique takes the advantages
of ultrashort pulses uniquely and would be a timely test for the current
attosecond technology.Comment: 10 pages, 6 figure
Electron tomography at 2.4 {\AA} resolution
Transmission electron microscopy (TEM) is a powerful imaging tool that has
found broad application in materials science, nanoscience and biology(1-3).
With the introduction of aberration-corrected electron lenses, both the spatial
resolution and image quality in TEM have been significantly improved(4,5) and
resolution below 0.5 {\AA} has been demonstrated(6). To reveal the 3D structure
of thin samples, electron tomography is the method of choice(7-11), with
resolutions of ~1 nm^3 currently achievable(10,11). Recently, discrete
tomography has been used to generate a 3D atomic reconstruction of a silver
nanoparticle 2-3 nm in diameter(12), but this statistical method assumes prior
knowledge of the particle's lattice structure and requires that the atoms fit
rigidly on that lattice. Here we report the experimental demonstration of a
general electron tomography method that achieves atomic scale resolution
without initial assumptions about the sample structure. By combining a novel
projection alignment and tomographic reconstruction method with scanning
transmission electron microscopy, we have determined the 3D structure of a ~10
nm gold nanoparticle at 2.4 {\AA} resolution. While we cannot definitively
locate all of the atoms inside the nanoparticle, individual atoms are observed
in some regions of the particle and several grains are identified at three
dimensions. The 3D surface morphology and internal lattice structure revealed
are consistent with a distorted icosahedral multiply-twinned particle. We
anticipate that this general method can be applied not only to determine the 3D
structure of nanomaterials at atomic scale resolution(13-15), but also to
improve the spatial resolution and image quality in other tomography
fields(7,9,16-20).Comment: 27 pages, 17 figure
Condensate wave function and elementary excitations of bosonic polar molecules: beyond the first Born approximation
We investigate the condensate wave function and elementary excitations of
strongly interacting bosonic polar molecules in a harmonic trap, treating the
scattering amplitude beyond the standard first Born approximation (FBA). By
using an appropriate trial wave function in the variational method, effects of
the leading order correction beyond the FBA have been investigated and shown to
be significantly enhanced when the system is close to the phase boundary of
collapse. How such leading order effect of going beyond the FBA can be observed
in a realistic experiment is also discussed.Comment: 7 pages, 4 figure
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