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 $^1S$, $^1P$, and $^1D$ states, including the background continua, near the $2s2p(^1P)$ 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