433 research outputs found
Computational Design of Flexible Electride with Nontrivial Band Topology
Electrides, with their excess electrons distributed in crystal cavities playing the role of anions, exhibit a variety of unique electronic and magnetic properties. In this work, we employ the first-principles crystal structure prediction to identify a new prototype of A3B electride in which both interlayer spacings and intralayer vacancies provide channels to accommodate the excess electrons in the crystal. This A3B type of structure is calculated to be thermodynamically stable for two alkaline metals oxides (Rb3O and K3O). Remarkably, the unique feature of multiple types of cavities makes the spatial arrangement of anionic electrons highly flexible via elastic strain engineering and chemical substitution, in contrast to the previously reported electrides characterized by a single topology of interstitial electrons. More importantly, our first-principles calculations reveal that Rb3O is a topological Dirac nodal line semimetal, which is induced by the band inversion at the general electronic k momentums in the Brillouin zone associated with the intersitial electric charges. The discovery of flexible electride in combining with topological electronic properties opens an avenue for electride design and shows great promises in electronic device applications
3D MHD Flux Emergence Experiments: Idealized models and coronal interactions
This paper reviews some of the many 3D numerical experiments of the emergence
of magnetic fields from the solar interior and the subsequent interaction with
the pre-existing coronal magnetic field. The models described here are
idealized, in the sense that the internal energy equation only involves the
adiabatic, Ohmic and viscous shock heating terms. However, provided the main
aim is to investigate the dynamical evolution, this is adequate. Many
interesting observational phenomena are explained by these models in a
self-consistent manner.Comment: Review article, accepted for publication in Solar Physic
Simplifying The Non-Manifold Topology Of Multi-Partitioning Surface Networks
In bio-medical imaging, multi-partitioning surface networks: MPSNs) are very useful to model complex organs with multiple anatomical regions, such as a mouse brain. However, MPSNs are usually constructed from image data and might contain complex geometric and topological features. There has been much research on reducing the geometric complexity of a general surface: non-manifold or not) and the topological complexity of a closed, manifold surface. But there has been no attempt so far to reduce redundant topological features which are unique to non-manifold surfaces, such as curves and points where multiple sheets of surfaces join. In this thesis, we design interactive and automated means for removing redundant non-manifold topological features in MPSNs, which is a special class of non-manifold surfaces. The core of our approach is a mesh surgery operator that can effectively simplify the non-manifold topology while preserving the validity of the MPSN. The operator is implemented in an interactive user interface, allowing user-guided simplification of the input. We further develop an automatic algorithm that invokes the operator following a greedy heuristic. The algorithm is based on a novel, abstract representation of a non-manifold surface as a graph, which allows efficient discovery and scoring of possible surgery operations without the need for explicitly performing the surgeries on the mesh geometry
Multiscale Phenomenology of the Cosmic Web
We analyze the structure and connectivity of the distinct morphologies that
define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF),
we dissect the matter distribution of a cosmological CDM N-body
computer simulation into cluster, filaments and walls. The MMF is ideally
suited to adress both the anisotropic morphological character of filaments and
sheets, as well as the multiscale nature of the hierarchically evolved cosmic
matter distribution. The results of our study may be summarized as follows:
i).- While all morphologies occupy a roughly well defined range in density,
this alone is not sufficient to differentiate between them given their overlap.
Environment defined only in terms of density fails to incorporate the intrinsic
dynamics of each morphology. This plays an important role in both linear and
non linear interactions between haloes. ii).- Most of the mass in the Universe
is concentrated in filaments, narrowly followed by clusters. In terms of
volume, clusters only represent a minute fraction, and filaments not more than
9%. Walls are relatively inconspicous in terms of mass and volume. iii).- On
average, massive clusters are connected to more filaments than low mass
clusters. Clusters with M h have on average
two connecting filaments, while clusters with M
h have on average five connecting filaments. iv).- Density profiles
indicate that the typical width of filaments is 2\Mpch. Walls have less well
defined boundaries with widths between 5-8 Mpc h. In their interior,
filaments have a power-law density profile with slope ,
corresponding to an isothermal density profile.Comment: 28 pages, 22 figures, accepted for publication in MNRAS. For a
high-res version see http://www.astro.rug.nl/~weygaert/webmorph_mmf.pd
Multivariate Topology Simplification
Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph
A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface
Given a graph cellularly embedded on a surface of genus , a
cut graph is a subgraph of such that cutting along yields a
topological disk. We provide a fixed parameter tractable approximation scheme
for the problem of computing the shortest cut graph, that is, for any
, we show how to compute a approximation of
the shortest cut graph in time .
Our techniques first rely on the computation of a spanner for the problem
using the technique of brick decompositions, to reduce the problem to the case
of bounded tree-width. Then, to solve the bounded tree-width case, we introduce
a variant of the surface-cut decomposition of Ru\'e, Sau and Thilikos, which
may be of independent interest
Quantifying Homology Classes
We develop a method for measuring homology classes. This involves three
problems. First, we define the size of a homology class, using ideas from
relative homology. Second, we define an optimal basis of a homology group to be
the basis whose elements' size have the minimal sum. We provide a greedy
algorithm to compute the optimal basis and measure classes in it. The algorithm
runs in time, where is the size of the simplicial
complex and is the Betti number of the homology group. Third, we
discuss different ways of localizing homology classes and prove some hardness
results
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