2,222 research outputs found
Application of a multi-site mean-field theory to the disordered Bose-Hubbard model
We present a multi-site formulation of mean-field theory applied to the
disordered Bose-Hubbard model. In this approach the lattice is partitioned into
clusters, each isolated cluster being treated exactly, with inter-cluster
hopping being treated approximately. The theory allows for the possibility of a
different superfluid order parameter at every site in the lattice, such as what
has been used in previously published site-decoupled mean-field theories, but a
multi-site formulation also allows for the inclusion of spatial correlations
allowing us, e.g., to calculate the correlation length (over the length scale
of each cluster). We present our numerical results for a two-dimensional
system. This theory is shown to produce a phase diagram in which the stability
of the Mott insulator phase is larger than that predicted by site-decoupled
single-site mean-field theory. Two different methods are given for the
identification of the Bose glass-to-superfluid transition, one an approximation
based on the behaviour of the condensate fraction, and one of which relies on
obtaining the spatial variation of the order parameter correlation. The
relation of our results to a recent proposal that both transitions are non
self-averaging is discussed.Comment: Accepted for publication in Physical Review
Structure identification methods for atomistic simulations of crystalline materials
We discuss existing and new computational analysis techniques to classify
local atomic arrangements in large-scale atomistic computer simulations of
crystalline solids. This article includes a performance comparison of typical
analysis algorithms such as Common Neighbor Analysis, Centrosymmetry Analysis,
Bond Angle Analysis, Bond Order Analysis, and Voronoi Analysis. In addition we
propose a simple extension to the Common Neighbor Analysis method that makes it
suitable for multi-phase systems. Finally, we introduce a new structure
identification algorithm, the Neighbor Distance Analysis, that is designed to
identify atomic structure units in grain boundaries
Methods of Hierarchical Clustering
We survey agglomerative hierarchical clustering algorithms and discuss
efficient implementations that are available in R and other software
environments. We look at hierarchical self-organizing maps, and mixture models.
We review grid-based clustering, focusing on hierarchical density-based
approaches. Finally we describe a recently developed very efficient (linear
time) hierarchical clustering algorithm, which can also be viewed as a
hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference
Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects
Numerical modeling of nematic liquid crystals using the tensorial Landau-de
Gennes (LdG) theory provides detailed insights into the structure and
energetics of the enormous variety of possible topological defect
configurations that may arise when the liquid crystal is in contact with
colloidal inclusions or structured boundaries. However, these methods can be
computationally expensive, making it challenging to predict (meta)stable
configurations involving several colloidal particles, and they are often
restricted to system sizes well below the experimental scale. Here we present
an open-source software package that exploits the embarrassingly parallel
structure of the lattice discretization of the LdG approach. Our
implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate
simulations using both CPU and GPU resources in either single- or multiple-core
configurations. We make use of an efficient minimization algorithm, the Fast
Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale
parallelization, requiring little additional memory or computational cost while
offering performance competitive with other commonly used methods. In
multi-core operation we are able to scale simulations up to supra-micron length
scales of experimental relevance, and in single-core operation the simulation
package includes a user-friendly GUI environment for rapid prototyping of
interfacial features and the multifarious defect states they can promote. To
demonstrate this software package, we examine in detail the competition between
curvilinear disclinations and point-like hedgehog defects as size scale,
material properties, and geometric features are varied. We also study the
effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph
The infinite cyclohedron and its automorphism group
Cyclohedra are a well-known infinite familiy of finite-dimensional polytopes
that can be constructed from centrally symmetric triangulations of even-sided
polygons. In this article we introduce an infinite-dimensional analogue and
prove that the group of symmetries of our construction is a semidirect product
of a degree 2 central extension of Thompson's infinite finitely presented
simple group T with the cyclic group of order 2. These results are inspired by
a similar recent analysis by the first author of the automorphism group of an
infinite-dimensional associahedron.Comment: 18 pages, 8 figure
A spatial analysis of multivariate output from regional climate models
Climate models have become an important tool in the study of climate and
climate change, and ensemble experiments consisting of multiple climate-model
runs are used in studying and quantifying the uncertainty in climate-model
output. However, there are often only a limited number of model runs available
for a particular experiment, and one of the statistical challenges is to
characterize the distribution of the model output. To that end, we have
developed a multivariate hierarchical approach, at the heart of which is a new
representation of a multivariate Markov random field. This approach allows for
flexible modeling of the multivariate spatial dependencies, including the
cross-dependencies between variables. We demonstrate this statistical model on
an ensemble arising from a regional-climate-model experiment over the western
United States, and we focus on the projected change in seasonal temperature and
precipitation over the next 50 years.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS369 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Diamond Dicing
In OLAP, analysts often select an interesting sample of the data. For
example, an analyst might focus on products bringing revenues of at least 100
000 dollars, or on shops having sales greater than 400 000 dollars. However,
current systems do not allow the application of both of these thresholds
simultaneously, selecting products and shops satisfying both thresholds. For
such purposes, we introduce the diamond cube operator, filling a gap among
existing data warehouse operations.
Because of the interaction between dimensions the computation of diamond
cubes is challenging. We compare and test various algorithms on large data sets
of more than 100 million facts. We find that while it is possible to implement
diamonds in SQL, it is inefficient. Indeed, our custom implementation can be a
hundred times faster than popular database engines (including a row-store and a
column-store).Comment: 29 page
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