74,471 research outputs found
On-off intermittency and amplitude-phase synchronization in Keplerian shear flows
We study the development of coherent structures in local simulations of the
magnetorotational instability in accretion discs in regimes of on-off
intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102
(2010)], we have shown that the laminar and bursty states due to the on-off
spatiotemporal intermittency in a one-dimensional model of nonlinear waves
correspond, respectively, to nonattracting coherent structures with higher and
lower degrees of amplitude-phase synchronization. In this paper we extend these
results to a three-dimensional model of magnetized Keplerian shear flows.
Keeping the kinetic Reynolds number and the magnetic Prandtl number fixed, we
investigate two different intermittent regimes by varying the plasma beta
parameter. The first regime is characterized by turbulent patterns interrupted
by the recurrent emergence of a large-scale coherent structure known as
two-channel flow, where the state of the system can be described by a single
Fourier mode. The second regime is dominated by the turbulence with sporadic
emergence of coherent structures with shapes that are reminiscent of a
perturbed channel flow. By computing the Fourier power and phase spectral
entropies in three-dimensions, we show that the large-scale coherent structures
are characterized by a high degree of amplitude-phase synchronization.Comment: 17 pages, 10 figure
Microstructural evolution in two-dimensional two-phase polycrystals
In two-dimensional polycrystals composed of [alpha]-phase and [beta]-phase grains the stability of [alpha][alpha][alpha], [beta][beta][beta], [alpha][alpha][beta] and [alpha][beta][beta] three-grain junctions and [alpha][beta][alpha][beta] four-grain junctions depends on the [alpha]-[alpha], [beta]-[beta] and [alpha]-[beta] interfacial energies. A computer simulation which generates thermodynamically consistent microstructures for arbitrary interfacial energies has been utilized to investigate microstructural evolution in such polycrystals when phase volume is not conserved. Since grain shapes, phase volume, and phase arrangements are dictated by interfacial energies, clustered-, alternating-, isolated-, and single-phase microstructures occur in different interfacial energy regimes. Despite great differences in microstructure, polycrystals which contain only three-grain junctions evolve with normal grain growth kinetics. In contrast, structures containing flexible four-grain junctions eventually stop evolving. We conclude that two-dimensional polycrystals continually evolve when grain junction angles are thermodynamically fixed, while grain growth ultimately ceases when grain junction angles may vary. Predictions concerning three-dimensional and phase-volume conserved systems are made.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30895/1/0000564.pd
Galaxy Cluster Shapes and Systematic Errors in H0 Measured by the Sunyaev-Zel'dovich Effect
Imaging of the Sunyaev-Zel'dovich (SZ) effect in galaxy clusters combined
with cluster plasma x-ray diagnostics can measure the cosmic distance scale to
high redshift. Projecting the inverse-Compton scattering and x-ray emission
along the cluster line-of-sight introduces systematic errors in the Hubble
constant, H0, because the true shape of the cluster is not known. I present a
study of the systematic errors in the value of H0, as determined by the x-ray
and SZ properties of theoretical samples of triaxial isothermal ``beta'' model
clusters, caused by projection effects and observer orientation. I calculate
estimates for H0 for each cluster based on their large and small apparent
angular core radii and their arithmetic mean. I demonstrate that the estimates
for H0 for a sample of 25 clusters have 99.7% confidence intervals for the mean
estimated H0 analyzing the clusters using either their large or mean angular
core radius are within 14% of the ``true'' (assumed) value of H0 (and enclose
it), for a triaxial beta model cluster sample possessing a distribution of
apparent x-ray cluster ellipticities consistent with that of observed x-ray
clusters. This limit on the systematic error in H0 caused by cluster shape
assumes that each sample beta model cluster has fixed shape; deviations from
constant shape within the clusters may introduce additional uncertainty or bias
into this result.Comment: Accepted for publication in the Astrophysical Journal, 24 March 1998;
4 pages, 2 figure
Sixteen space-filling curves and traversals for d-dimensional cubes and simplices
This article describes sixteen different ways to traverse d-dimensional space
recursively in a way that is well-defined for any number of dimensions. Each of
these traversals has distinct properties that may be beneficial for certain
applications. Some of the traversals are novel, some have been known in
principle but had not been described adequately for any number of dimensions,
some of the traversals have been known. This article is the first to present
them all in a consistent notation system. Furthermore, with this article, tools
are provided to enumerate points in a regular grid in the order in which they
are visited by each traversal. In particular, we cover: five discontinuous
traversals based on subdividing cubes into 2^d subcubes: Z-traversal (Morton
indexing), U-traversal, Gray-code traversal, Double-Gray-code traversal, and
Inside-out traversal; two discontinuous traversals based on subdividing
simplices into 2^d subsimplices: the Hill-Z traversal and the Maehara-reflected
traversal; five continuous traversals based on subdividing cubes into 2^d
subcubes: the Base-camp Hilbert curve, the Harmonious Hilbert curve, the Alfa
Hilbert curve, the Beta Hilbert curve, and the Butz-Hilbert curve; four
continuous traversals based on subdividing cubes into 3^d subcubes: the Peano
curve, the Coil curve, the Half-coil curve, and the Meurthe curve. All of these
traversals are self-similar in the sense that the traversal in each of the
subcubes or subsimplices of a cube or simplex, on any level of recursive
subdivision, can be obtained by scaling, translating, rotating, reflecting
and/or reversing the traversal of the complete unit cube or simplex.Comment: 28 pages, 12 figures. v2: fixed a confusing typo on page 12, line
Making Nuclei Out Of The Skyrme Crystal
A new method for approximating Skyrme solutions is developed. It consists of
cutting sections out of the Skyrme crystal and smoothly interpolating between
the boundary and spatial infinity. Several field configurations are
constructed, and their energies calculated. The surface energy (per unit area)
of an infinite flat plane of the crystal is also calculated, and the result
used to derive a formula analogous to the semi-empirical mass formula of
nuclear physics. This formula can be used to give some idea of what the Skyrme
model predicts about volume and surface energies of the nucleus over a broad
range of baryon numbers.Comment: 20 pages, uuencoded ps file `crystal.uu'. The LaTeX version can be
obtained by emailing [email protected] or [email protected]
Distribution on Warp Maps for Alignment of Open and Closed Curves
Alignment of curve data is an integral part of their statistical analysis,
and can be achieved using model- or optimization-based approaches. The
parameter space is usually the set of monotone, continuous warp maps of a
domain. Infinite-dimensional nature of the parameter space encourages sampling
based approaches, which require a distribution on the set of warp maps.
Moreover, the distribution should also enable sampling in the presence of
important landmark information on the curves which constrain the warp maps. For
alignment of closed and open curves in , possibly with
landmark information, we provide a constructive, point-process based definition
of a distribution on the set of warp maps of and the unit circle
that is (1) simple to sample from, and (2) possesses the
desiderata for decomposition of the alignment problem with landmark constraints
into multiple unconstrained ones. For warp maps on , the distribution is
related to the Dirichlet process. We demonstrate its utility by using it as a
prior distribution on warp maps in a Bayesian model for alignment of two
univariate curves, and as a proposal distribution in a stochastic algorithm
that optimizes a suitable alignment functional for higher-dimensional curves.
Several examples from simulated and real datasets are provided
PocketPicker: analysis of ligand binding-sites with shape descriptors
Background Identification and evaluation of surface binding-pockets and occluded cavities are initial steps in protein structure-based drug design. Characterizing the active site's shape as well as the distribution of surrounding residues plays an important role for a variety of applications such as automated ligand docking or in situ modeling. Comparing the shape similarity of binding site geometries of related proteins provides further insights into the mechanisms of ligand binding. Results We present PocketPicker, an automated grid-based technique for the prediction of protein binding pockets that specifies the shape of a potential binding-site with regard to its buriedness. The method was applied to a representative set of protein-ligand complexes and their corresponding apo-protein structures to evaluate the quality of binding-site predictions. The performance of the pocket detection routine was compared to results achieved with the existing methods CAST, LIGSITE, LIGSITEcs, PASS and SURFNET. Success rates PocketPicker were comparable to those of LIGSITEcs and outperformed the other tools. We introduce a descriptor that translates the arrangement of grid points delineating a detected binding-site into a correlation vector. We show that this shape descriptor is suited for comparative analyses of similar binding-site geometry by examining induced-fit phenomena in aldose reductase. This new method uses information derived from calculations of the buriedness of potential binding-sites. Conclusions The pocket prediction routine of PocketPicker is a useful tool for identification of potential protein binding-pockets. It produces a convenient representation of binding-site shapes including an intuitive description of their accessibility. The shape-descriptor for automated classification of binding-site geometries can be used as an additional tool complementing elaborate manual inspections
Measuring the 3D shape of X-ray clusters
Observations and numerical simulations of galaxy clusters strongly indicate
that the hot intracluster x-ray emitting gas is not spherically symmetric. In
many earlier studies spherical symmetry has been assumed partly because of
limited data quality, however new deep observations and instrumental designs
will make it possible to go beyond that assumption. Measuring the temperature
and density profiles are of interest when observing the x-ray gas, however the
spatial shape of the gas itself also carries very useful information. For
example, it is believed that the x-ray gas shape in the inner parts of galaxy
clusters is greatly affected by feedback mechanisms, cooling and rotation, and
measuring this shape can therefore indirectly provide information on these
mechanisms. In this paper we present a novel method to measure the
three-dimensional shape of the intracluster x-ray emitting gas. We can measure
the shape from the x-ray observations only, i.e. the method does not require
combination with independent measurements of e.g. the cluster mass or density
profile. This is possible when one uses the full spectral information contained
in the observed spectra. We demonstrate the method by measuring radial
dependent shapes along the line of sight for CHANDRA mock data. We find that at
least 10^6 photons are required to get a 5-{\sigma} detection of shape for an
x-ray gas having realistic features such as a cool core and a double powerlaw
for the density profile. We illustrate how Bayes' theorem is used to find the
best fitting model of the x-ray gas, an analysis that is very important in a
real observational scenario where the true spatial shape is unknown. Not
including a shape in the fit may propagate to a mass bias if the x-ray is used
to estimate the total cluster mass. We discuss this mass bias for a class of
spacial shapes.Comment: 29 pages, 16 figure
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