51,667 research outputs found
Einstein equations in the null quasi-spherical gauge III: numerical algorithms
We describe numerical techniques used in the construction of our 4th order
evolution for the full Einstein equations, and assess the accuracy of
representative solutions. The code is based on a null gauge with a
quasi-spherical radial coordinate, and simulates the interaction of a single
black hole with gravitational radiation. Techniques used include spherical
harmonic representations, convolution spline interpolation and filtering, and
an RK4 "method of lines" evolution. For sample initial data of "intermediate"
size (gravitational field with 19% of the black hole mass), the code is
accurate to 1 part in 10^5, until null time z=55 when the coordinate condition
breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed
MCViNE -- An object oriented Monte Carlo neutron ray tracing simulation package
MCViNE (Monte-Carlo VIrtual Neutron Experiment) is a versatile Monte Carlo
(MC) neutron ray-tracing program that provides researchers with tools for
performing computer modeling and simulations that mirror real neutron
scattering experiments. By adopting modern software engineering practices such
as using composite and visitor design patterns for representing and accessing
neutron scatterers, and using recursive algorithms for multiple scattering,
MCViNE is flexible enough to handle sophisticated neutron scattering problems
including, for example, neutron detection by complex detector systems, and
single and multiple scattering events in a variety of samples and sample
environments. In addition, MCViNE can take advantage of simulation components
in linear-chain-based MC ray tracing packages widely used in instrument design
and optimization, as well as NumPy-based components that make prototypes useful
and easy to develop. These developments have enabled us to carry out detailed
simulations of neutron scattering experiments with non-trivial samples in
time-of-flight inelastic instruments at the Spallation Neutron Source. Examples
of such simulations for powder and single-crystal samples with various
scattering kernels, including kernels for phonon and magnon scattering, are
presented. With simulations that closely reproduce experimental results,
scattering mechanisms can be turned on and off to determine how they contribute
to the measured scattering intensities, improving our understanding of the
underlying physics.Comment: 34 pages, 14 figure
Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways
Diverse classes of proteins function through large-scale conformational
changes; sophisticated enhanced sampling methods have been proposed to generate
these macromolecular transition paths. As such paths are curves in a
high-dimensional space, they have been difficult to compare quantitatively, a
prerequisite to, for instance, assess the quality of different sampling
algorithms. The Path Similarity Analysis (PSA) approach alleviates these
difficulties by utilizing the full information in 3N-dimensional trajectories
in configuration space. PSA employs the Hausdorff or Fr\'echet path
metrics---adopted from computational geometry---enabling us to quantify path
(dis)similarity, while the new concept of a Hausdorff-pair map permits the
extraction of atomic-scale determinants responsible for path differences.
Combined with clustering techniques, PSA facilitates the comparison of many
paths, including collections of transition ensembles. We use the closed-to-open
transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for
the assessment enhanced sampling algorithms---to examine multiple microsecond
equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free
form alongside transition ensembles from the MD-based dynamic importance
sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting
algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for
instance, that differences in DIMS-MD and FRODA paths were mediated by a set of
conserved salt bridges whose charge-charge interactions are fully modeled in
DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis
methods relying on pre-defined collective variables, such as native contacts or
geometric quantities, can be used synergistically with PSA, as well as the
application of PSA to more complex systems such as membrane transporter
proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information
includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also
available from journal site
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
We study the topology of the Megaparsec Cosmic Web in terms of the
scale-dependent Betti numbers, which formalize the topological information
content of the cosmic mass distribution. While the Betti numbers do not fully
quantify topology, they extend the information beyond conventional cosmological
studies of topology in terms of genus and Euler characteristic. The richer
information content of Betti numbers goes along the availability of fast
algorithms to compute them.
For continuous density fields, we determine the scale-dependence of Betti
numbers by invoking the cosmologically familiar filtration of sublevel or
superlevel sets defined by density thresholds. For the discrete galaxy
distribution, however, the analysis is based on the alpha shapes of the
particles. These simplicial complexes constitute an ordered sequence of nested
subsets of the Delaunay tessellation, a filtration defined by the scale
parameter, . As they are homotopy equivalent to the sublevel sets of
the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive
understanding for the behavior of Betti numbers as a function of , and
their relation to the morphological patterns in the Cosmic Web, we first study
them within the context of simple heuristic Voronoi clustering models.
Subsequently, we address the topology of structures emerging in the standard
LCDM scenario and in cosmological scenarios with alternative dark energy
content. The evolution and scale-dependence of the Betti numbers is shown to
reflect the hierarchical evolution of the Cosmic Web and yields a promising
measure of cosmological parameters. We also discuss the expected Betti numbers
as a function of the density threshold for superlevel sets of a Gaussian random
field.Comment: 42 pages, 14 figure
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