20,233 research outputs found
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
Transport-Based Neural Style Transfer for Smoke Simulations
Artistically controlling fluids has always been a challenging task.
Optimization techniques rely on approximating simulation states towards target
velocity or density field configurations, which are often handcrafted by
artists to indirectly control smoke dynamics. Patch synthesis techniques
transfer image textures or simulation features to a target flow field. However,
these are either limited to adding structural patterns or augmenting coarse
flows with turbulent structures, and hence cannot capture the full spectrum of
different styles and semantically complex structures. In this paper, we propose
the first Transport-based Neural Style Transfer (TNST) algorithm for volumetric
smoke data. Our method is able to transfer features from natural images to
smoke simulations, enabling general content-aware manipulations ranging from
simple patterns to intricate motifs. The proposed algorithm is physically
inspired, since it computes the density transport from a source input smoke to
a desired target configuration. Our transport-based approach allows direct
control over the divergence of the stylization velocity field by optimizing
incompressible and irrotational potentials that transport smoke towards
stylization. Temporal consistency is ensured by transporting and aligning
subsequent stylized velocities, and 3D reconstructions are computed by
seamlessly merging stylizations from different camera viewpoints.Comment: ACM Transaction on Graphics (SIGGRAPH ASIA 2019), additional
materials: http://www.byungsoo.me/project/neural-flow-styl
A simulation method for determining the optical response of highly complex photonic structures of biological origin
We present a method based on a time domain simulation of wave propagation
that allows studying the optical response of a broad range of dielectric
photonic structures. This method is particularly suitable for dealing with
complex biological structures. One of the main features of the proposed
approach is the simple and intuitive way of defining the setup and the photonic
structure to be simulated, which can be done by feeding the simulation with a
digital image of the structure. We also develop a set of techniques to process
the behavior of the evolving waves within the simulation. These techniques
include a direction filter, that permits decoupling of waves travelling
simultaneously in different directions, a dynamic differential absorber, to
cancel the waves reflected at the edges of the simulation space, a
multi-frequency excitation scheme based on a filter that allows decoupling
waves of different wavelengths travelling simultaneously, and a
near-to-far-field approach to evaluate the resulting wavefield outside the
simulation domain. We validate the code and, as an example, apply it to the
complex structure found in a microorganism called Diachea leucopoda, which
exhibits a multicolor iridescent appearance.Comment: 43 pages, 19 figure
Change of Scaling and Appearance of Scale-Free Size Distribution in Aggregation Kinetics by Additive Rules
The idealized general model of aggregate growth is considered on the basis of
the simple additive rules that correspond to one-step aggregation process. The
two idealized cases were analytically investigated and simulated by Monte Carlo
method in the Desktop Grid distributed computing environment to analyze
"pile-up" and "wall" cluster distributions in different aggregation scenarios.
Several aspects of aggregation kinetics (change of scaling, change of size
distribution type, and appearance of scale-free size distribution) driven by
"zero cluster size" boundary condition were determined by analysis of evolving
cumulative distribution functions. The "pile-up" case with a \textit{minimum}
active surface (singularity) could imitate piling up aggregations of
dislocations, and the case with a \textit{maximum} active surface could imitate
arrangements of dislocations in walls. The change of scaling law (for pile-ups
and walls) and availability of scale-free distributions (for walls) were
analytically shown and confirmed by scaling, fitting, moment, and bootstrapping
analyses of simulated probability density and cumulative distribution
functions. The initial "singular" \textit{symmetric} distribution of pile-ups
evolves by the "infinite" diffusive scaling law and later it is replaced by the
other "semi-infinite" diffusive scaling law with \textit{asymmetric}
distribution of pile-ups. In contrast, the initial "singular"
\textit{symmetric} distributions of walls initially evolve by the diffusive
scaling law and later it is replaced by the other ballistic (linear) scaling
law with \textit{scale-free} exponential distributions without distinctive
peaks. The conclusion was made as to possible applications of such approach for
scaling, fitting, moment, and bootstrapping analyses of distributions in
simulated and experimental data.Comment: 37 pages, 16 figures, 1 table; accepted preprint version after
comments of reviewers, Physica A: Statistical Mechanics and its Applications
(2014
A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Mollusk shells are an ideal model system for understanding the morpho-elastic
basis of morphological evolution of invertebrates' exoskeletons. During the
formation of the shell, the mantle tissue secretes proteins and minerals that
calcify to form a new incremental layer of the exoskeleton. Most of the
existing literature on the morphology of mollusks is descriptive. The
mathematical understanding of the underlying coupling between pre-existing
shell morphology, de novo surface deposition and morpho-elastic volume growth
is at a nascent stage, primarily limited to reduced geometric representations.
Here, we propose a general, three-dimensional computational framework coupling
pre-existing morphology, incremental surface growth by accretion, and
morpho-elastic volume growth. We exercise this framework by applying it to
explain the stepwise morphogenesis of seashells during growth: new material
surfaces are laid down by accretive growth on the mantle whose form is
determined by its morpho-elastic growth. Calcification of the newest surfaces
extends the shell as well as creates a new scaffold that constrains the next
growth step. We study the effects of surface and volumetric growth rates, and
of previously deposited shell geometries on the resulting modes of mantle
deformation, and therefore of the developing shell's morphology. Connections
are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material
is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS
Computational Biolog
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