2,934 research outputs found
Curvature-controlled defect dynamics in active systems
We have studied the collective motion of polar active particles confined to
ellipsoidal surfaces. The geometric constraints lead to the formation of
vortices that encircle surface points of constant curvature (umbilics). We have
found that collective motion patterns are particularly rich on ellipsoids, with
four umbilics where vortices tend to be located near pairs of umbilical points
to minimize their interaction energy. Our results provide a new perspective on
the migration of living cells, which most likely use the information provided
from the curved substrate geometry to guide their collective motion.Comment: Accepted manuscript. 8 pages, 7 Figures. Movies of the motion
patterns can be found at
https://www.youtube.com/playlist?list=PLEsE7_tnqXZ_U258VwxES8KAJTV_eO43
Reducing artifacts in surface meshes extracted from binary volumes
We present a mesh filtering method for surfaces extracted from binary volume data which guarantees a smooth
and correct representation of the original binary sampled surface, even if the original volume data is inaccessible
or unknown. This method reduces the typical block and staircase artifacts but adheres to the underlying binary
volume data yielding an accurate and smooth representation. The proposed method is closest to the technique of
Constrained Elastic Surface Nets (CESN). CESN is a specialized surface extraction method with a subsequent
iterative smoothing process, which uses the binary input data as a set of constraints. In contrast to CESN, our
method processes surface meshes extracted by means of Marching Cubes and does not require the binary volume.
It acts directly and solely on the surface mesh and is thus feasible even for surface meshes of inaccessible
or unknown volume data. This is possible by reconstructing information concerning the binary volume from
artifacts in the extracted mesh and applying a relaxation method constrained to the reconstructed information
Degree Constrained Triangulation of Annular Regions and Point Sites
Generating constrained triangulations of point sites distributed in the plane is a significant problem in computational geometry. We present theoretical and experimental investigation results for generating triangulations for polygons and point sites that address node degree constraints. We characterize point sites that have almost all vertices of odd degree. We present experimental results on the node degree distribution of Delaunay triangulations of point sites generated randomly. Additionally, we present a heuristic algorithm for triangulating a given normal annular region with an increment of even degree nodes
Quality Improvements in Extruded Meshes Using Topologically Adaptive Generalized Elements
In this dissertation, a novel method to extrude near-body meshes from surface meshes of arbitrary topology that exploits topologically adaptive generalized elements to improve mesh quality is presented. Specifically, an advancing layer algorithm to generate near-body meshes which are appropriate for viscous fluid flows is discussed. First, an orthogonal two-layer algebraic reference mesh is generated. The reference mesh is then smoothed using a locally three-dimensional Poisson-type mesh generation equation that is generalized to smooth extruded meshes of arbitrary surface topology. Local quality improvement operations such as edge collapse, face refinement, and local reconnection are performed in each layer to drive the mesh toward isotropy. An automatic marching thickness reduction algorithm is used to extrude from multiple geometries in close proximity. A global face refinement algorithm is used to improve the transition from the extruded mesh to the voidilling tetrahedral mesh. A few example meshes along with quality plots are presented to demonstrate the efficacy of the algorithms developed
Physics Of Eclipsing Binaries. II. Towards the Increased Model Fidelity
The precision of photometric and spectroscopic observations has been
systematically improved in the last decade, mostly thanks to space-borne
photometric missions and ground-based spectrographs dedicated to finding
exoplanets. The field of eclipsing binary stars strongly benefited from this
development. Eclipsing binaries serve as critical tools for determining
fundamental stellar properties (masses, radii, temperatures and luminosities),
yet the models are not capable of reproducing observed data well either because
of the missing physics or because of insufficient precision. This led to a
predicament where radiative and dynamical effects, insofar buried in noise,
started showing up routinely in the data, but were not accounted for in the
models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an
open source modeling code for computing theoretical light and radial velocity
curves that addresses both problems by incorporating missing physics and by
increasing the computational fidelity. In particular, we discuss triangulation
as a superior surface discretization algorithm, meshing of rotating single
stars, light time travel effect, advanced phase computation, volume
conservation in eccentric orbits, and improved computation of local intensity
across the stellar surfaces that includes photon-weighted mode, enhanced limb
darkening treatment, better reflection treatment and Doppler boosting. Here we
present the concepts on which PHOEBE is built on and proofs of concept that
demonstrate the increased model fidelity.Comment: 60 pages, 15 figures, published in ApJS; accompanied by the release
of PHOEBE 2.0 on http://phoebe-project.or
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