84 research outputs found
GPU-accelerated ray-casting for 3D fiber orientation analysis
Orientation analysis of fibers is widely applied in the fields of medical, material and life sciences. The orientation information allows predicting properties and behavior of materials to validate and guide a fabrication process of materials with controlled fiber orientation. Meanwhile, development of detector systems for high-resolution non-invasive 3D imaging techniques led to a significant increase in the amount of generated data per a sample up to dozens of gigabytes. Though plenty of 3D orientation estimation algorithms were developed in recent years, neither of them can process large datasets in a reasonable amount of time. This fact complicates the further analysis and makes impossible fast feedback to adjust fabrication parameters. In this work, we present a new method for quantifying the 3D orientation of fibers. The GPU implementation of the proposed method surpasses another popular method for 3D orientation analysis regarding accuracy and speed. The validation of both methods was performed on a synthetic dataset with varying parameters of fibers. Moreover, the proposed method was applied to perform orientation analysis of scaffolds with different fibrous micro-architecture studied with the synchrotron μCT imaging setup. Each acquired dataset of size 600x600x450 voxels was analyzed in less 2 minutes using standard PC equipped with a single GPU
The resonance spectrum of the cusp map in the space of analytic functions
We prove that the Frobenius--Perron operator of the cusp map
, (which is an approximation of the
Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions
corresponding to eigenvalues different from 0 and 1. We also prove that for any
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment and some finite or
countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy
spaces is adde
Rotated multifractal network generator
The recently introduced multifractal network generator (MFNG), has been shown
to provide a simple and flexible tool for creating random graphs with very
diverse features. The MFNG is based on multifractal measures embedded in 2d,
leading also to isolated nodes, whose number is relatively low for realistic
cases, but may become dominant in the limiting case of infinitely large network
sizes. Here we discuss the relation between this effect and the information
dimension for the 1d projection of the link probability measure (LPM), and
argue that the node isolation can be avoided by a simple transformation of the
LPM based on rotation.Comment: Accepted for publication in JSTA
Resonances of the cusp family
We study a family of chaotic maps with limit cases the tent map and the cusp
map (the cusp family). We discuss the spectral properties of the corresponding
Frobenius--Perron operator in different function spaces including spaces of
analytic functions. A numerical study of the eigenvalues and eigenfunctions is
performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.
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