60,157 research outputs found
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis
The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.
Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media
The resistive or non-resistive nature of the extracellular space in the brain
is still debated, and is an important issue for correctly modeling
extracellular potentials. Here, we first show theoretically that if the medium
is resistive, the frequency scaling should be the same for electroencephalogram
(EEG) and magnetoencephalogram (MEG) signals at low frequencies (<10 Hz). To
test this prediction, we analyzed the spectrum of simultaneous EEG and MEG
measurements in four human subjects. The frequency scaling of EEG displays
coherent variations across the brain, in general between 1/f and 1/f^2, and
tends to be smaller in parietal/temporal regions. In a given region, although
the variability of the frequency scaling exponent was higher for MEG compared
to EEG, both signals consistently scale with a different exponent. In some
cases, the scaling was similar, but only when the signal-to-noise ratio of the
MEG was low. Several methods of noise correction for environmental and
instrumental noise were tested, and they all increased the difference between
EEG and MEG scaling. In conclusion, there is a significant difference in
frequency scaling between EEG and MEG, which can be explained if the
extracellular medium (including other layers such as dura matter and skull) is
globally non-resistive.Comment: Submitted to Journal of Computational Neuroscienc
Robust error estimates in weak norms for advection dominated transport problems with rough data
We consider mixing problems in the form of transient convection--diffusion
equations with a velocity vector field with multiscale character and rough
data. We assume that the velocity field has two scales, a coarse scale with
slow spatial variation, which is responsible for advective transport and a fine
scale with small amplitude that contributes to the mixing. For this problem we
consider the estimation of filtered error quantities for solutions computed
using a finite element method with symmetric stabilization. A posteriori error
estimates and a priori error estimates are derived using the multiscale
decomposition of the advective velocity to improve stability. All estimates are
independent both of the P\'eclet number and of the regularity of the exact
solution
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