1,319 research outputs found
Neutrino transport in type II supernovae: Boltzmann solver vs. Monte Carlo method
We have coded a Boltzmann solver based on a finite difference scheme (S_N
method) aiming at calculations of neutrino transport in type II supernovae.
Close comparison between the Boltzmann solver and a Monte Carlo transport code
has been made for realistic atmospheres of post bounce core models under the
assumption of a static background. We have also investigated in detail the
dependence of the results on the numbers of radial, angular, and energy grid
points and the way to discretize the spatial advection term which is used in
the Boltzmann solver. A general relativistic calculation has been done for one
of the models. We find overall good agreement between the two methods. However,
because of a relatively small number of angular grid points (which is
inevitable due to limitations of the computation time) the Boltzmann solver
tends to underestimate the flux factor and the Eddington factor outside the
(mean) ``neutrinosphere'' where the angular distribution of the neutrinos
becomes highly anisotropic. This fact suggests that one has to be cautious in
applying the Boltzmann solver to a calculation of the neutrino heating in the
hot-bubble region because it might tend to overestimate the local energy
deposition rate. A comparison shows that this trend is opposite to the results
obtained with a multi-group flux-limited diffusion approximation of neutrino
transport. The accuracy of the Boltzmann solver can be considerably improved by
using a variable angular mesh to increase the angular resolution in the
semi-transparent regime.Comment: 19 pages, 17 figures, submitted to A&
Hypergraph -Laplacian: A Differential Geometry View
The graph Laplacian plays key roles in information processing of relational
data, and has analogies with the Laplacian in differential geometry. In this
paper, we generalize the analogy between graph Laplacian and differential
geometry to the hypergraph setting, and propose a novel hypergraph
-Laplacian. Unlike the existing two-node graph Laplacians, this
generalization makes it possible to analyze hypergraphs, where the edges are
allowed to connect any number of nodes. Moreover, we propose a semi-supervised
learning method based on the proposed hypergraph -Laplacian, and formalize
them as the analogue to the Dirichlet problem, which often appears in physics.
We further explore theoretical connections to normalized hypergraph cut on a
hypergraph, and propose normalized cut corresponding to hypergraph
-Laplacian. The proposed -Laplacian is shown to outperform standard
hypergraph Laplacians in the experiment on a hypergraph semi-supervised
learning and normalized cut setting.Comment: Extended version of our AAAI-18 pape
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