1,633 research outputs found
A weighted first-order formulation for solving anisotropic diffusion equations with deep neural networks
In this paper, a new weighted first-order formulation is proposed for solving
the anisotropic diffusion equations with deep neural networks. For many
numerical schemes, the accurate approximation of anisotropic heat flux is
crucial for the overall accuracy. In this work, the heat flux is firstly
decomposed into two components along the two eigenvectors of the diffusion
tensor, thus the anisotropic heat flux approximation is converted into the
approximation of two isotropic components.
Moreover, to handle the possible jump of the diffusion tensor across the
interface, the weighted first-order formulation is obtained by multiplying this
first-order formulation by a weighted function. By the decaying property of the
weighted function, the weighted first-order formulation is always well-defined
in the pointwise way. Finally, the weighted first-order formulation is solved
with deep neural network approximation. Compared to the neural network
approximation with the original second-order elliptic formulation, the proposed
method can significantly improve the accuracy, especially for the discontinuous
anisotropic diffusion problems
Shedding light on the pion production in heavy-ion collisions for constraining the high-density symmetry energy
Within the framework of the quantum molecular dynamics transport model, the
pion production and constraint of the high-density symmetry energy in heavy-ion
collisions near threshold energy have been thoroughly investigated. The energy
conservation in the decay of resonances and reabsorption of pions in nuclear
medium are taken into account. The density profile of pion production, energy
conservation and pion potential are analyzed by the model. The isospin
diffusion in the low-density region (0.2 - 0.8) and
high-density region (1.2 - 1.8) is investigated by
analyzing the neutron/proton and ratios in the isotopic
reactions of Sn + Sn and Sn + Sn at the
incident energy of 270 MeV/nucleon, in which the symmetry energy manifests the
opposite contribution. The controversial conclusion of the
ratio for constraining the high-density symmetry energy by different transport
models is clarified. A soft symmetry energy with the slope parameter of
MeV by using the standard error analysis within the
range of is obtained by analyzing the experimental data from the
SRIT collaboration.Comment: 8 pages, 7 figure
Collective flows of clusters and pions in heavy-ion collisions at GeV energies
Within the framework of the quantum molecular dynamics transport model, the
collective flows of clusters and pions in heavy-ion collisions have been
systematically investigated. The clusters are recognized by the Wigner
phase-space density approach at the stage of freeze out in nuclear collisions,
i.e., deuteron, triton, He and . The directed and elliptic flows
of protons and deuterons in the reaction of Au+Au at incident
energy 1.23\emph{A} GeV are nicely consistent with the recent HADES data. The
higher order collective flows, i.e., triangular and quadrangle flows, manifest
the opposite trends with the less amplitude in comparison with the rapidity
distributions of directed and elliptic flows. The flow structure of He
and is very similar to the proton spectra. The influence of the pion
potential on the pion production is systematically investigated and compared
with the FOPI data via the transverse momentum, longitudinal rapidity and
collective flows in collisions of Au + Au. It is manifested
that the pion yields are slightly suppressed in the domain of mid-rapidity and
high momentum. The antiflow phenomena is reduced by implementing the pion
potential and more consistent with the FOPI data in collisions of
Au+Au at the incident energy 1.5\emph{A} GeV.Comment: 11 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:2302.0213
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