582 research outputs found
Elements with finite Coxeter part in an affine Weyl group
Let be an affine Weyl group and be the
natural projection to the corresponding finite Weyl group. We say that has finite Coxeter part if is conjugate to a Coxeter element of
. The elements with finite Coxeter part is a union of conjugacy classes of
. We show that for each conjugacy class of with finite
Coxeter part there exits a unique maximal proper parabolic subgroup of
, such that the set of minimal length elements in is exactly
the set of Coxeter elements in . Similar results hold for twisted
conjugacy classes.Comment: 9 page
On affine Deligne-Lusztig varieties for Sp_4(L)
In this paper, we study the emptiness/nonemptiness and the dimension formulas
of affine Deligne-Lusztig varieties for . We mainly calculate the
degree of class polynomials for the Iwahori-Hecke algebra of type
. Then, give an explicit description on the
emptiness/nonemptiness and dimension formulas of affine Deligne-Lusztig
varieties for the group .Comment: 30 page
DMIS: Dynamic Mesh-based Importance Sampling for Training Physics-Informed Neural Networks
Modeling dynamics in the form of partial differential equations (PDEs) is an
effectual way to understand real-world physics processes. For complex physics
systems, analytical solutions are not available and numerical solutions are
widely-used. However, traditional numerical algorithms are computationally
expensive and challenging in handling multiphysics systems. Recently, using
neural networks to solve PDEs has made significant progress, called
physics-informed neural networks (PINNs). PINNs encode physical laws into
neural networks and learn the continuous solutions of PDEs. For the training of
PINNs, existing methods suffer from the problems of inefficiency and unstable
convergence, since the PDE residuals require calculating automatic
differentiation. In this paper, we propose Dynamic Mesh-based Importance
Sampling (DMIS) to tackle these problems. DMIS is a novel sampling scheme based
on importance sampling, which constructs a dynamic triangular mesh to estimate
sample weights efficiently. DMIS has broad applicability and can be easily
integrated into existing methods. The evaluation of DMIS on three widely-used
benchmarks shows that DMIS improves the convergence speed and accuracy in the
meantime. Especially in solving the highly nonlinear Schr\"odinger Equation,
compared with state-of-the-art methods, DMIS shows up to 46% smaller root mean
square error and five times faster convergence speed. Code are available at
https://github.com/MatrixBrain/DMIS.Comment: Accepted to AAAl-2
Effects of Coronal Density and Magnetic Field Distributions on a Global Solar EUV Wave
We investigate a global extreme-ultraviolet (EUV) wave associated with a
coronal mass ejection (CME)-driven shock on 2017 September 10. The EUV wave is
transmitted by north- and south-polar coronal holes (CHs), which is observed by
the Solar Dynamics Observatory (SDO) and Solar Terrestrial Relations
Observatory A (STEREO-A) from opposite sides of the Sun. We obtain key findings
on how the EUV wave interacts with multiple coronal structures, and on its
connection with the CME-driven shock: (1) the transmitted EUV wave is still
connected with the shock that is incurvated to the Sun, after the shock has
reached the opposite side of the eruption; (2) the south CH transmitted EUV
wave is accelerated inside an on-disk, low-density region with closed magnetic
fields, which implies that an EUV wave can be accelerated in both open and
closed magnetic field regions; (3) part of the primary EUV wavefront turns
around a bright point (BP) with a bipolar magnetic structure when it approaches
a dim, low-density filament channel near the BP; (4) the primary EUV wave is
diffused and apparently halted near the boundaries of remote active regions
(ARs) that are far from the eruption, and no obvious AR related secondary waves
are detected; (5) the EUV wave extends to an unprecedented scale of ~360{\deg}
in latitudes, which is attributed to the polar CH transmission. These results
provide insights into the effects of coronal density and magnetic field
distributions on the evolution of an EUV wave, and into the connection between
the EUV wave and the associated CME-driven shock.Comment: 16 pages, 8 figures, and 3 animations available at
http://doi.org/10.13140/RG.2.2.12408.29442 ,
http://doi.org/10.13140/RG.2.2.25830.06723 , and
http://doi.org/10.13140/RG.2.2.19119.18088 ; published in Ap
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