Well-posedness of 1-D compressible Euler-Poisson equations with physical vacuum

This paper is concerned with the 1-D compressible Euler-Poisson equations with moving physical vacuum boundary condition. It is usually used to describe the motion of a self-gravitating inviscid gaseous star. The local well-posedness of classical solutions is established in the case of the adiabatic index $1<\gamma<3$.Comment: 28 page

Glassy Dynamics in a Frustrated Spin System: Role of Defects

In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis of the model suggests that defects play a major role in dictating the dynamics as the glass transition is approached.Comment: 9 pages, 5 figures, accepted in J. Phys.: Condensed Matter, proceedings of the Trieste workshop on "Unifying Concepts in Glass Physics

Possible Realization and Protection of Valley-Polarized Quantum Hall Effect in Mn/WS2

By using the first-principles calculations and model analyses, we found that the combination of defected tungsten disulfide monolayer and sparse manganese adsorption may give a KK` valley spin splitting up to 210 meV. This system also has a tunable magnetic anisotropy energy, a clean band gap, and an appropriate band alignment, with the Fermi level sitting right above the top of valence bands at the K-valleys. Therefore, it can be used for the realization of the valley-polarized anomalous Hall effect and for the exploration of other valley related physics without using optical methods. A protective environment can be formed by covering it with a hexagonal BN layer, without much disturbance to the benign properties of Mn/WS2.Comment: 16 pages, 4 figure

Learning Deep CNN Denoiser Prior for Image Restoration

Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and drawbacks, e.g., model-based optimization methods are flexible for handling different inverse problems but are usually time-consuming with sophisticated priors for the purpose of good performance; in the meanwhile, discriminative learning methods have fast testing speed but their application range is greatly restricted by the specialized task. Recent works have revealed that, with the aid of variable splitting techniques, denoiser prior can be plugged in as a modular part of model-based optimization methods to solve other inverse problems (e.g., deblurring). Such an integration induces considerable advantage when the denoiser is obtained via discriminative learning. However, the study of integration with fast discriminative denoiser prior is still lacking. To this end, this paper aims to train a set of fast and effective CNN (convolutional neural network) denoisers and integrate them into model-based optimization method to solve other inverse problems. Experimental results demonstrate that the learned set of denoisers not only achieve promising Gaussian denoising results but also can be used as prior to deliver good performance for various low-level vision applications.Comment: Accepted to CVPR 2017. Code: https://github.com/cszn/ircn