Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System

A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta V=Q^{2}, & \text{in }\mathbb{R}^{3}\\ V(x)\to0 & \mbox{as }x\to\infty. \end{cases} is given in this paper: existence, uniqueness, regularity and asymptotic behavior at infinity, where $C_{S}>0$ is a constant. To the author's knowledge, this is the first uniqueness result on SPS system

Liouville Type Theorem For A Nonlinear Neumann Problem

Consider the following nonlinear Neumann problem $$\begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on }\partial\mathbb{R}_{+}^{n+1},\\ u\ge0 & \text{in }\mathbb{R}_{+}^{n+1}, \end{cases}$$ $a\in(-1,1)$. A Liouville type theorem and its applications are given under suitable conditions on $f$. Our tool is the famous moving plane method.Comment: This paper has been withdrawn by the author due to a poor writin

Electronically phase separated nano-network in antiferromagnetic insulating LaMnO3/PrMnO3/CaMnO3 tricolor superlattice

Strongly correlated materials often exhibit an electronic phase separation (EPS) phenomena whose domain pattern is random in nature. The ability to control the spatial arrangement of the electronic phases at microscopic scales is highly desirable for tailoring their macroscopic properties and/or designing novel electronic devices. Here we report the formation of EPS nanoscale network in a mono-atomically stacked LaMnO3/CaMnO3/PrMnO3 superlattice grown on SrTiO3 (STO) (001) substrate, which is known to have an antiferromagnetic (AFM) insulating ground state. The EPS nano-network is a consequence of an internal strain relaxation triggered by the structural domain formation of the underlying STO substrate at low temperatures. The same nanoscale network pattern can be reproduced upon temperature cycling allowing us to employ different local imaging techniques to directly compare the magnetic and transport state of a single EPS domain. Our results confirm the one-to-one correspondence between ferromagnetic (AFM) to metallic (insulating) state in manganite. It also represents a significant step in a paradigm shift from passively characterizing EPS in strongly correlated systems to actively engaging in its manipulation

Insight-HXMT observations of Swift J0243.6+6124 during its 2017-2018 outburst

The recently discovered neutron star transient Swift J0243.6+6124 has been monitored by {\it the Hard X-ray Modulation Telescope} ({\it Insight-\rm HXMT). Based on the obtained data, we investigate the broadband spectrum of the source throughout the outburst. We estimate the broadband flux of the source and search for possible cyclotron line in the broadband spectrum. No evidence of line-like features is, however, found up to $\rm 150~keV$. In the absence of any cyclotron line in its energy spectrum, we estimate the magnetic field of the source based on the observed spin evolution of the neutron star by applying two accretion torque models. In both cases, we get consistent results with $B\rm \sim 10^{13}~G$, $D\rm \sim 6~kpc$ and peak luminosity of $\rm >10^{39}~erg~s^{-1}$ which makes the source the first Galactic ultraluminous X-ray source hosting a neutron star.Comment: publishe

Overview to the Hard X-ray Modulation Telescope (Insight-HXMT) Satellite

As China's first X-ray astronomical satellite, the Hard X-ray Modulation Telescope (HXMT), which was dubbed as Insight-HXMT after the launch on June 15, 2017, is a wide-band (1-250 keV) slat-collimator-based X-ray astronomy satellite with the capability of all-sky monitoring in 0.2-3 MeV. It was designed to perform pointing, scanning and gamma-ray burst (GRB) observations and, based on the Direct Demodulation Method (DDM), the image of the scanned sky region can be reconstructed. Here we give an overview of the mission and its progresses, including payload, core sciences, ground calibration/facility, ground segment, data archive, software, in-orbit performance, calibration, background model, observations and some preliminary results.Comment: 29 pages, 40 figures, 6 tables, to appear in Sci. China-Phys. Mech. Astron. arXiv admin note: text overlap with arXiv:1910.0443

Uniqueness of positive solutions to some Nonlinear Neumann Problems

Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem ⎧ ⎨ ⎩ div (ya∇u(x, y)) = 0, x ∈ Rn,y > 0, lim y→0+yauy(x, y) = −f(u(x, 0)), x ∈ Rn, under general nonlinearity assumptions on the function f : R → R for any constant a ∈ (−1, 1).peerReviewe

Asymptotic behaviors of solutions to quasilinear elliptic equations with hardy potential

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f(u), x ∈ RN , where 1 <p<N, 0 ≤ μ < ((N − p)/p) p, m > 0 and f is a continuous function.peerReviewe