arXiv subjects

Hua Zhang

Publications and source records attributed to Hua Zhang.

113 records · Page 7Linked to original sources

arXiv2008

Magnetic properties of undoped Cu2O fine powders with magnetic impurities and/or cation vacancies

Fine powders of micron- and submicron-sized particles of undoped Cu2O semiconductor, with three different sizes and morphologies have been synthesized by different chemical processes. These samples include nanospheres 200 nm in diameter, octahedra of size 1 micron, and polyhedra of size 800 nm. They exhibit a wide spectrum of magnetic properties. At low temperature, T = 5 K, the octahedron sample is diamagnetic. The nanosphere is paramagnetic. The other two polyhedron samples synthesized in different runs by the same process are found to show different magnetic properties. One of them exhibits weak ferromagnetism with T_C = 455 K and saturation magnetization, M_S = 0.19 emu/g at T = 5 K, while the other is paramagnetic. The total magnetic moment estimated from the detected impurity concentration of Fe, Co, and Ni, is too small to account for the observed magnetism by one to two orders of magnitude. Calculations by the density functional theory (DFT) reveal that cation vacancies in the Cu2O lattice are one of the possible causes of induced magnetic moments. The results further predict that the defect-induced magnetic moments favour a ferromagnetically coupled ground state if the local concentration of cation vacancies, n_C, exceeds 12.5%. This offers a possible scenario to explain the observed magnetic properties. The limitations of the investigations in the present work, in particular in the theoretical calculations, are discussed and possible areas for further study are suggested.

cond-mat.mtrl-sci↗

arXiv2008

Global well-posedness and inviscid limit for the modified Korteweg-de Vries-Burgers equation

Considering the Cauchy problem for the modified Korteweg-de Vries-Burgers equation $u_t+u_{xxx}+ε|\partial_x|^{2α}u=2(u^{3})_x, u(0)=ϕ$, where $0<ε,α\leq 1$ and $u$ is a real-valued function, we show that it is uniformly globally well-posed in $H^s (s\geq1)$ for all $ε\in (0,1]$. Moreover, we prove that for any $s\geq 1$ and $T>0$, its solution converges in $C([0,T]; H^s)$ to that of the MKdV equation if $ε$ tends to 0.

math.AP↗

arXiv2008

Global Well-posedness for the fourth order nonlinear Schrödinger equations with small rough data in high demension

For $n\geq 2$, we establish the smooth effects for the solutions of the linear fourth order Shrödinger equation in anisotropic Lebesgue spaces with $\Box_k$-decomposition. Using these estimates, we study the Cauchy problem for the fourth order nonlinear Schrödinger equations with three order derivatives and obtain the global well posedness for this problem with small data in modulation space $M^{9/2}_{2,1}({\Real^{n}})$.

math.AP↗

arXiv2008

Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data

For $n\geq 3$, we study the Cauchy problem for the fourth order nonlinear Schrödinger equations, for which the existence of the scattering operators and the global well-posedness of solutions with small data in Besov spaces $B^{s}_{2,1}(\R^n)$ are obtained. In one spatial dimension, we get the global well-posedness result with small data in the critical homogeneous Besov spaces $\dot{B}^{s}_{2,1}$. As a by-product, the existence of the scattering operators with small data is also obtained. In order to show these results, the global version of the estimates for the maximal functions and the local smoothing effects on the fourth order Schrödinger semi-groups are established.

math.AP↗

arXiv2005

A $C^{r}$ Closing Lemma for a Class of Symplectic Diffeomorphisms

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense.

math.DS↗