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Hongjun Gao

Publications and source records attributed to Hongjun Gao.

At least 55 records · Page 3Linked to original sources
arXiv2019

Electronic Structure of Exfoliated Millimeter-Sized Monolayer WSe2 on Silicon Wafer

The monolayer WSe2 is interesting and important for future application in nanoelectronics, spintronics and valleytronics devices, because it has the largest spin splitting and longest valley coherence time among all the known monolayer transition-metal dichalcogenides (TMDs). To obtain the large-area monolayer TMDs' crystal is the first step to manufacture scalable and high-performance electronic devices. In this letter, we have successfully fabricated millimeter-sized monolayer WSe2 single crystals with very high quality, based on our improved mechanical exfoliation method. With such superior samples, using standard high resolution angle-resolved photoemission spectroscopy, we did comprehensive electronic band structure measurements on our monolayer WSe2. The overall band features point it to be a 1.2eV direct band gap semiconductor. Its spin-splitting of the valence band at K point is found as 460 meV, which is 30 meV less than the corresponding band splitting in its bulk counterpart. The effective hole masses of valence bands are determined as 2.344 me at Gamma, and 0.529 me as well as 0.532 me at K for the upper and lower branch of splitting bands, respectively. And screening effect from substrate is shown to substantially impact on the electronic properties. Our results provide important insights into band structure engineering in monolayer TMDs. Our monolayer WSe2 crystals may constitute a valuable device platform.

cond-mat.mes-hall↗
arXiv2018

Periodic solution of stochastic process in the distributional sense

In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of periodic solution on bounded domain. Lastly, for the case that probability density function exists, we obtain the existence periodic solutions of the probability density function corresponding to the stochastic process by using the technique of deterministic partial differential equations.

math.PR↗
arXiv2018

Black Arsenic: A Layered Semiconductor with Extreme in-plane Anisotropy

Two-dimensional (2D) layered materials emerge in recent years as a new platform to host novel electronic, optical or excitonic physics and develop unprecedented nanoelectronic and energy applications. By definition, these materials are strongly anisotropic between within the basal plane and cross the plane. The structural and property anisotropies inside their basal plane, however, are much less investigated. Herein, we report a rare chemical form of arsenic, called black-arsenic (b-As), as an extremely anisotropic layered semiconductor. We have performed systematic characterization on the structural, electronic, thermal and electrical properties of b-As single crystals, with particular focus on its anisotropies along two in-plane principle axes, armchair (AC) and zigzag (ZZ). Our analysis shows that b-As exhibits higher or comparable electronic, thermal and electric transport anisotropies between the AC and ZZ directions than any other known 2D crystals. Such extreme in-plane anisotropies are able to potentially implement novel ideas for scientific research and device applications.

cond-mat.mtrl-sci↗
arXiv2018

The effect of noise intensity on stochastic parabolic equations

In the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabolic equations. By utilising Itô's formula and the energy estimate method, we obtain the excitation indices of the energy solutions $u$ at any finite time $t$. Furthermore, we improve certain existing results in the literature by presenting a comparably simple method to show those existing results.

math.PR↗
arXiv2018

Regularity of stochastic nonlocal diffusion equations

In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the Hölder continuity (locally in the whole state space $\mathbb{R}^d$) for mild solutions of stochastic nonlocal diffusion equations in the sense that the solutions $u$ belong to the space $C^γ(D_T;L^p(Ω))$ with the optimal Hölder continuity index $γ$ (which is given explicitly), where $D_T:=[0,T]\times D$ for $T>0$, and $D\subset\mathbb{R}^d$ being a bounded domain. Then, by utilising tail estimates, we are able to obtain the estimates of mild solutions in $L^p(Ω;C^{γ^*}(D_T))$. What's more, we give an explicit formula between the two index $γ$ and $γ^*$. Moreover, we prove Hölder continuity for mild solutions on bounded domains. Finally, we present a new criteria to justify Hölder continuity for the solutions on bounded domains. The novelty of this paper is that our method are suitable to the case of time-space white noise.

math.PR↗
arXiv2018

Exponential Stability of Solutions to Stochastic Differential Equations Driven by G-Levy Process

In this paper, BDG-type inequality for G-stochastic calculus with respect to G-Levy process is obtained and solutions of stochastic differential equations driven by G-Levy process under non-Lipschitz condition are constructed. Moreover, we establish the mean square exponential stability and quasi sure exponential stability of the solutions be means of G-Lyapunov function method. An example is presented to illustrate the efficiency of the obtained results.

math.PR↗
arXiv2017

A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise

This paper is concerned with the stochastic generalized Ginzburg-Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of an initial-boundary value problem with homogeneous Dirichlet boundary condition. However, for the generalized Ginzburg-Landau equation, such a locally monotonic condition of the nonlinear term can not be satisfied in a straight way. For this, we utilize the characteristic structure of nonlinear term and refined analysis to overcome this gap.

math.AP↗
arXiv2017

Existence and uniqueness of $W^{1,r}_{loc}$-solutions for stochastic transport equations

We investigate a stochastic transport equation driven by a multiplicative noise. For $L^q(0,T;W^{1,p}({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient and $W^{1,r}({\mathbb R}^d)$ initial data, we obtain the existence and uniqueness of stochastic strong solutions (in $W^{1,r}_{loc}({\mathbb R}^d))$.In particular, when $r=\infty$, we establish a Lipschitz estimate for solutions and this question is opened by Fedrizzi and Flandoli in case of $L^q(0,T;L^p({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient. Moreover, opposite to the deterministic case where $L^q(0,T;W^{1,p}({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient and $W^{1,p}({\mathbb R}^d)$ initial data may induce non-existence for strong solutions (in $W^{1,p}_{loc}({\mathbb R}^d)$), we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. It is an interesting example of a deterministic PDE that becomes well-posed under the influence of a multiplicative Brownian type noise. We extend the existing results \cite{FF2,FGP1} partially.

math.AP↗
arXiv2017

Strong solution for stochastic transport equations with irregular drift: existence and non-existence

We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a $q$-integrable (in time), bounded and $α$-Hölder continuous (in space) drift coefficient. More precisely, we show that for a Sobolev differentiable initial condition, there exists a unique stochastic strong solution when $α>2/q$, while for $α+1<2/q$ with spatial dimension higher than one, we can choose proper initial data and drift coefficients so that there is no stochastic strong solutions.

math.AP↗
arXiv2017

An exact solution for geophysical trapped waves in the presence of an underlying current

In this paper we propose an exact and explicit nonlinear solution to the governing equations which retains all the Coriolis terms. In the presence of an underlying current, we seek the trapped waves induced by these solutions in Northern and Southern hemisphere respectively, showing that the retention of the Coriolis force in the governing equations affects significantly the range of the admissible following and adverse currents.

math.AP↗
arXiv2017

BMO estimates for stochastic singular integral operators and its application to PDEs with Lévy noise

In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises \bess du_t(x)=Δ^{\fracα{2}}u_t(x)dt+\sum_{k=1}^\infty\int_{\mathbb{R}^m}g^k(t,x)z\tilde N_k(dz,dt),\ \ \ u_0=0,\ 0\leq t\leq T, \eess where $Δ^{\fracα{2}}=-(-Δ)^{\fracα{2}}$, and $\int_{\mathbb{R}^m}z\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump Lévy processes with Lévy measure of $ν^k$. Following the idea of \cite{Kim}, we obtain the $q$-th order BMO quasi-norm of the $\fracα{q_0}$-order derivative of $u$ is controlled by the norm of $g$.

math.PR↗
arXiv2017

Morrey-Campanato estimates for the moments of stochastic integral operators and its application to SPDEs

In this paper, we are concerned with the estimates for the moments of stochastic convolution integrals. We first deal with the stochastic singular integral operators and we aim to derive the Morrey-Campanato estimates for the $p$-moments (for $p\ge1$). Then, by utilising the embedding theory between the Campanato space and Hölder space, we establish the norm of $C^{θ,θ/2}(\bar D)$, where $θ\ge0, \bar D=\bar G\times[0,T]$ for arbitrarily fixed $T\in(0,\infty)$ and $G\subset\mathbb{R}^d$. As an application, we consider the following stochastic (fractional) heat equations with additive noises \bess du_t(x)=Δ^αu_t(x)dt+g(t,x)dη_t,\ \ \ u_0=0,\ 0\leq t\leq T, x\in G, \eess where $Δ^α=-(-Δ)^α$ with $0<α\leq1$ (the fractional Laplacian), $g:[0,T]\times G\timesΩ\to\mathbb{R}$ is a joint measurable coefficient, and $η_t, t\in[0,T]$, is either the Brownian motion or a Lévy process on a given filtered probability space $(Ω,\mathcal{F},P;\{\mathcal{F}_t\}_{t\in[0,T]})$. The Schauder estimate for the $p$-moments of the solution of the above equation is obtained. The novelty of the present paper is that we obtain the Schauder estimate for parabolic stochastic partial differential equations with Lévy noise.

math.PR↗
arXiv2016

Stochastic 3D Navier-Stokes equations with nonlinear damping: martingale solution, strong solution and small time large deviation principles

In this paper, by using classical Faedo-Galerkin approximation and compactness method, the existence of martingale solutions for the stochastic 3D Navier-Stokes equations with nonlinear damping is obtained. The existence and uniqueness of strong solution are proved for $β> 3$ with any $α>0$ and $α\geq \frac12$ as $β= 3$. Meanwhile, a small time large deviation principle for the stochastic 3D Navier-Stokes equation with damping is proved for $β> 3$ with any $α>0$ and $α\geq \frac12$ as $β= 3$.

math.AP↗
arXiv2016

Direct observation of local Rashba spin polarization and spin-layer locking in centrosymmetric monolayer PtSe$_2$

The generally accepted view that spin polarization is induced by the asymmetry of the global crystal space group has limited the search for spintronics [1] materials to non-centrosymmetric materials. Recently it has been suggested that spin polarization originates fundamentally from local atomic site asymmetries [2], and therefore centrosymmetric materials may exhibit previously overlooked spin polarizations. Here by using spin- and angle-resolved photoemission spectroscopy (spin-ARPES), we report helical spin texture induced by local Rashba effect (R-2) in centrosymmetric monolayer PtSe$_2$ film. First-principles calculations and effective analytical model support the spin-layer locking picture: in contrast to the spin splitting in conventional Rashba effect (R-1), the opposite spin polarizations induced by R-2 are degenerate in energy while spatially separated in the top and bottom Se layers. These results not only enrich our understanding of spin polarization physics, but also may find applications in electrically tunable spintronics.

cond-mat.mtrl-sci↗
arXiv2015

Analysis of a non-autonomous mutualism model driven by Levy jumps

This article is concerned with a mutualism ecological model with Levy noise. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded and stochastic permanence. The sufficient conditions for the system to be extinct are given and the condition for the system to be persistent are also established.

math.AP↗
arXiv2014

Analysis of a mutualism model with stochastic perturbations

This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic permanence. The sufficient conditions for the system to be extinct are given and the condition for the system to be persistent are also established. At last, some figures are presented to illustrate our main results.

math.AP↗