arXiv subjects

Hang Chen

Publications and source records attributed to Hang Chen.

98 records · Page 6Linked to original sources

arXiv2019

Investigation of spin orbit torque driven dynamics in ferromagnetic heterostructures

We use time-resolved (TR) measurements based on the polar magneto-optical Kerr effect (MOKE) to study the magnetization dynamics excited by spin orbit torques in Py (Permalloy)/Pt and Ta/CoFeB bilayers. The analysis reveals that the field-like (FL) spin orbit torque (SOT) dominates the amplitude of the first oscillation cycle of the magnetization precession and the damping-like (DL) torque determines the final steady-state magnetization. In our bilayer samples, we have extracted the effective fields, hFL and hDL, of the two SOTs from the time-resolved magnetization oscillation spectrum. The extracted values are in good agreement with those extracted from time-integrated DCMOKE measurements, suggesting that the SOTs do not change at high frequencies. We also find that the amplitude ratio of the first oscillation to steady state is linearly proportional to the ratio hFL/hDL. The first oscillation amplitude is inversely proportional to, whereas the steady state value is independent of, the applied external field along the current direction.

cond-mat.mtrl-sci↗

arXiv2019

Assessment of central serous chorioretinopathy (CSC) depicted on color fundus photographs using deep Learning

To investigate whether and to what extent central serous chorioretinopathy (CSC) depicted on color fundus photographs can be assessed using deep learning technology. We collected a total of 2,504 fundus images acquired on different subjects. We verified the CSC status of these images using their corresponding optical coherence tomography (OCT) images. A total of 1,329 images depicted CSC. These images were preprocessed and normalized. This resulting dataset was randomly split into three parts in the ratio of 8:1:1 respectively for training, validation, and testing purposes. We used the deep learning architecture termed InceptionV3 to train the classifier. We performed nonparametric receiver operating characteristic (ROC) analyses to assess the capability of the developed algorithm to identify CSC. The Kappa coefficient between the two raters was 0.48 (p < 0.001), while the Kappa coefficients between the computer and the two raters were 0.59 (p < 0.001) and 0.33 (p < 0.05).Our experiments showed that the computer algorithm based on deep learning can assess CSC depicted on color fundus photographs in a relatively reliable and consistent way.

cs.CV↗

arXiv2018

Sharp Reilly-type inequalities for submanifolds in space forms

Let $M$ be an $n(>2)$-dimensional closed orientable submanifold in an $(n+p)$-dimensional space form $\mathbb{R}^{n+p}(c)$. We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on $M$ defined by $L_{T}f=-div(T\nabla f)$, where $T$ is a general symmetric, positive definite and divergence-free $(1,1)$-tensor on $M$. The upper bound is given in terms of an integration involving $tr T$ and $|H_T|^2$, where $tr T$ is the trace of the tensor $T$ and $H_T=\sum_{i=1}^nA(Te_i,e_i)$ is a normal vector field associated with $T$ and the second fundamental form $A$ of $M$. Furthermore, we give the sufficient and necessary conditions when the upper bound is attained. Our main theorem can be viewed as an extension of the famous `Reilly inequality'. The operator $L_{T}$ can be regarded as a natural generalization of the well-known operator $L_r$ which is the linearized operator of the first variation of the $(r+1)$-th mean curvature for hypersurfaces in a space form. As applications of our main theorem, we generalize the results of Grosjean ([16]) and Li-Wang ([19]) for hypersurfaces to higher codimension case.

math.DG↗

arXiv2018

Reilly-type inequalities for $p$-Laplacian on submanifolds in space forms

Let $M$ be an $n$-dimensional closed orientable submanifold in an $N$-dimensional space form. When $1<p \le \frac n2 + 1$, we obtain an upper bound for the first nonzero eigenvalue of the $p$-Laplacian in terms of the mean curvature of $M$ and the curvature of the space form. This generalizes the Reilly inequality for the Laplacian [9, 15] to the $p$-Laplacian and extends the work of [8] for the $p$-Laplacian.

math.DG↗

arXiv2018

Rigidity of minimal submanifolds in space forms

In this paper, we consider the rigidity for an $n(\geq 4)$-dimensional submanfolds $M^n$ with parallel mean curvature in the space form ${\mathbb M}^{n+p}_c$ when the integral Ricci curvature of $M$ has some bound. We prove that, if $c+H^2>0$ and $\|\mathrm{Ric}_{-}^λ\|_{n/2}< ε(n,c, λ, H)$ for $λ$ satisfying $ \frac{n-2}{n-1} (c+H^2) < λ\le c+H^2$, then $M$ is the totally umbilical sphere $\mathbb{S}^n(\tfrac{1}{\sqrt{c+H^2}})$. Here $H$ is the norm of the parallel mean curvature of $M$, and $ε(n,c,λ, H)$ is a positive constant depending only on $n, c,λ$ and $H$. This extends some of the earlier work of [15] from pointwise Ricci curvature lower bound to inetgral Ricci curvature lower bound.

math.DG↗

arXiv2017

Hadronic coupling constants of $g_{σππ}$ in lattice QCD

We investigate the coupling constant $g_{σππ}$ for the hadronic decay $σ\toππ$ only using the relevant three-point function, which is evaluated by the moving-wall source technique with a pretty good noise-to-signal ratio. This simulation is carried out on a $40^3\times96$ MILC gauge configuration with $N_f=2+1$ flavor of the "Asqtad" improved staggered dynamical sea quarks at the lattice spacing $a \approx 0.09$ fm. Our estimated value for this given MILC fine lattice gauge ensemble $g_{σππ}=2.71(42)$ GeV.

hep-lat↗

arXiv2012

On stable compact minimal submanifolds of Riemannian product manifolds

In this paper, we prove a classification theorem for the stable compact minimal submanifolds of the Riemannian product of an $m_1$-dimensional ($m_1\geq3$) hypersurface $M_1$ in the Euclidean space and any Riemannian manifold $M_2$, when the sectional curvature $K_{M_1}$ of $M_1$ satisfies $\frac{1}{\sqrt{m_1-1}}\leq K_{M_1}\leq 1.$ This gives a generalization to the results of F. Torralbo and F. Urbano [9], where they obtained a classification theorem for the stable minimal submanifolds of the Riemannian product of a sphere and any Riemannian manifold. In particular, when the ambient space is an $m$-dimensional ($m\geq3$) complete hypersurface $M$ in the Euclidean space, if the sectional curvature $K_{M}$ of $M$ satisfies $\frac{1}{\sqrt{m+1}}\leq K_{M}\leq 1$, then we conclude that there exist no stable compact minimal submanifolds in $M$.

math.DG↗

arXiv2011

Constant Angle Surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$

In this article we study surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$ for which the $\mathbb{R}$-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature vector.

math.DG↗