arXiv subjects

Ya Gao

Publications and source records attributed to Ya Gao.

48 records · Page 3Linked to original sources

arXiv2021

Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$ along the inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $\mathscr{H}^{n}(1)$, as time tends to infinity.

math.DG↗

arXiv2021

An anisotropic inverse mean curvature flow for spacelike graphic curves in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$

In this paper, we consider the evolution of spacelike graphic curves defined over a piece of hyperbola $\mathscr{H}^{1}(1)$, of center at origin and radius $1$, in the $2$ dimensional Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic curves converge smoothly to a piece of hyperbola of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $\mathscr{H}^{1}(1)$, as time tends to infinity.

math.DG↗

arXiv2021

Inverse Gauss curvature flow in a time cone of Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$ along the inverse Gauss curvature flow (i.e., the evolving speed equals the $(-1/n)$-th power of the Gaussian curvature) with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of the spacelike graph of a positive constant function defined over the piece of $\mathscr{H}^{n}(1)$ as time tends to infinity.

math.DG↗

arXiv2021

An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $\mathscr{H}^{n} (1)$, as time tends to infinity. Clearly, this conclusion is an extension of our previous work [2].

math.DG↗

arXiv2021

Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$

In this paper, we investigate the evolution of spacelike curves in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$ along prescribed geometric flows (including the classical curve shortening flow or mean curvature flow as a special case), which correspond to a class of quasilinear parabolic initial boundary value problems, and can prove that this flow exists for all time. Moreover, we can also show that the evolving spacelike curves converge to a spacelike straight line or a spacelike Grim Reaper curve as time tends to infinity.

math.DG↗

arXiv2021

A stability result for translating space-like graphs in Lorentz manifolds

In this paper, we investigate space-like graphs defined over a domain $Ω\subset M^{n}$ in the Lorentz manifold $M^{n}\times\mathbb{R}$ with the metric $-ds^{2}+σ$, where $M^{n}$ is a complete Riemannian $n$-manifold with the metric $σ$, $Ω$ has piecewise smooth boundary, and $\mathbb{R}$ denotes the Euclidean $1$-space. We can prove an interesting stability result for translating space-like graphs in $M^{n}\times\mathbb{R}$ under a conformal transformation.

math.DG↗

arXiv2020

Dicke States Generation via Selective Interactions in Dicke-Stark Model

We propose a method to create selective interactions with Dicke-Stark model by means of time-dependent perturbation theory. By choosing the proper rotating framework, we find that the time oscillating terms depend on the number of atomic excitations and the number of photonic excitations. Consequently, the Rabi oscillation between selective states can be realized by properly choosing the frequency of the two-level system. The second order selective interactions can also be studied with this method. Then various states such as Dicke states, superposition of Dicke states and GHZ states can be created by means of such selective interactions. The numerical results show that high fidelity Dicke states and Greenberger-Horne-Zeilinger states can be created by choosing the proper frequency of two-level system and controlling the evolution time.

quant-ph↗

arXiv2020

Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$

In this paper, we can prove the existence and uniqueness of solutions to the constant mean curvature (CMC for short) equation with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\mathbb{R}$ is the Euclidean $1$-space. Equivalently, this conclusion gives the existence of CMC graphic hypersurfaces defined over a compact strictly convex domain $Ω\subset M^{n}$ and having arbitrary contact angle.

math.DG↗

arXiv2020

Translating solutions of the nonparametric mean curvature flow with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$

In this paper, we can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\mathbb{R}$ is the Euclidean $1$-space.

math.DG↗

arXiv2019

Evaluation of the $θ_K$ and the Mixing angle $θ_{h_1}$

The $θ_K$ has been re-evaluated via mass relations and latest experimental results, meanwhile, the $M_{K_{1B}}$ also be obtained. Based on the singlet-octet mixing model and quark-flavor mixing model, the $θ_{h_1}$ has been recalculated with a modified formula, by inputting $M_{K_{1B}}$ instead of $θ_K$. The values are calculated to be $|{θ_K}| = {(42.6 \pm 2.2)^ \circ }$, $M_{K_{1B}} = 1333.9 \pm 4.6\ {\rm{MeV}}/c^{2}$ and $θ_{h_1} = 29.5\pm 2.0^\circ$. Using these calculations as input, we predict that the branching fraction of $J/ψ\to η'(η)h_1(1170)$ is about one order higher than that of $J/ψ\to η'(η)h_1(1415)$, which can be measured in future experiments to test the validity of these two models.

hep-ph↗

arXiv2019

Dynamic and programmable cellular-scale granules enable tissue-like materials

Tissue-like materials are required in many robotic systems to improve human-machine interactions. However, the mechanical properties of living tissues are difficult to replicate. Synthetic materials are not usually capable of simultaneously displaying the behaviors of the cellular ensemble and the extracellular matrix. A particular challenge is identification of a cell-like synthetic component which is tightly integrated with its matrix and also responsive to external stimuli at the population level. Here, we demonstrate that cellular-scale hydrated starch granules, an underexplored component in materials science, can turn conventional hydrogels into tissue-like materials when composites are formed. Using several synchrotron-based X-ray techniques, we reveal the mechanically-induced motion and training dynamics of the starch granules in the hydrogel matrix. These dynamic behaviors enable multiple tissue-like properties such as strain-stiffening, anisotropy, mechanical heterogeneity, programmability, mechanochemistry, impact absorption, and self-healability. The starch-hydrogel composites can be processed as robotic skins that maintain these tissue-like characteristics.

cond-mat.soft↗

arXiv2017

Network-Scale Traffic Modeling and Forecasting with Graphical Lasso and Neural Networks

Traffic flow forecasting, especially the short-term case, is an important topic in intelligent transportation systems (ITS). This paper does a lot of research on network-scale modeling and forecasting of short-term traffic flows. Firstly, we propose the concepts of single-link and multi-link models of traffic flow forecasting. Secondly, we construct four prediction models by combining the two models with single-task learning and multi-task learning. The combination of the multi-link model and multi-task learning not only improves the experimental efficiency but also the prediction accuracy. Moreover, a new multi-link single-task approach that combines graphical lasso (GL) with neural network (NN) is proposed. GL provides a general methodology for solving problems involving lots of variables. Using L1 regularization, GL builds a sparse graphical model making use of the sparse inverse covariance matrix. In addition, Gaussian process regression (GPR) is a classic regression algorithm in Bayesian machine learning. Although there is wide research on GPR, there are few applications of GPR in traffic flow forecasting. In this paper, we apply GPR to traffic flow forecasting and show its potential. Through sufficient experiments, we compare all of the proposed approaches and make an overall assessment at last.

cs.LG↗