arXiv subjects

Tao Tao

Publications and source records attributed to Tao Tao.

40 records · Page 3Linked to original sources

arXiv2017

Sharp interface limit of a diffuse interface model for tumor-growth

We consider the asymptotic limit of a diffuse interface model for tumor-growth when a parameter $\varepsilon$ proportional to the thickness of the diffuse interface goes to zero. An approximate solution which shows explicitly the behavior of the true solution for small $\varepsilon$ will be constructed by using matched expansion method. Based on the energy method, a spectral condition in particular, we establish a smallness estimate of the difference between the approximate solution and the true solution.

math.AP↗

arXiv2016

On the zero-viscosity limit of the Navier-Stokes equations in the half-space

We consider the zero viscosity limit of the incompressible Navier-Stokes equations with non-slip boundary condition in the half-space for the initial vorticity located away from the boundary. By using the vorticity formulation and Cauchy-Kowaleskaya theorem, Maekawa proved the local in time convergence of the Navier-Stokes equations in the half- plane to the Euler equations outside a boundary layer and to the Prandtl equations in the boundary layer. In this paper, we develop the direct energy method to generalize Maekawa's result to the half-space.

math.AP↗

arXiv2015

On The Continuous Periodic Weak Slution of Boussinesq Equations

The Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics. We show the existence of continuous periodic weak solutions of the Boussinesq equations which satisfies the prescribed kinetic energy or some other prescribed property. Our results represent the conversions between internal energy and mechanical energy.

math.AP↗

arXiv2013

Iterative Grassmannian Optimization for Robust Image Alignment

Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found application in many areas of computer vision. In image and video processing and face recognition, the opportunity to process massive image databases is emerging as people upload photo and video data online in unprecedented volumes. However, data quality and consistency is not controlled in any way, and the massiveness of the data poses a serious computational challenge. In this paper we present t-GRASTA, or "Transformed GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm)". t-GRASTA iteratively performs incremental gradient descent constrained to the Grassmann manifold of subspaces in order to simultaneously estimate a decomposition of a collection of images into a low-rank subspace, a sparse part of occlusions and foreground objects, and a transformation such as rotation or translation of the image. We show that t-GRASTA is 4 $\times$ faster than state-of-the-art algorithms, has half the memory requirement, and can achieve alignment for face images as well as jittered camera surveillance images.

cs.CV↗