This report considers methods for the solution of the time dependent Stokes Darcy problem that can be implemented by use of existing surface water and ground water codes. Porous media problems for groundwater flows overwhelmingly use mixed discretizations due to their superior conservation properties and the conservation for problems on large domains with relatively coarse meshes.

The Navier-Stokes equation coupled with the Darcy equation through interface conditions has attracted scientists’ attention due to its wide range of applications and significant difficulty in the nonlinearity and interface conditions. This presentation discusses a multi-physics domain decomposition method for decoupling the coupled Navier-Stokes-Darcy system with the Beavers-Joseph interface condition. The wellposedness of this system is first showed by using a branch of singular solutions and the existing theoretical results on the Beavers-Joseph interface condition.

In this talk, I will discuss quantile regression with group-specific parameters when the group membership is unknown. Identifying groups with homogeneous parameters can be viewed as a model-based clustering problem. I will first introduce a concave fusion penalization method that can perform simultaneous parameter estimation and group identification. The method relies on penalizing the differences of parameters between pairs of units and thus could be computationally costly for large samples. Next I will introduce an iterative two-step algorithm using a similar idea of k-means clustering to identify groups and estimate group-specific parameters for panel data. In practice the signal differentiating groups may vary across quantiles though the group membership may be common.

In this talk, I will discuss quantile regression with group-specific parameters when the group membership is unknown. Identifying groups with homogeneous parameters can be viewed as a model-based clustering problem. I will first introduce a concave fusion penalization method that can perform simultaneous parameter estimation and group identification. The method relies on penalizing the differences of parameters between pairs of units and thus could be computationally costly for large samples. Next I will introduce an iterative two-step algorithm using a similar idea of k-means clustering to identify groups and estimate group-specific parameters for panel data.

Exponential growth of the semiconductor industry, historically driven by transistor scaling, is now facing fundamental challenges. In this talk, I will discuss an emerging class of devices that, by merging electronic with ionics, offer the potential to control the materials’ electronic properties in-situ and have led to promising memory and circuit concepts. These devices exhibit history-dependent, resistive switching behavior and are termed memristors (memory + resistor) or resistive memory (RRAM) devices. I will discuss our efforts on the development and optimization of memristor devices and integrated systems, including techniques of controlling the dynamic ionic migration processes and associated modeling efforts. Functional high-density crossbar arrays have been integrated directly on top of CMOS circuits using a back-end-of-line (BEOL) process, enabling hybrid non-volatile memory and reconfigurable circuit applications.

Dirichlet problems for the second order elliptic partial differential equations have been studied for many years and obtained many existence results in 1980s. But there has been little research on Neumann problem in the past thirty years. In this talk, we will especially introduce Neumann problem for mean curvature equations and give the existence Theorem of classical solutions of mean curvature equations. The key point is to prove the boundary gradient estimate. (This is a joint work with Prof. Xinan Ma.

We discuss some results and problems concerning the construction of quantum channels with desired properties. No quantum mechanics background is required. Basic linear algebra knowledge is assumed.

Cone spherical, flat and hyperbolic metrics are conformal metrics with constant curvature +1; 0 and -1, respectively, and with finitely many conical singularities on compact Riemann surfaces. The Gauss-Bonnet formula gives a natural necessary condition for the existence of such three kinds of metrics with prescribed conical singularities on compact Riemann surfaces. The condition is also sufficient for both flat and hyperbolic metrics. However, it is not the case for cone spherical metrics, whose existence has been an open problem over twenty years. In this talk, we shall report the respectable audience the recent progresses on cone spherical metrics via Complex Analysis and Algebraic Geometry, which consist of several joint research works with Qing Chen, Lingguang Li, Jijian Song, Yingyi Wu and some of my (former) students.

The talk consists of four sections: 1. The algebras Wd,f Wd, Kd, gld 2. Shen’s monomorphism 3. Modules over Wn 4. The results This talk is based on: [X. Guo, G. Liu, R. Lu, K. Zhao, Simple Witt modules that are finitely generated over the Cartan subalgebra, arXiv:1705.03393].

We introduce a notion of a Nijenhuis operator on a pre-Lie algebra from the deformation theory. Then we explain the relationships between Nijenhuis operators and O-operators and Rota-Baxter operators. In particular, one can use Nijenhuis operators on a pre-Lie algebra to construct compatible O-operators as well as compatible L-dendriform algebras. The roles of Nijenhuis operators on pre-Lie algebras in some geometric structures are also interpreted.