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- Shidong Jiang, L Greengard
- 2004

We present a fast algorithm for the evaluation of the exact nonreflecting boundary conditions for the SchrSdinger equation in one dimension. The exact nonrefleeting boundary condition contains a nonloeal term which is a convolution integral in time, with a kernel proportional to 1/v~. The key observation is that this integral can be split into two parts: a… (More)

- Zhi Liang, Zydrunas Gimbutas, Leslie Greengard, Jingfang Huang, Shidong Jiang
- J. Comput. Physics
- 2013

A detailed analysis is presented of all pseudo-differential operators of orders up to 2 encountered in classical potential theory in two dimensions. Each of the operators under investigation turns out to be a sum of one or more of standard operators (second derivative, derivative of the Hilbert transform, etc.), and an integral operator with smooth kernel.… (More)

A second kind integral equation formulation is presented for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples. The formulation is a simplification of the equation previously… (More)

- Yanming Wang, Shidong Jiang, +6 authors Yong Huang
- Chemical communications
- 2013

An anisotropic biocompatible composite PCL-PTFE film was used to guide smooth muscle cell outgrowth along defined directions.

- Shidong Jiang, Shravan K. Veerapaneni, Leslie Greengard
- SIAM J. Scientific Computing
- 2012

We present an integral equation formulation for the unsteady Stokes equations in two dimensions. This problem is of interest in its own right, as a model for slow viscous flow, but perhaps more importantly, as an ingredient in the solution of the full, incompressible Navier-Stokes equations. Using the unsteady Green's function, the velocity evolves… (More)

- Guoxing Li, Jinhua Sun, Wenpeng Hou, Shidong Jiang, Yong Huang, Jianxin Geng
- Nature communications
- 2016

Sulfur is a promising cathode material for lithium-sulfur batteries because of its high theoretical capacity (1,675 mA h g(-1)); however, its low electrical conductivity and the instability of sulfur-based electrodes limit its practical application. Here we report a facile in situ method for preparing three-dimensional porous graphitic carbon composites… (More)

- Shidong Jiang, Leslie Greengard, Weizhu Bao
- SIAM J. Scientific Computing
- 2014

We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel U (x) and a density function ρ(x) = |ψ(x)| 2 for some complex-valued wave function ψ(x), permitting the formal use of Fourier methods. These are… (More)

We present a fast algorithm for the evaluation of exact nonreflecting boundary conditions for the time-dependent Schrödinger equation in two dimensions on the unit circle. After separation of variables, the exact outgoing condition for each Fourier mode contains a nonlocal term which is a convolution integral in time. The kernel for that convolution is the… (More)

- Huanli Dong, Shidong Jiang, +8 authors Xiong Gong
- Journal of the American Chemical Society
- 2009

In this paper, we show that well-defined, highly crystalline nanowires of a rigid rod conjugated polymer, a poly(para-phenylene ethynylene)s derivative with thioacetate end groups (TA-PPE), can be obtained by self-assembling from a dilute solution. Structural analyses demonstrate the nanowires with an orthorhombic crystal unit cell wherein the lattice… (More)