A Generalized Multiscale Finite Element Method for the Brinkman Equation

In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the Brinkman model. In the fine grid, we use mixed finite element method with the velocity and pressure being continuous piecewise quadratic and piecewise constant finite element spaces, respectively. Using the GMsFEM framework we construct suitable coarse-scale spaces for the velocity and pressure that yield a robust mixed GMsFEM. We develop a novel approach to construct a coarse approximation for the velocity snapshot space and a robust small offline space for the velocity space. The stability of the mixed GMsFEM and a priori error estimates are derived. A variety of two-dimensional numerical examples are presented to illustrate the effectiveness of the algorithm.Comment: 22 page

Ultrastrong coupling few-photon scattering theory

We study the scattering of photons by a two-level system ultrastrongly coupled to a one-dimensional waveguide. Using a combination of the polaron transformation with scattering theory we can compute the one-photon scattering properties of the qubit for a broad range of coupling strengths, estimating resonance frequencies, lineshapes and linewidths. We validate numerically and analytically the accuracy of this technique up to $\alpha=0.3$, close to the Toulouse point $\alpha=1/2$, where inelastic scattering becomes relevant. These methods model recent experiments with superconducting circuits [P. Forn-D{\'\i}az et al., Nat. Phys. (2016)]

Generation of indistinguishable and pure heralded single photons with tunable bandwidth

We describe a new scheme to fully control the joint spectrum of paired photons generated in spontaneous parametric down-conversion. We show the capability of this method to generate frequency-uncorrelated photon pairs that are pure and indistinguishable, and whose bandwidth can be readily tuned. Importantly, the scheme we propose here can be implemented in any nonlinear crystal and frequency band of interest.Comment: 3 pages, 3 figure

Research on Pre-Service Teachers Multicultural Understanding: A Case Study of Exchange Student In Southwest University

Facing the global challenges of teacher education development and reform, the cultivation of teachers need to international vision and multicultural understanding. This paper selected exchange students of southwest university they went to university of Windsor as a case study, used interview and questionnaire survey research methods, explored the exchange students the basic understanding and view about multicultural understanding; It is attempted to explain the Chinese students at the university of Windsor during the internship experience culture influence, further find the multicultural understanding on the significance and value of pre-service teachers’ professional development