Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient

This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local approximation property. Our methodology is based on the compactness of the solution operator restricted on local regions of the spatial domain, and does not depend on any scale-separation or periodicity assumption of the coefficient. We focus on a special type of basis functions that are harmonic on each element and have optimal approximation property. We first reduce our problem to approximating the trace of the solution space on each edge of the underlying mesh, and then achieve this goal through the singular value decomposition of an oversampling operator. Rigorous error estimates can be obtained through thresholding in constructing the basis functions. Numerical results for several problems with multiple spatial scales and high contrast inclusions are presented to demonstrate the compactness of the local solution space and the capacity of our method in identifying and exploiting this compact structure to achieve computational savings

Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations

We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in numerical computation. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find agree with direct simulation of the model and seem to have some stability

Menu or mandate? EU governance and party politics in Poland

This study was funded by China Scholarship Council (No. 201708060001).This article examines how the European Union (EU) has impacted party politics in Poland. Before the 2004 accession, party politics in Poland were turbulent. In this period, the EU, as a reference point, helped to create a pro- and anti-EU party cleavage. With this impact admitted, the article turns to the post-accession party politics. Centering on the nationalist Law and Justice (Prawo i Sprawiedliwość, PiS), the article attempts to explore the EU’s impact on the PiS by studying the latter’s adaptation preferences. To do so, I employ James N. Rosenau’s political adaptation theory. Central to the article is the argument that since political parties are the protagonists in member states’ domestic politics, the EU can only affect the party politics in Poland indirectly, but not inconsequentially. Without mandate notwithstanding, the EU can create bottom-up pressures through civil society; meanwhile, since EU norms and political parties’ particular interests are not necessarily incompatible, the EU can take the initiatives to make a balance between them through policy innovations.Publisher PDFPeer reviewe

Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations

We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier-Stokes equations, which demonstrates the potential stabilizing effect of convection

Dynamic modeling and sliding mode control of single cylinder double annular channels MRF damper

In order to satisfy the adjusting of recoil system of the gun to different firing conditions, a magneto-rheological fluid (MRF) damper with double annular channel is proposed, which can satisfy the maximum recoil displacement and reduce the force acting on the gun carriage. The double annular channels MRF damper has less zero field damping force and has a larger range of resistance regulation. The dynamic model of MRF damper considering inertia effect is established, and the mechanical properties of MRF damper are tested. The experimental results shown that the calculated values are in good agreement with the experimental values. According to the gun recoil dynamic model of MRF damper, a sliding mode tracking controller based on constant velocity reaching law is designed, and the recoil process of the gun is simulated. The results shown that the MRF damper damping force under the sliding mode control algorithm has a plateau effect, which can be used in the recoil motion control of the gun