On the Regularity for 3D Navier-Stokes Equation

This paper deals with the influence of boundary values on the regularity of 3D incompressible Navier-Stokes equation, which is separated into two parts: First part, we consider the potential theory of unsteady 3D Stokes flow. In order to consider Dirichlet and Neumann boundary values, we establish the Green's formula, and then give the double layer and single layer potentials. Second part, based on problems separated and the potential theory we reach the integral representations of the solutions with respect to Dirichlet and Neumann boundary conditions. Consequently we change the integral representations of solutions from velocity form into vorticity form so that we can construct schemes in favor of numerical computation in this way. Finally we analyze the regularity of the initial-boundary value problems for Navier-Stokes equation, and obtain regular solutions by assuming the regularity on the boundary and data.Comment: modificatio

Some issues about neutrino processes in color superconducting quark matter

Several relevant issues in computing neutrino emissivity in Urca processes in color superconducting quark matter are addressed. These include: (1) The constraint on $u$ quark abundance is given from electric neutrality and the triangle relation among Fermi momenta for participants. (2) The phase space defined by Fermi momentum reduction of quarks is discussed in QCD and NJL model. (3) Fermi effective model of weak interaction is reviewed with special focus on its form in Nambu-Gorkov basis.Comment: Contribution to the proceedings of the Sixth China-Japan Joint Nuclear Physics Symposium, May 16-20, Shanghai China. aipproc format, 8 pages, 5 figure

Sidelobe Suppression for Capon Beamforming with Mainlobe to Sidelobe Power Ratio Maximization

High sidelobe level is a major disadvantage of the Capon beamforming. To suppress the sidelobe, this paper introduces a mainlobe to sidelobe power ratio constraint to the Capon beamforming. it minimizes the sidelobe power while keeping the mainlobe power constant. Simulations show that the obtained beamformer outperforms the Capon beamformer.Comment: 8 pages, 2 figure