CONVERGENCE OF CHORIN-MARSDEN FORMULA FOR THE NAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

1.IntroductionDifferentkindsoffractionalstepmethodshavebeenappliedtosolvetheinitialboundaryvalueproblemsoftheNavier--Stokesequationsforviscousincompressibleflow.Thevortexmethoddevelopedin[5]byChorinisaschemewiththreeintermediatestepswheretheeffectsofconvectionandviscosityareseparated,andvortexsheetsarecreatedalongtheboundary.Asetofvortexblobsisintroducedtoapproximatethevorticityfield.Thesevortexblobsmovealongtheparticletrajectoriesintheconvectionstep,andtheymoverandomlyinthediffusionstep.The…     

The stability of a quantized vortex in a dilute Bose gas confined to a toroidal trap

We investigate the stability of a quantized vortex in a weakly interacting Bose gas, trapped in a toroidal container with hard walls. Calculating the excitation spectrum numerically and determining the stability condition by the Landau criterion, we examine the effect of reducing the confinement region of the condensate on the vortex stability. We find that tight confinement of the condensate increases the stabilization of the quantized vortex because an increase in the zero sound velocity due to tight confinement prevents the emergence of the elementary excitation which breaks superfluidity of the Bose system. We also discuss the experimental setup to observe such an effect.     

Unsteady effects on flame extinction limits during gaseous and two-phase flame/vortex interactions

In highly fluctuating flows, it happens that high values of the strain-rate do not induce extinction of the flame front. Unsteady effects minimize the flame response to rapidly varying strain fields. In the present study, the effects of time-dependent flows on non-premixed flames are investigated during flame/vortex interactions. Gaseous flames and spray flames in the external sheath combustion regime are considered. To analyse the flame/vortex interaction process, the velocity field and the flame geometry are simultaneously determined using particle imaging velocimetry and laser-induced fluorescence of the CH radical. The influence of vortex flows on the extinction limits for different vortex parameters and for different gaseous and two-phase flames is examined. If the external perturbation is applied over an extended period of time, the extinction strain-rate is that corresponding to the steady-state flame, and this critical value mainly depends on the fuel and oxidizer compositions and the injection temperature. If the external perturbation is applied during a short period of time, extinction occurs at strain-rates above the steady-state extinction strain-rate. This deviation appears for flow fluctuation timescales below steady flame diffusion timescales. This behaviour is induced by diffusive processes, limiting the ability of the flame to respond to highly fluctuating flows. With respect to unsteady effects, the spray flames investigated in this article behave essentially like gaseous flames, because evaporation takes place in a thin layer before the flame front. Extinction limits are only slightly modified by the spray, controlling process being the competition between aerodynamic and diffusive timescales.     

高压下 MgB2 超导的涡旋动力学研究*

我们首次通过磁弛豫的方法系统研究了高压下 MgB2 样品的磁通钉扎以及涡旋动力学, 测量了其在不同温度和磁场下的磁化强度 M 随时间t 的衰变, 即 M(t) . 根据集体蠕动理论, 明确了高压效应在低磁场时抑制了磁衰变速率, 但在高场下大大的加快了磁衰变. 高压降低了临界电流密度J c 和钉扎能. 另外, 在 MgB2 样品里低场下没有观测到弹性蠕变向塑性蠕变的转变.