Three-dimensional Dynamics of Quan

我们研究了超流氦中量子化涡的三维动力学。首先，我们研究了模拟通道表面粗糙度的涡旋钉钉。在讨论了涡旋被吸引到钉住点的条件后，研究了钉住点的承载力；一个固定点只能保持少于5个漩涡。所得的临界脱屑速度与一些热逆流实验结果进行了比较。其次，研究了旋转超流体的涡旋动力学。已知旋转的超流体会形成一组平行于旋转轴的漩涡，但对其动力学知之甚少。因此，我们进行了二维分析，研究了典型的动力学问题自旋下降过程中涡阵的形成及其衰减。然而，仅仅进行二维分析是不足以了解真实系统的。因此进行了三维分析。对旋转球形容器中超流体的数值计算发现，在边界处形成成核小涡所需的容器角速度大于观测到的单涡成核临界角速度；在实际系统中，非成核涡和一些残余涡可能起着重要的作用。详细研究了自旋降过程中阵列的衰减。研究了孤子沿涡旋的传播。

We have studied three-dimensional dynamics of quantized vortices in superfluid helium. First, we investigated vortex pinning that simulates the roughness of the channel surface. After the condition that vortices are attracted to a pinning site is discussed, the capacity of a pinning site is studied ; a pinning site can keep only less than five vortices. The obtained critical depinning velocities are compared with some experimental results for thermal counterflow. Secondly, vortex dynamics in rotating superfluid is studied. A rotating superfluid is known to form an array of vortices which are paralled to the rotational axis, yet very little is understood about the dynamics. Thus we made two-dimensional analysis, studying the formation of vortex arrays and its decay in spin-down processes which are typical of dynamical problems. However, only two-dimensional analysis is insufficient to understand the real system. Hence three-dimensional analysis was made. The numerical calculation for a superfluid in a rotating spherical vessel found that the angular velocity of the vessel necessary for stretching a small vortex nucleated at the boundary is larger than the observed critical angular velocity for one-vortex nucleation ; not a nucleated vortex but some remnant vortices may play an important role in a real system. The array decay through the spin-down processes is studied in detail. The propagation of a soliton along a vortex is investigated.