Three-dimensional Dynamics of Quan

我们研究了超流氦中量子化涡旋的三维动力学。首先，我们研究了模拟沟道表面粗糙度的涡钉扎。在讨论了钉扎位置吸引涡旋的条件后，研究了钉扎位置的容量，一个钉扎位置只能保持少于5个涡旋。将所得到的临界脱钉速度与热逆流实验结果进行了比较。其次，研究了旋转超流体中的涡旋动力学。众所周知，旋转的超流体会形成一系列平行于旋转轴的涡流，但人们对其动力学知之甚少。因此，我们进行了二维分析，研究了旋涡阵列的形成及其在自旋下降过程中的衰减，这是典型的动力学问题。然而，仅有二维分析是不足以理解真实系统的。在此基础上进行了三维分析。对旋转球形容器中超流体的数值计算发现，在边界处成核的小涡拉伸所需的容器的角速度大于观察到的单涡成核的临界角速度，而不是成核涡，而是一些残留的涡在实际系统中可能起到重要作用。详细研究了阵列在自旋下降过程中的衰减过程。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.