Turitsyn Konstantin S, Lai Lipeng, Zhang Wendy W
Physics Department and the James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.
Phys Rev Lett. 2009 Sep 18;103(12):124501. doi: 10.1103/PhysRevLett.103.124501. Epub 2009 Sep 14.
The disconnection of an underwater bubble illustrates how slight initial asymmetries can prevent the formation of a finite-time singularity. Creating a singularity by focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present. We show a slight azimuthal asymmetry in the initial shape of the bubble neck excites vibrations that persist over time. As a result, the focusing singularity is generically preempted by a smooth contact.
水下气泡的断开说明了轻微的初始不对称性如何能够阻止有限时间奇点的形成。通过将有限量的能量动态地聚焦到极小量的物质中以产生奇点,这要求初始条件是完全对称的。而在现实中,总是存在不完美之处。我们发现,气泡颈部初始形状中轻微的方位角不对称会激发随时间持续存在的振动。结果,聚焦奇点通常会被平滑接触所取代。