Stability Problems in Plasma Physics, Stellar Dynamics and Classical Field Theory

由该奖项资助的研究将解决等离子体物理、恒星动力学和超导电性方面的问题。PI将构建模拟这些现象的偏微分方程组的稳态解，并将研究其动态稳定性。具体地说，将研究无碰撞等离子体的弗拉索夫模型、多变星系的模型以及显示涡旋的超导和超流模型。该奖项将资助对大量单个粒子相互作用现象的数学模型的研究。这些现象可能发生在等离子体、荧光灯内部的物理状态、制造微芯片的反应堆以及太阳内部。在这种情况下，原子粒子通过电磁力相互作用。相关现象也发生在宇宙尺度上，例如在星系中，相互作用的粒子是整个恒星，相互作用是通过引力进行的。这些非常不同的情况下的数学模型有相似之处。这项研究将研究平衡构型，如等离子体辅助制造设备的稳态操作或星系的稳定旋转，并试图了解其稳定性或稳定性丧失的方式。不稳定性可能意味着制造过程的效率降低或星系中旋臂的形成。

The research that is funded with this award will address problems inplasma physics, stellar dynamics, and superconductivity. The PI willconstruct steady state solutions of the partial differential equations thatmodel these phenomena and will study their dynamic stability. Specifically, the Vlasov model for collisionless plasmas, models for polytropic galaxies,and models for superconductivity and superfluidity that exhibit vortices willbe investigated. This award will fund research on mathematical models for phenomena inwhich huge numbers of individual particles interact. These phenomena can occur in plasmas, the physical state of the interior of fluorescent lights, manufacturing reactors for microchips, and of the interior of the sun. In this case, atomic particles interact by means of electromagnetic forces. Related phenomena also occur on cosmic scales, for instance in galaxies, where the interacting particles are entire stars and the interaction is by means of gravitation. The mathematical models for these very different situations have similarities. The research will study equilibrium configurations such as the steady state operation of a plasma-assisted manufacturing device or the steady rotation of a galaxy and seek to understand its stability or the ways in which stability is lost. Instability may mean loss of efficiency for a manufacturing process or the formation of spiral arms in a galaxy.