Nonlinear Stability and Instability of Fluid and Plasma Equilibria

研究员研究流体和等离子体中平衡的稳定性和不稳定性，重点是流体中的二维欧拉方程和等离子体物理学和恒星动力学中的弗拉索夫系统。 他的目标是发展一般方法ofinding线性增长模式（特别是非对称modesand边界模式），调查非线性稳定性under夏普线性稳定性准则和非单调平衡，不能处理的通常的能量Casimir方法，并建立非线性不稳定性的线性不稳定性时，粒子轨迹是不可积的。 等离子体是一种由粒子组成的气体，每个粒子都带有正电荷或负电荷，每种电荷的浓度大致相等。 宇宙的大部分都是等离子体;例子包括太阳风、电离层、银河系星云和彗星尾巴。 等离子体也出现在物理学和工程学中，例如核聚变。 研究者研究流体和等离子体中平衡的稳定性和不稳定性。数学的进步增强了我们对控制稳定性和不稳定性的物理机制的理解，因此可以导致更好的数值方法来模拟这些复杂的现象。 流体稳定性对于理解海浪和大气运动的机制以及工程应用都很重要。 等离子体稳定性的问题出现在太阳黑子、基础等离子体物理、聚变机设计和等离子体显示设备等不同领域。

The investigator studies the stability and instability ofequilibria in fluids and plasmas, focusing on the two-dimensionalEuler equation in fluids and on Vlasov systems in plasma physicsand stellar dynamics. He aims to develop general methods offinding linearly growing modes (especially for asymmetric modesand boundary modes), to investigate nonlinear stability undersharp linear stability criteria and for non-monotonic equilibriathat cannot be handled by the usual energy-Casimir method, and toestablish nonlinear instability from linear instability when theparticle trajectory is non-integrable. A plasma is a gas composed of particles, each carrying apositive or negative electrical charge, with approximately equalconcentrations of each charge. Most of the universe is plasma;examples include the solar wind, the ionosphere, galactic nebulae,and comet tails. Plasmas also arise in physics and engineering,for instance in nuclear fusion. The investigator studies thestability and instability of equilibria in fluids and plasmas. Mathematical advances here enhance our understanding of thephysical mechanisms that govern stability and instability, and socan lead to better numerical methods for simulations of thesecomplex phenomena. Fluid stability is important in understandingthe mechanisms of ocean waves and the movements of the atmosphereas well as in engineering applications. Questions of plasmastability arise in areas as diverse as sunspots, fundamentalplasma physics, the design of fusion machines, and plasma displaydevices.