Nonequilibrium Dynamical Systems

9710608布朗这笔拨款是对这个职业生涯中期派的研究计划的更新。这位来自EPSCoR态的理论家精通数值和分析技术，从动力学蒙特卡罗到实空间重整化群和有限尺寸标度等。他研究了空间关联和涨落在非平衡相变中的作用。这些相变可以在非均相催化的不同稳定状态之间，或者在高速公路或数据网络流的不同交通流状态之间。这些问题在数学上是相关的，属于外力驱动的非线性系统范式。它们可以表现出向稳定状态的转变，到周期性的时间或空间振荡，甚至是混沌行为。%振荡的化学反应、高速公路上的走走停停的交通以及网络数据流中的类似现象之间有什么共同之处？它们都是数学上相关的问题，涉及受外部驱动力影响的非线性系统。有不同的行为模式，不同模式之间的转换是这次续签拨款的研究主题。这位来自EPSCoR州的职业生涯中期PI正在成为使用尖端工具对这些问题进行复杂数学分析的领导者。***

9710608 Browne This grant is a renewal of this mid-career PI's research program. Coming from an EPSCOR state, this theorist has emerged as an ambidextrous expert in both numerical and analytical techniques, ranging from kinetic Monte Carlo to real space renormalization group and finite size scaling etc. He studies the role of spatial correlations and fluctuations in nonequilibrium phase transitions. These phase transitions can be between different steady states in heterogeneous catalysis or in various states of traffic flow on highways or data network flow. These problems are mathematically related as belonging to the paradigm of nonlinear systems driven by external forces. They can exhibit transitions to steady states, to periodic temporal or spatial oscillations and even chaotic behavior. %%% What is common between oscillating chemical reactions, stop and go traffic on highways and similar phenomena in network data flow? They are all mathematically related as problems involving nonlinear systems subject to external driving forces. There are different patterns of behavior and the transitions between different patterns are the subject of study in this renewal grant. This mid-career PI from an EPSCOR state is emerging as a leader in sophisticated mathematical analysis of these problems using cutting edge tools. ***