Synchronization, Collective Behavior and Spatiotemporal Dynamics in Chemical Systems

在这个由化学系化学结构、动力学和机制计划(CSDM-A)资助的项目中，Kenneth Showalter教授和他的学生正在研究化学系统中的复杂动力学行为，以深入了解人造和生物系统中的新型动力学行为。在实验研究中发展对这种行为的理解有助于开发与某些生物和合成动力系统(如计算机网络)的行为相关的数学模型描述。对同步和集体行为的新状态的研究将为深入了解普遍存在于生命系统中的基本动态行为提供见解。对降水系统中波传播的研究将为化学波提供新的机制，这种机制依赖于介质的结构特征，很像许多生物系统中的波行为。耦合化学振荡器的网络将在实验室实验和计算模拟中进行研究。最近发现的嵌合体状态，其中同步振子和非同步振子群体共存，将被进一步研究，重点是二维耦合振子阵列中的螺旋嵌合体状态。我们还将利用二维振荡器阵列对耦合化学振荡器网络中的相位滞后同步进行进一步的实验研究，这将允许广泛的网络拓扑和耦合方案。理论上预测的回声现象将在耦合化学振荡器群体中进行研究。化学振荡器的二维阵列将允许足够大的种群，以允许检测和表征回声行为。将研究传播降水波的新构型和实例。将开发用于研究基于两性氢氧化钠-三氯化铝体系的再溶解沉淀带中的传播波的开放反应器配置。将研究导致类湍流动力学的不稳定螺旋波行为以及波浪堆积，其中波浪与其前面的波浪碰撞。将进一步开发一个传播降水波的通用三维计算模型，并将该模型扩展到描述开放式反应堆配置中的波动行为。

In this project funded by the Chemical Structure, Dynamics and Mechanisms Program (CSDM-A) of the Chemistry Division, Professor Kenneth Showalter and his students are studying complex dynamical behavior in chemical systems to gain insights into new types of dynamical behavior in man-made and living systems. Developing an understanding of such behavior in experimental studies facilitates the development of mathematical model descriptions that are relevant to the behavior of certain living organisms as well as synthetic dynamical systems such as computer networks. Research on new states of synchronization and collective behavior will provide insights into basic dynamical behaviors pervasive in living systems. Research on propagating waves in precipitation systems will offer new mechanisms for chemical waves that rely on structural features of the medium, much like wave behavior found in many biological systems.Networks of coupled chemical oscillators will be investigated in laboratory experiments and computational simulations. The recently discovered chimera state, in which populations of synchronized and unsynchronized oscillators coexist, will be further investigated, with the focus on the spiral chimera state in two-dimensional arrays of coupled oscillators. Further experimental investigations of phase-lag synchronization in networks of coupled chemical oscillators will also be carried out with two-dimensional oscillator arrays, which will allow a wide variety of network topologies and coupling schemes. Theoretically predicted echo phenomena will be investigated in populations of coupled chemical oscillators. Two-dimensional arrays of chemical oscillators will permit sufficiently large populations to allow the detection and characterization of echo behavior. New configurations and examples of propagating precipitation waves will be investigated. Open-reactor configurations will be developed for studies of propagating waves in redissolution precipitation bands based on the amphoteric sodium hydroxide-aluminum chloride system. Unstable spiral wave behavior leading to turbulence-like dynamics will be investigated as well as wave stacking, where waves collide with the waves ahead of them. Further development of a general three-dimensional computational model for propagating precipitation waves will be carried out as well as extending the model to describe wave behavior in open reactor configurations