Wave turbulence and collective behavior models for wave equations with short- and long-range interactions
Wave turbulence and collective behavior models for wave equations with short- and long-range interactions
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DOI：
10.23952/cot.2022.2
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
A. Aceves;R. Alonso;Minh-Binh Tran
中科院分区：
文献类型：
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作者：
A. Aceves;R. Alonso;Minh-Binh Tran
在这项工作中，我们讨论的情况下，可能会导致波湍流和集体行为的动力学方程。当波动方程具有局部微分算子时，波动湍流动力学模型出现在动力学极限。将晶格上的波动方程看作非谐振子链，用非局域的微分算子（长程相互作用）代替局域的微分算子（短程相互作用），在分子混沌假设下，得到了一个新的平均场极限下的Vlasov型动力学模型，它使人联想到非谐振子代替单个粒子的集体行为模型.献给教授罗兰Glowinski 85岁生日
In this work, we discuss a situation which could lead to both wave turbulence and collective behavior kinetic equations. The wave turbulence kinetic models appear in the kinetic limit when the wave equations have local differential operators. Viewing wave equations on the lattice as chains of anharmonic oscillators and replacing the local differential operators (shortrange interactions) by non-local ones (long-range interactions), we arrive at a new Vlasov-type kinetic model in the mean field limit under the molecular chaos assumption reminiscent of models for collective behavior in which anharmonic oscillators replace individual particles. Dedicated to the 85th birthday of Professor Roland Glowinski