Roy Dipankar, Pandit Rahul
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India.
Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
Phys Rev E. 2020 Mar;101(3-1):030103. doi: 10.1103/PhysRevE.101.030103.
Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) stochastic partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state of the one-dimensional Kuramoto-Sivashinsky (KS) deterministic PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile h(x,t) for different initial conditions. We establish, therefore, that the statistical properties of the one-dimensional (1D) KS PDE in this state are in the 1D KPZ universality class.
特雷西 - 威多姆分布和baik - 雷恩斯分布作为一维 Kardar - Parisi - Zhang（KPZ）随机偏微分方程（PDE）中高度涨落的通用极限分布出现。通过进行广泛的伪谱直接数值模拟，以获得不同初始条件下Kuramoto - Sivashinsky（KS）确定性PDE的时空演化，我们在一维KS确定性PDE的时空混沌、非平衡但统计稳定状态中得到了相同的通用分布。因此，我们确定处于这种状态的一维（1D）KS PDE的统计特性属于1D KPZ普适类。
