Kumar Premashis, Gangopadhyay Gautam
S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 106, India.
Phys Rev E. 2020 Apr;101(4-1):042204. doi: 10.1103/PhysRevE.101.042204.
A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion is best reflected through a critical control parameter and wave number containing both the self- and cross-diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model, to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogolyubov averaging method. Due to Hopf instability it is observed that the cross-diffusion parameters can be a source of huge change in free-energy and concentration profiles.
对于存在交叉扩散的、超出传统图灵模式的开放非线性系统，考虑对动态不稳定性的非平衡热力学进行系统介绍。交叉扩散存在时图灵不稳定性的改变条件，最好通过一个包含自扩散系数和交叉扩散系数的临界控制参数和波数来体现。我们主要关注平稳模式形成过程中图灵 - 霍普夫相互作用的熵成本和能量成本。根据反应扩散方程中图灵 - 霍普夫余维不稳定性的相对位置，它阐明了两个方面：模式形成的能量成本，特别是霍普夫不稳定性如何被用来决定平稳浓度分布，以及揭示非平衡相变的可能性。在布鲁塞尔振子模型中，为了理解这些现象，我们使用多尺度克雷洛夫 - 博戈柳博夫平均方法，通过相关的复金兹堡 - 朗道方程进行了分析。由于霍普夫不稳定性，观察到交叉扩散参数可能是自由能和浓度分布发生巨大变化的一个来源。
