动力学粗化的混沌和随机普适性之间的转换

Enrique Rodríguez-Fernández, R. Cuerno
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引用次数: 3

摘要

非平衡空间扩展系统的动力学通常由波动控制,如确定性混沌或固有随机性。这反映为一般尺度不变或动力学粗糙化行为,可分为由临界指数值和场波动的概率分布函数(PDF)定义的普适性类。已知适当的几何约束可以在保持指数值不变的情况下改变PDF的次要特征,从而产生通用性子类。研究Kuramoto-Sivashinsky方程作为时空混沌的范例,我们表明,在尊重指数值的同时,普遍波动(混沌或随机)的物理性质也可以改变普世性类,因为PDF发生了实质性的改变。这种转变发生在随机噪声振幅的非零值,可能适合于实验验证。
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Transition between chaotic and stochastic universality classes of kinetic roughening
The dynamics of non-equilibrium spatially extended systems are often dominated by fluctuations, due to e.g.\ deterministic chaos or to intrinsic stochasticity. This reflects into generic scale invariant or kinetic roughening behavior that can be classified into universality classes defined by critical exponent values and by the probability distribution function (PDF) of field fluctuations. Suitable geometrical constraints are known to change secondary features of the PDF while keeping the values of the exponents unchanged, inducing universality subclasses. Working on the Kuramoto-Sivashinsky equation as a paradigm of spatiotemporal chaos, we show that the physical nature of the prevailing fluctuations (chaotic or stochastic) can also change the universality class while respecting the exponent values, as the PDF is substantially altered. This transition takes place at a non-zero value of the stochastic noise amplitude and may be suitable for experimental verification.
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