湍流混合对非平衡临界行为的影响
Effects of turbulent mixing on the nonequilibrium critical behaviour
摘要：
本文研究了湍流混合对非平衡系统在吸收态和涨落态之间的二级相变附近的临界行为的影响。该模型描述了代理的传播（例如，传染病），属于有向键渗流过程（又称简单传染病过程）的普适类，等价于Reggeon场论.湍流平流速度场由Obukhov-Kraichnan的快速变化系综模拟：高斯统计与关联函数< vv>\propto δ（t-t '）k^{-d-ε}，其中k是波数，0<ε <2是自由参数。使用场论的重整化群，我们表明，根据之间的关系的指数重整化群方程，该系统揭示了不同类型的大规模渐近行为，与四个可能的不动点。除了已知的制度（普通扩散，普通定向渗流过程，和被动平流标量场），存在一个新的非平衡普适性类的建立，并计算相应的临界尺寸的双展开的第一阶在ESTA和\varepsilon =4-d（一圈近似）。然而，事实证明，当Reggeon模型的非线性不相关并且药剂的扩散完全由湍流传输决定时，最现实的值λ =4/3（Kolmogorov充分发展的湍流）和d=2或3对应于被动标量场的情况。
英文摘要：
We study effects of turbulent mixing on the critical behaviour of a nonequilibrium system near its second-order phase transition between the absorbing and fluctuating states. The model describes the spreading of an agent (e.g., infectious disease) in a reaction-diffusion system and belongs to the universality class of the directed bond percolation process, also known as simple epidemic process, and is equivalent to the Reggeon field theory. The turbulent advecting velocity field is modelled by the Obukhov--Kraichnan's rapid-change ensemble: Gaussian statistics with the correlation function < vv> \propto δ(t-t') k^{-d-ξ}, where k is the wave number and 0<ξ<2 is a free parameter. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξand the space dimensionality d, the system reveals different types of large-scale asymptotic behaviour, associated with four possible fixed points of the renormalization group equations. In addition to known regimes (ordinary diffusion, ordinary directed percolation process, and passively advected scalar field), existence of a new nonequilibrium universality class is established, and the corresponding critical dimensions are calculated to first order of the double expansion in ξand \varepsilon=4-d (one-loop approximation). It turns out, however, that the most realistic values ξ=4/3 (Kolmogorov's fully developed turbulence) and d=2 or 3 correspond to the case of passive scalar field, when the nonlinearity of the Reggeon model is irrelevant and the spreading of the agent is completely determined by the turbulent transfer.
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