Is Turbulence as Simple as Tossing a Coin?

Work probability distribution and tossing a biased coin

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modelling other physical phenomena where rare events play an important role.

Random Networks Tossing Biased Coins

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with, asymptotically, scale-free outdegree and compact indegree. Entries in each row of the adjacency matrix are set to be zero or one according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graph…

Pseudo Random Coins Show More Heads Than Tails

Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more heads than tails. This bias explains the empirically observed failure of some random number generators in random walk experiments. It can be traced down to the special role of the value zero in the algebra of finite fields.

充分发展流体动力学turbulence的非广延统计力学方法

Non-extensive statistical mechanics approach to fully developed hydrodynamic turbulence

我们应用非广延方法对充分发展的湍流进行统计分析。通过极值化Tsallis熵得到的距离r处的速度差的概率密度函数与湍流实验中测量的结果吻合得很好。我们导出了超平坦因子F_m与非延拓性参数q之间的一组关系式，可用于从实验测量的结构函数中直接提取函数q（r）。我们评论各种非广泛的方法来计算矩标度指数zeta_m。

Generalized statistical mechanics and fully developed turbulence

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating friction forces, where Tsallis statistics can be rigorously proved.