Experiments of Dissipative Systems with Many Degrees of Freedom (from the view point of nonlinear dynamics and fluctuations)

我们从多自由度耗散系统中选择了两个原型实验系统。一个是充分发展的热湍流实验。另一个是关于培养的神经细胞网络的实验。在第一项研究中，热湍流，我们开发了瑞利-贝纳德对流单元，使我们能够通过使用汞，一种低普朗特数（Pr）流体来探索湍流自由对流中最高雷诺数之一。低普朗特数流体（Pr=0.024）的瑞利数（Ra）为10^<11>，雷诺数为5 × 10^5，并发现两个边界层与其他流体不同（Pr>=1）。Nusselt数随Ra的标度指数为0.29+-0.01，与硬湍流的标度指数接近。两个边界层匹配收缩，缩放指数接近-0.29。因此，理论上预测的最终标度为1/2，即使两个边界层已经交叉，也没有观察到。这导致一种猜想，即最终标度制度可能不存在。在第二项研究中，我们从大鼠胚胎皮层（E17）中分离出脑细胞进行游离培养。神经元和神经胶质细胞在玻璃板上生长并形成高度连接的网络结构。利用Ca^<2+>敏感荧光染料，同时光学测量了数百个细胞的Ca^<2+>活性。我们在网络中发现了Ca^<2+>的同步爆破振荡，并分类了集体动力学行为。通过单克隆抗体染色对网络的连通性和结构进行评价。首次量化神经元-神经元、神经元-胶质和胶质-胶质之间相关系数分布函数的演化，以表征神经网络的发育过程。

We selected two prototype experimental systems from dissipative systems with many degrees of freedom. One is the experiment of fully developed thermal turbulence. The other is an experiment on networks of cultured neural cells.In the first study, thermal turbulence, we developed Rayleigh-Benard convection cell that enables us to explore one of the highest Reynolds numbers in turbulent free convection by using mercury, a low Prandtl number (Pr) fluid. We attained 10^<11> in Rayleigh number (Ra) and 5x10^5 in Reynolds number for the low Prandtl number fluid (Pr=0.024), and found that two boundary layers are inverted unlike with other fluids (Pr>=1). The scaling exponent of Nusselt number with Ra was 0.29+-0.01, which is close to that of hard turbulence. Two boundary layers match and shrink with the scaling exponent close to -0.29. Therefore theoretically predicted ultimate scaling, 1/2, did not observed even the two boundary layers have crossed. This leads a conjecture that the ultimate scaling regime may not exist.In the second study, we made dissociated culture of brain cells, which are dissected from cortex of rat embryo (E17). Neuron and glia cells grow on the glass plate and develop highly connected network structures. By using Ca^<2+> sensitive fluorescent dye, Ca^<2+> activities of a few hundreds of cells were optically measured simultaneously. We found synchronous bursting Ca^<2+> oscillation in the networks, and classified collective dynamical behavior. Connectivity and structure of the network were evaluated by using monochronal antibody staining. Evolution of distribution function of correlation coefficients between neuron-neuron, neuron-glia, and glia-glia, was firstly quantified to characterize the developmental process of the networks.