Derivation Of A Nonlinear Reynolds Stress Model Using Renormalization Group Analysis And Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Delta EEG Activity in Left Orbitofrontal Cortex in Rats Related to Food Reward and Craving

眶额叶皮质与中脑边缘多巴胺奖赏系统有着复杂的相互纤维联系.先前的研究探讨了药物成瘾过程中眶额叶皮质的脑电活动.在本实验中,将探讨食物奖赏和渴求过程中该皮质的脑电活动.实验采用了两个环境:对照环境和食物刺激相关的环境.首先,训练大鼠在食物刺激相关的环境中吃巧克力花生豆,而后在该环境中设置两种不同的刺激方式:能看到和闻到但不能吃到(渴求实验),或者仍旧可以吃到巧克力花生豆(奖赏实验):同时进行左侧眶额叶皮质的脑电记录.结果发现,在食物刺激相关的环境中大鼠Delta频段(2-4Hz)的脑电活动与食物刺激显著相关,此外,与在对照环境中相比,其相对功率在食物渴求时下降而在食物奖赏时升高.本实验表明,食物相关的奖励可以改变大鼠眶额叶皮质的脑电活动,而且,Delta频段的脑电活动能够作为监测该奖励的一个指标.