Statistical description of depth-dependent turbulent velocity measured in Taihu Lake, China

Quantitative description of turbulence using simple physical/mathematical models remains a challenge in classical physics and hydrologic dynamics. This study monitored the turbulence velocity field at the surface and bottom of Taihu Lake, in China, a large shallow lake with a heterogeneous complex system, and conducted a statistical analysis of the data for the local turbulent structure. Results show that the measured turbulent flows with finite Reynolds numbers exhibit properties of non-Gaussian distribution. Compared with the normal distribution, the Levy distribution with meaningful parameters can better characterize the tailing behavior of the measured turbulence. Exit-distance statistics and multiscaling extended self-similarity(ESS) were used to interpret turbulence dynamics with different scale structures. Results show that the probability density function of the reverse structure distance and the multiscaling ESS can effectively capture the turbulent flow dynamics varying with water depth. These results provide an approach for quantitatively analyzing multiscale turbulence in large natural lakes.

On the Dynamic Equilibrium in Homeostasis

We studied the homeostatic equilibrium of the healthy organism. The homeostasis is controlled by oppositely effective physiologic feedback signal-pairs in various time-scales. We show the entropy of every signal in this state is identical and constant: SE = 1.8. The controlling physiological signals fluctuate around their average values. The fluctuation is time-fractal, (pink-noise), which characterizes the homeostasis. The aging is the degradation of the competing pairs of signals, decreasing the complexity of the organism. This way, the color of the noise gradually changes to brown. A special scaling process occurs during the aging: the exponent of the frequency dependence of the power density function grows in this process from 1 to 2, but the homeostasis of the system is unchanged.

Lumped parameter model based surgical planning for CABG

The current 3D CABG model is time consuming,a lumped parameter CABG model may solve this problem.A coronary lumped parameter model without stenosis and graft was constructed.The stenosis resistance was calculated and graft model was constructed.After calculation,the graft flow results of CABG lumped parameter model fit well with 3D CABG model results.

Raising approximation order of refinable vector by increasing multiplicity

An algorithm is presented for raising an approximation order of any given or thogonal multiscaling function with the dilation factor a. Let Ф(x) = [φ1(x), φ2 (x), … , φr (x)]Tbe an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function Фnew(x) = [ ФT(x),φr+1(x), φr+2(x),… ,φr+s(x)]T with the approximation order m + L(L ∈ Z+). In other words, we raise the approximation order of multiscaling function Ф(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function Ф(x) = [φ1(x), φ2(x), … , φr (x)]T is symmetric, then the new orthogo nal multiscaling function Фnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given.

MULTISCALING APPROACH BASED ON MORPHOLOGICAL FILTERING

In this paper, it is argued that the mathematical morphological method seems to be morereasonable and powerful in studying vision problems than Marr ’s approach which uses deri-vatives of Gaussian-shaped filters in different sizes. To show the validity of this method,an application is given to form scale-space image of a 2-D shape employing morphologicalopening filtering. Proof is given to show that the morphological opening filter has the pro-perty of not introducing additional zero-crossings as one moves to coarser scale. This con-tradicts the conclusion by Poggio et al. that the Gaussian filter is the only filter with thisremarkable property. Besides, the opening filter is computationally simpler than theGaussian filter.