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.

Construction of Finite Element Multiscaling Function with Three Coefficients

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.

Raising approximation order of refinable vector by increasing multiplicity

An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a. Let φ(x) = [φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function φnew(x) = [ φT(x). f3r+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 φ(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function φ(x) = [φ1 (x), φ2(x), …, φr(x)]T is symmetric, then the new orthogonal multiscaling function φnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given.

Scatter of fatigue data owing to material microscopic effects

A common phenomenon of fatigue test data reported in the open literature such as S-N curves exhibits the scatter of points for a group of same specimens under the same loading condition.The reason is well known that the microstructure is different from specimen to specimen even in the same group.Specifically,a fatigue failure process is a multi-scale problem so that a fatigue failure model should have the ability to take the microscopic effect into account.A physically-based trans-scale crack model is established and the analytical solution is obtained by coupling the micro-and macro-scale.Obtained is the trans-scale stress intensity factor as well as the trans-scale strain energy density(SED)factor.By taking this trans-scale SEDF as a key controlling parameter for the fatigue crack propagation from micro-to macro-scale,a trans-scale fatigue crack growth model is proposed in this work which can reflect the microscopic effect and scale transition in a fatigue process.The fatigue test data of aluminum alloy LY12 plate specimens is chosen to check the model.Two S-N experimental curves for cyclic stress ratio R=0.02 and R=0.6 are selected.The scattering test data points and two S-N curves for both R=0.02 and R=0.6 are exactly re-produced by application of the proposed model.It is demonstrated that the proposed model is able to reflect the multiscaling effect in a fatigue process.The result also shows that the microscopic effect has a pronounced influence on the fatigue life of specimens.

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.

Multiscale approach to micro/macro fatigue crack growth in 2024-T3 aluminum panel

When two contacting solid surfaces are tightly closed and invisible to the naked eye, the discontinuity is said to be microscopic regardless of whether its length is short or long. By this definition, it is not sufficient to distinguish the difference between a micro- and macro-crack by using the length parameter. Microcracks in high strength metal alloys have been known to be sev- eral centimeters or longer. Considered in this work is a dual scale fatigue crack growth model where the main crack can be mi- cro or macro but there prevails an inherent microscopic tip region that is damaged depending on the irregularities of the micro- structure. This region is referred to as the ＂micro-tip＂ and can be simulated by a sharp wedge with different angles in addition to mixed boundary conditions. The combination is sufficient to model microscopic entities in the form of voids, inclusions, precipitations, interfaces, in addition to subgrain imperfections, or cluster of dislocations. This is accomplished by using the method of ＂singularity representation＂ such that closed form asymptotic solutions can be obtained for the development of fa- tigue crack growth rate relations with three parameters. They include： （1） the crack surface tightness o-＊ represented by Cro/Cr~ = 0.3-0.5 for short cracks in region I, and 0.1-0.2 for long cracks in region II, （2） the micro/macro material properties reflected by the shear modulus ratio/1＂ （=,L/micro/]-/macro varying between 2 and 5） and （3） the most sensitive parameter d＊ being the micro-tip characteristic length d＊ （=d/do） whose magnitude decreases in the direction of region I ---~II. The existing fatigue crack growth data for 2024-T3 and 7075-T6 aluminum sheets are used to reinterpret the two-parameter da/dN=C（AK）n relation where AK has now been re-derived for a microcrack with surfaces tightly in contact. The contact force will depend on the mean stress ~m or mean stress ratio R as the primary parameter and on the stress amplitude era as the secondary parameter.

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.