Development and Application of a Power Law Constitutive Model for Eddy Current Dampers

Eddy current dampers (ECDs) have emerged as highly desirable solutions for vibration control due to theirexceptional damping performance and durability. However, the existing constitutive models present challenges tothe widespread implementation of ECD technology, and there is limited availability of finite element analysis (FEA)software capable of accurately modeling the behavior of ECDs. This study addresses these issues by developing anewconstitutivemodel that is both easily understandable and user-friendly for FEAsoftware. By utilizing numericalresults obtained from electromagnetic FEA, a novel power law constitutive model is proposed to capture thenonlinear behavior of ECDs. The effectiveness of the power law constitutive model is validated throughmechanicalproperty tests and numerical seismic analysis. Furthermore, a detailed description of the application process ofthe power law constitutive model in ANSYS FEA software is provided. To facilitate the preliminary design ofECDs, an analytical derivation of energy dissipation and parameter optimization for ECDs under harmonicmotionis performed. The results demonstrate that the power law constitutive model serves as a viable alternative forconducting dynamic analysis using FEA and optimizing parameters for ECDs.

Bayesian estimation of a power law process with incomplete data

Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.

Failure analysis on China power grid based on power law

This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance （SWV） and rescaled rangestatistics （R/S）, this paper studies the blackout data in China power system during 1988-1997. The result of analysis shows that the blackout data of 1994-1997 coincides well with the autocorrelation. Furthermore, it is found that the function of blackout probability vs. blackout size exhibits power law distribution.

Power Law网络中一种资源定位机制的设计与仿真

如何有效地进行资源定位是影响广域网内分布式系统性能的重要因素,已有的一些资源查找算法引入了小世界原理来提高定位效率和降低网络负载,但没有较好解决小世界网络的构造问题。在Kleinberg小世界模型的基础上,利用幂率网络特性,提出了一个小世界网络的构造方法PLSWCP(Power Law oriented Small World Construction Protocol),并给出了该方法的数学分析和实现。该方法是分布式的,不必拥有全局知识,每个节点只需维护局部视图,即可使资源定位具有小世界特征所带来的优化的时间复杂度。分析和实验结果表明,该方法可以提高资源定位的效率,具有良好的扩展性,自适应性和负载均衡性。

A New Idea of Fractal-Fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.

Drag characteristics of power law fluids on an upstream moving surface

The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.

Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.

The Fractional Power Law of Wind Wave Growth in Deep Water for Short Fetch

Combining the 3/2 power law proposed by Toba with the significant wave energy balance equation for wind waves, wave growth in deep water for short fetch is investigated. It is found that the variations of wave height and period with fetch have the form of power function with fractional exponents 3/8 and 1/4 respectively. Using these exponents in the power functions and through data fitting, the concise wind wave growth relations for short fetch are obtained.

OBTAINING THE CRITICAL DRAW RATIO OF DRAW RESONANCE IN MELT SPINNING FOR POWER LAW POLYMER FLUIDS

A direct difference method has been developed for Non-Newtonian power law fluids to solve the simultaneous non-linear partial differential equations of melt spinning, and to determine the critical draw ratio for draw resonance. The results show that for shear thin fluids, the logarithm of the critical draw ratio has a well defined linear relationship with the power index for isothermal and uniform tension melt spinning. When the power index approaches zero, the critical draw ratio points at unity, indicating no melt spinning can be processed stably for such fluids. For shear thick fluids, the critical draw ratio increases in a more rapid way with increasing the power index.

Power Law Distributions in the Experiment for Adjustment of the Ion Source of the NBI System

The experiential adjustment process in an experiment on the ion source of the neutral beam injector system for the HT-7 Tokamak is reported in this paper. With regard to the data obtained in the same condition, in arranging the arc current intensities of every shot with a decay rank, the distributions of the arc current intensity correspond to the power laws, and the distribution obtained in the condition with the cryo-pump corresponds to the double Pareto distribution. Using the similar study method, the distributions of the arc duration are close to the power laws too. These power law distributions are formed rather naturally instead of being the results of purposeful seeking.

Approximate analytical solutions and approximate value of skin friction coeffcient for boundary layer of power law fluids

This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTH CRACK ON ELASTIC-ELASTIC POWER LAW CREEPING BIMATERIAL INTERFACE

A mechanical model was established for modeⅡinterfacial crack static growing along an elastic_elastic power law creeping bimaterial interface. For two kinds of boundary conditions on crack faces, traction free and frictional contact, asymptotic solutions of the stress and strain near tip_crack were given. Results derived indicate that the stress and strain have the same singularity, there is not the oscillatory singularity in the field; the creep power_hardening index n and the ratio of Young's module notably influence the crack_tip field in region of elastic power law creeping material and n only influences distribution of stresses and strains in region of elastic material. When n is bigger, the creeping deformation is dominant and stress fields become steady,which does not change with n. Poisson's ratio does not affect the distributing of the crack_tip field.

A Theoretical Explanation of the Causes of Popular Elements and Income Power Law Distribution Based on Data Analysis

The known statistical data show that the distribution of popular elements and people’s income presents the characteristics of power law distribution.At present,the explanation for this phenomenon is mostly through the“rich get richer”theory,but the author believes that this theory has major flaws and fails to provide a reasonable explanation for many phenomena.Therefore,the author expands some empirical and recognized theories in a similar direction in logic,and derives a logical mathematical model through the derivation of mathematical formulas,so as to explain the phenomenon that the distribution of popular elements and people’s income presents a power-law distribution.Then,by analyzing various characteristics of social networks and comparing them with some phenomena in nature,the conclusion can be extended to all self-organizing groups in nature.

Power Law for the Rates of Different Numbers of Chronic Diseases among Elderly Chinese People

Chronic disease is an important factor that affect the health of elderly people. We analyzed the 2006 and 2010 data from the Chinese Urban and Rural Elderly Population Surveys, which are nationally representative surveys of elderly people aged 60 years and above. We found that there existed a typical power-law distribution for the rates of different numbers of chronic diseases among elderly Chinese people. A Kolmogorov-Smirnov test indicated that the result was robust, and the power exponents were approximately ?2.5. In addition, a paired t-test was conducted, which demonstrated that the rates of different numbers of chronic diseases did not have significant urban-rural differences, time differences or gender differences.

Experimental research on breakup of 2D power law liquid film

On account of limited knowledge of the breakup of power law liquid film, the process of its disintegration and atomization was studied by using a planar liquid film. A linear stability analysis was adopted to predict the breakup characteristics of the power law film. The predicting formulas of stripping breakup length and diameter of ligament were put forward presently. Through high-speed photography and laser light sheet illumination,different breakup characteristics of flat power law film under different conditions were derived. The characteristic dimension of breakup regimes were defined and extracted. The effects of several parameters(injection pressure,ambient pressure, nozzle structure and fluid property) on the stripping breakup length and spray angle were investigated. The results revealed that increasing both the velocity of liquid film and the ambient pressure facilitated the breakup of film, reduced the stripping breakup length and enlarged the spray angle in different extents. The comparison between theoretical and experimental results was conducted to validate the feasibility of the linear stability theory.

Application of power law to vertical distribution of longshore currents

The vertical profiles of longshore currents have been examined experimentally over plane and barred beaches. In most cases, the vertical profiles of longshore currents are expressed by the logarithmic law. The power law is not commonly used to describe the profile of longshore currents. In this paper, however, a power-type formula is proposed to describe the vertical profiles of longshore currents. The formula has two parameters: the power law index (a) and the depth-averaged velocity. Based on previous studies, power law indices were set as a=1/10 and a=1/7. Depth-averaged velocity can be obtained through measurement. The fitting of the measured velocity profiles to a=1/10 and a=1/7 was assessed for the vertical longshore profiles. The vertical profile of longshore currents is well described by the power-type formula with a=1/10 for a plane beach. However, for a barred beach, different values of a needed to be used for different regions. For the region from the bar trough to the offshore side of the bar crest, the vertical profiles of longshore currents given by the power-type formula with a=1/10 and a=1/7 fit the data well. However, the fit was slightly better with a=1/10 than that with a=1/7. For the data over the trough region of cross-shore distribution of the depth-averaged longshore currents, the power formula with a=1/3 provided a good fit. The formulas with a=1/10 and a=1/7 were further examined using published data from four sources covering laboratory and field experiments. The results indicate that the power-type formula fits the data well for the laboratory and field data with a=1/10.

An optimized framework for degree distribution in LT codes based on power law

LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)k number of encoded symbols to recover the original information. The degree distribution function in the LT codes helps to generate a random graph also referred as tanner graph. The artifact of tanner graph is responsible for computational complexity and overhead in the LT codes. Intuitively, a well designed degree distribution can be used for an efficient implementation of LT codes. The degree distribution function is studied as a function of power law, and LT codes are classified into two different categories: SFLT and RLT codes. Also, two different degree distributions are proposed and analyzed for SFLT codes which guarantee optimal performance in terms of computational complexity and overhead.

On energy boundary layer equations in power law non-Newtonian fluids

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

Calculation Method of Power Law Fluid Equivalent Permeability Considering Capillary Shape

While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.

Exact Solutions of a Power Law Fluid Model in Posttreatment Analysis of Wire Coating with Linearly Varying Boundary Temperature

In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.