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.

Empirical Scaling Laws of Neutral Beam Injection Power in HL-2A Tokamak

We present an experimental method to obtain neutral beam injection （NBI） power scaling laws with operating parameters of the NBI system on HL-2A, including the beam divergence angle, the beam power transmission efficiency, the neutralization efficiency and so on. With the empirical scaling laws, the estimating power can be obtained in every shot of experiment on time, therefore the important parameters such as the energy confinement time can be obtained precisely. The simulation results by the tokamak simulation code （TSC） show that the evolution of the plasma parameters is in good agreement with the experimental results by using the NBI power from the empirical scaling law.

Range-Renewal Processes:SLLNs and Power Laws

Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN results(of Dvoretzky-Erdos'type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1+γThey also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent 2.This exponent is obviously independent of the parameterγ∈(0,1),which is a surprise to us at first sight.

Power Laws and Skew Distributions

Power-law distributions and other skew distributions,observed in various models and real systems,are considered.A model,describing evolving systems with increasing number of elements,is considered to study the distribution over element sizes.Stationary power-law distributions are found.Certain non-stationary skew distributions are obtained and analyzed,based on exact solutions and numerical simulations.

高分子溶液sol—gel相转移Power—Law公式的修正

本文在大量实验基础上对长期以来使用的高分子溶液sol—gel相转移的Power—law公式η_r∝(f_c—f)^(-k)作了进一步的探讨。在式中引入有关体系性质的参量和实验的边界条件后,可将公式变为η_r∝[1—(f/f_c)α]^(-k)。而修正后的公式更加接近实验事实。参数α反映了溶液中溶质、溶剂以及添加的金属阳离子间的相互作用情况,从而得到的结果也更加可靠。

Macro Impact of the Law on Prevention and Control of Atmospheric Pollution on Power Industry Development

The newly revised and enlarged main contents of the Law of Prevention and Control of Atmospheric Pollution are described, The macro impacts of the law on the power industry development are analyzed mainly in respects to power demand and readjustment of power structure and layout. clean production and pollution control level, scientific management of environmental protection, in accordance with law as well as changes of construction and operation costs. And finally, several questions worthy to be noted in course of implementation of the new law are enumerated.

基于Power-Law原则的P2P实现

由于Napster,Gnutella和Freenet的巨大成功,端对端技术在搭建分布式应用上吸引了工业界和媒体的注意。基于P2P的项目大多要面对一些基本的问题,这包括了安全性、可靠性和路由。但是,由于网络规模的问题,传统的技术并不能直接应用于P2P系统。本文将介绍一种基于Power-Law原则的P2P模型。

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.

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.

Characteristics of Convection Heat Transfer in Power⁃Law Fluid Saturated Porous Media Channel

Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.

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.

SOLUTION OF THE RAYLEIGH PROBLEM FOR A POWER-LAW NON-NEWTONIAN CONDUCTING FLUID VIA GROUP METHOD

An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

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.