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.

Microwave-Assisted Transition Metal Nanostructure Synthesis: Power-Law Signature Verification

A power-law (y = cxn) signature between process energy budget (kJ) and process energy density (kJ·ml-1) of microwave-assisted synthesis of silver and gold nanostructures has been recently described [Law and Denis. AJAC, 14(4), 149-174, (2023)]. This study explores this relation further for palladium, platinum, and zinc oxide nanostructures. Parametric cluster analysis and statistical analysis is used to test the power-law signature of over four orders of magnitude as a function of six microwave applicator-types metal precursor, non-Green Chemistry synthesis and claimed Green Chemistry. It is found that for the claimed Green Chemistry, process energy budget ranges from 0.291 to 900 kJ, with a residual error ranging between −33 to +25.9 kJ·ml-1. The non-Green Chemistry synthesis has a higher process energy budget range from 3.2 kJ to 3.3 MJ, with a residual error of −33.3 to +245.3 kJ·ml-1. It is also found that the energy profile over time produced by software controlled digestion applicators is poorly reported which leads to residual error problematic outliers that produce possible phase-transition in the power-law signature. The original Au and Ag database and new Pd, Pt and ZnO database (with and without problematic outliers) yield a global microwave-assisted synthesis power-law signature constants of c = 0.7172 ± 0.3214 kJ·ml-1 at x-axes = 0.001 kJ, and the exponent, n = 0.791 ± 0.055. The information in this study is aimed to understand variations in historical microwave-assisted synthesis processes, and develop new scale-out synthesis through process intensification.

瞬态信号的双树复小波Power-Law检测

为克服离散小波变换平移不变性差的不足,通过构造的Hilbert变换对滤波器组,实现了双树复小波变换。建立了基于复小波变换系数的Power-Law检测器。推导了检测统计量的渐近性能和偏移系数,由输入信噪比损失给出了检测器参数的选择方法。利用仿真与实测数据进行了试验,并与基于离散小波变换的Power-Law检测器进行了比较。本文提出的小波方法能很好实现平移不变性,建立的检测器具有更大的偏移系数,在相同的信噪比和虚警概率下能够得到更高的检测概率。

静态随机共振的非高斯噪声中瞬态信号小波域Power-Law检测

研究非高斯噪声中微弱瞬态信号的检测。利用静态随机共振方法对微弱信号进行处理,使瞬态信号的信噪比得到增强。在小波域建立了新的Power-Law检测器。通过仿真实验对比发现,在相同的信噪比和虚警概率下,采用提出的方法可以得到更高的检测概率。

一种改进的Power-Law检测器在突发信号检测中的应用

根据短时突发通信信号的特点,提出了一种改进的基于高阶谱的power-law检测器。该方法利用高斯噪声和通信信号的高阶统计量存在较大差异的特点,对传统power-law检测器进行了改进。仿真结果表明,基于高阶谱的power-law检测器对短时突发通信信号的检测效果优于传统的基于DFT的power-law检测器。

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。

Analysis of precipitation characteristics of South and North China based on the power-law tail exponents

Precipitation sequence is a typical nonlinear and chaotic observational series,and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods,especially when analysing the regional characteristics of precipitation. In the context of 20 stations' daily precipitation series (from 1956 to 2000) in South China (SC) and North China (NC),we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm (briefly BG algorithm). For each station's precipitation series,we calculate the exponent of power-law tail (EPT) of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile,EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.

Computational analysis of the flow of pseudoplastic power-law fluids in a microchannel plate

The flow of pseudoplastic power-law fluids with different flow indexes at a microchannel plate was studied using computational fluid dynamic simulation.The velocity distribution along the microchannel plate and especially in the microchannel slits,flow pattern along the outlet arc and the pressure drop through the whole of microchannel plate were investigated at different power-law flow indexes.The results showed that the velocity profile in the microchannel slits for low flow index fluids was similar to the plug flow and had uniform pattern.Also the power-law fluids with lower flow indexes had lower stagnation zones near the outlet of the microchannel plate.The pressure drop through the microchannel plate showed huge differences between the fluids.The most interesting result was that the pressure drops for power-law fluids were very smaller than that of Newtonian fluids.In addition,the heat transfer of the fluids through the microchannel with different channel numbers in a wide range of Reynolds number was investigated.For power-law fluid with flow index(n=0.4),the Nusselt number increases continuously as the number of channels increases.The results highlight the potential use of using pseudoplastic fluids in the microheat exchangers which can lower the pressure drop and increase the heat transfer efficiency.

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 axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.

Effects of nonlinear velocity slip and temperature jump onpseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.

Simplified Wave Models Applicability to Shallow Mud Flows Modeled as Power-Law Fluids

Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.

Symmetries of boundary layer equations of power-law fluids of second grade

第二个等级的修改幂定律液体被考虑。模型是液体可以在展出正常压力的幂定律和第二等级液体的联合，砍变瘦或砍变厚行为。运动的方程为二维的不可压缩的流动被导出，并且从哪个界面层方程被导出。界面层方程的对称被关于幂定律使用谎言组理论，然后组分类发现索引被执行。由使用对称之一，也就是可伸缩的对称，部分微分系统被转变成一个平常的微分系统，它在古典界面层条件下面是数字地综合的。界面层上的幂定律索引和第二个等级系数的效果被显示出，答案与平常的秒等级液体答案被对比。

Mobile user forecast and power-law acceleration invariance of scale-free networks

This paper studies and predicts the number growth of China’s mobile users by using the power-law regression.We find that the number growth of the mobile users follows a power law.Motivated by the data on the evolution of the mobile users,we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model,in which the nodes grow following a power-law acceleration.The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process.This result shows that the model generates appropriate power-law connectivity distributions.Therefore,we find a power-law acceleration invariance of the scale-free networks.The numerical simulations of the models agree with the analytical results well.

Power-law Distribution of Normal Fault Displacement and Length and Estimation of Extensional Strain due to Normal Faults:A Case Study of the Sierra de San Miguelito, Mexico

The Sierra de San Miguelito is a relatively uplifted area and is constituted by a large amount of silicic volcanic rocks with ages from middle to late Cenozoic. The normal faults of the Sierra de San Miguelito are Domino-style and nearly parallel. The cumulative length and displacement of the faults obey power-law distribution. The fractal dimension of the fault traces is -1.49. Using the multi-line one-dimensional sampling, the calculated exponent of cumulative fault displacements is -0.66. A cumulative curve combining measurements of all four sections yielded a slope of -0.63. The displacement-length plot shows a non-linear relationship and large dispersion of data. The large dispersion in the plot is mainly due to the fault linkage during faulting. An estimation of extensional strain due to the normal faults is ca. 0.1830. The bed extension strain is always less than or equal to the horizontal extension strain. The deformation in the Sierra de San Miguelito occurred near the surface, producing pervasive faults and many faults are too small to appear in maps and sections at common scales. The stretching produced by small faults reach ca. 33% of the total horizontal elongation.

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.

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.

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

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.

MHD flow of power-law fluid on moving surface with power-law velocity and special injection/blowing

The problem of magnetohydrodynamic(MHD) flow on a moving surface with the power-law velocity and special injection/blowing is investigated. A scaling group transformation is used to reduce the governing equations to a system of ordinary differential equations. The skin friction coefficients of the MHD boundary layer flow are derived,and the approximate solutions of the flow characteristics are obtained with the homotopy analysis method(HAM). The approximate solutions are easily computed by use of a high order iterative procedure, and the effects of the power-law index, the magnetic parameter,and the special suction/blowing parameter on the dynamics are analyzed. The obtained results are compared with the numerical results published in the literature, verifying the reliability of the approximate solutions.