A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems

How to characterize the memory property of systems is a challenging issue in the modeling and analysis of complex systems. This study makes a comparative investigation of integer-order derivative, constant-order fractional derivative and two types of variable-order fractional derivatives in characterizing the memory property of systems. The advantages and potential applications of two variable-order derivative definitions are highlighted through a comparative analysis of anomalous relaxation process.     

Synchronization of variable-order fractional financial system via active control method

In this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.     

Proposal and design of an in-fiber all-optical fractional integrator

We theoretically and numerically demonstrate that a single fiber Bragg grating – conveniently apodized and of uniform period – operated in reflection can perform an arbitrary-order fractional integration of an input optical waveform. Analytical expressions were found relating the fractional integration order with the apodization profile of the fiber Bragg grating. This simple device shows a good accuracy calculating the fractional time integral of the complex field of arbitrary input optical waveforms.     

Design of an ultra-broadband all-optical fractional differentiator with a long-period fiber grating

We propose an all-optical in-fiber ultra-broadband fractional differentiator. We numerically demonstrate that a long-period grating inherently performs the temporal fractional differentiation on an optical pulse propagating in the fundamental fiber mode, within a certain spectral bandwidth around the resonance frequency. The device shows a good accuracy calculating the fractional time derivatives of the complex field of THz-bandwidth optical pulses.     

A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre polynomials. To do this, we extend the unknown functions and its derivatives using the shifted Legendre basis. These expansions and the properties of the shifted Legendre polynomials along with the spectral collocation method will help us to reduce the main problem to a set of nonlinear algebraic equations. Finally, The accuracy and efficiency of the proposed method are reported by some illustrative examples.     

A study of the kinetics of infrared luminescence using a stroboscopic synchronous integrator

Journal of Applied Spectroscopy -     

A conservative level set method suitable for variable-order approximations and unstructured meshes

This paper presents a formulation for free-surface computations capable of handling complex phenomena, such as wave breaking, without excessive mass loss or smearing of the interface. The formulation is suitable for discretizations using finite elements of any topology and order, or other approaches such as isogeometric and finite volume methods. Furthermore, the approach builds on standard level set tools and can therefore be used to augment existing implementations of level set methods with discrete conservation properties. Implementations of the method are tested on several difficult two- and three-dimensional problems, including two incompressible air/water flow problems with available experimental results. Linear and quadratic approximations on unstructured tetrahedral and trilinear approximations on hexahedral meshes were tested. Global conservation and agreement with experiments as well as computations by other researchers are obtained.     

A simple and inexpensive two channel boxcar integrator

It is shown that the inclusion of a small amount of primary ionisation makes the solution to the discharge equilibrium problem single valued.     

A symplectic integrator with arbitrary vector and scalar potentials

We study a new class of symplectic integrators for particles in arbitrary, time-dependent vector and scalar potentials. The methods were introduced in [Y.K. Wu, E. Forest, D.S. Robin, Phys. Rev. E 68 (2003) 046502] and are based on the ability to integrate Hamiltonians of the form (pi−ai²(q)) exactly for a finite time-step. We show that the integrators are symplectic in the non-relativistic case but not symplectic in the full six-dimensional phase space for relativistic Hamiltonians.     

A systematic experimental study of squeal initiation

A large-scale systematic experimental investigation into friction-induced vibration is described. A specially designed ‘pin-on-disc’ test rig is used, with dynamical properties which can be altered to allow different aspects of theoretically predicted behaviour to be probed. These dynamical properties have been carefully characterised, including an assessment of uncertainty in each parameter. A large volume of ‘squeal’ data has been generated, involving a sequence of different test conditions repeated over many days. The results were post-processed to extract the growth phase of instabilities and automatically assess their quality in terms of linearity and time-invariance, providing a rich source of high-quality data for several thousands of initiation events. A variety of ways to present the measured results is explored, highlighting trends and assessing repeatability. The experimental test rig exhibits a wide range of squeal behaviour, at frequencies ranging from tens of Hz to tens of kHz. At first glance the results are unrepeatable and twitchy, but the large quantity of data allows significant underlying structure to be demonstrated, shedding light on the roles of symmetry, pre-load, speed and structural perturbations, and also improving understanding of ‘repeatability’ in the context of squeal.     

符合测量实验方法研究

讨论研究了符合测量实验的有关问题，提出实验过程中的几个方法和技巧。     

A new generalized fractional Dirac soliton hierarchy and its fractional Hamiltonian structure

Based on the differential forms and exterior derivatives of fractional orders,Wu first presented the generalized Tu formula to construct the generalized Hamiltonian structure of the fractional soliton equation.We apply the generalized Tu formula to calculate the fractional Dirac soliton equation hierarchy and its Hamiltonian structure.The method can be generalized to the other fractional soliton hierarchy.     

A combined theoretical and experimental study on molecular photonics

A detailed account of quantum chemical procedures for estimating the rate constants of the photophysical processes at work in polyatomic organic molecules is given. The results obtained from combined experimental and theoretical research into the spectral-luminescent properties of acridine, 9-aminoacridine, 2,7-dimethyl-9-diphenylaminoacridine, and of their protonated forms are reported. The electronic absorption and fluorescence spectra of acridine have been investigated at room temperature in ethanol solution of varying pH and in other solvents of different chemical nature and polarity. The energy of excited states, the rate constants of the deactivation of the excited states, and the dipole moments obtained by quantum chemical methods for the examined compounds are presented. The findings of the investigations are discussed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 93–107, October, 2008.     

虚拟声屏障的数值及实验分析

虚拟声屏障(Virtual Sound Barrier,VSB)由若干控制声源和误差传感器构成,使用有源噪声控制方法在噪声环境中产生局部安静区域,“阻隔”声音但不“阻隔”空气和光,像一个无形的屏障对声音起作用。本文建立立体结构的VSB系统模型,从数值模拟和实验两方面说明在噪声来自于多个方向的普通房间中,通过该系统产生人头大小的静区是可行的。数值模拟表明即使在中频VSB系统也有良好的降噪效果。实验给出一种实用的圆柱状分布的16通道的VSB系统,在中低频条件下产生人头大小的静区,降噪可达10 dB以上。     

激光新阈值理论及其实验研究

本文对激光的阈值给出了新的理论解释，提出了激光新阈值理论，导出了激光新阈值条件的解析表达式，并对各类激光器分别进行了讨论，而且从实验上测量了激光器的阈值反转粒子数密度ｎｔｈ与允许激光器获得振荡放大的持续时间△ｔ之间的关系，其结果与激光新阈值理论结果相一致。     

A theoretical and experimental study of non-perfect grain boundary dislocations

The aim of this paper is to discuss the possible appearance of non-perfect grain boundary dislocations in grain boundaries in a variety of materials. To begin with, we survey some of the different theoretical treatments which enable grain boundary dislocations and grain boundary structures to be described. The emphasis is put on more recent ideas, and on illustrating the power of group theory in identifying non-perfect grain boundary dislocations. A derivation of the geometric characteristics of interfacial dislocations is carried out in a simple and tutorial way, in a number of representative examples. It is shown that grain boundary dislocations may be divided into three classes: (1) perfect grain boundary dislocations, (2) imperfect grain boundary dislocations, and (3) partial grain boundary dislocations. Experimental transmission electron microscope evidence is then presented for boundaries in the diamond cubic structure, and it is shown that imperfect and partial grain boundary dislocations play an important role in this system. Finally, a comparison of some grain boundary dislocation types in different materials is given.     

A computational and experimental study of resonators in three dimensions

In a previous work by the present authors, a computational and experimental investigation of the acoustic properties of two-dimensional slit resonators was carried out. The present paper reports the results of a study extending the previous work to three dimensions. This investigation has two basic objectives. The first is to validate the computed results from direct numerical simulations of the flow and acoustic fields of slit resonators in three dimensions by comparing with experimental measurements in a normal incidence impedance tube. The second objective is to study the flow physics of resonant liners responsible for sound wave dissipation. Extensive comparisons are provided between computed and measured acoustic liner properties with both discrete frequency and broadband sound sources. Good agreements are found over a wide range of frequencies and sound pressure levels. Direct numerical simulation confirms the previous finding in two dimensions that vortex shedding is the dominant dissipation mechanism at high sound pressure intensity. However, it is observed that the behavior of the shed vortices in three dimensions is quite different from those of two dimensions. In three dimensions, the shed vortices tend to evolve into ring (circular in plan form) vortices, even though the slit resonator opening from which the vortices are shed has an aspect ratio of 2.5. Under the excitation of discrete frequency sound, the shed vortices align themselves into two regularly spaced vortex trains moving away from the resonator opening in opposite directions. This is different from the chaotic shedding of vortices found in two-dimensional simulations. The effect of slit aspect ratio at a fixed porosity is briefly studied. For the range of liners considered in this investigation, it is found that the absorption coefficient of a liner increases when the open area of the single slit is subdivided into multiple, smaller slits.     

A speculative study of 23-order fractional Laplacian modeling of turbulence: some thoughts and conjectures

This study makes the first attempt to use the 23-order fractional Laplacian modeling of Kolmogorov -53 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. Nonlinear inertial interactions and molecular Brownian diffusivity are considered to be the bifractal mechanism behind multifractal scaling of moderate Reynolds number turbulence. Accordingly, a stochastic equation is proposed to describe turbulence intermittency. The 23-order fractional Laplacian representation is also used to model nonlinear interactions of fluctuating velocity components, and then we conjecture a fractional Reynolds equation, underlying fractal spacetime structures of Levy 23 stable distribution and the Kolmogorov scaling at inertial scales. The new perspective of this study is that the fractional calculus is an effective approach to modeling the chaotic fractal phenomena induced by nonlinear interactions.     

时频混合分步波束形成试验研究

讨论密集间距阵分步波束形成时频混合处理模型和拖曳试验结果、试验结果证明理论模型正确,可以工程实现.当子阵接收的背景噪声中流噪声是占优势的分量时,对试验子阵系统和相同条件下传统的半波长间距阵相比,系统性能指数提高了17dB左右。     

宽频带无源积分器的设计和实验

为获得宽频带的无源积分器,建立了考虑杂散参数的等效电路并进行了电路仿真。结果表明无源积分器的频响上限由杂散参数决定。对于相同结构的积分器,增大RC积分常数,会使杂散参数的影响加剧,导致积分器的高频响应变差。使用同轴结构可以减小电容的杂散电感,提高积分器的带宽。对制作的RC常数为10 μs的同轴式积分器进行了频响实验。实验结果表明：在偏差小于5％的范围内,同轴式积分器带宽为50 kHz～80 MHz。在D-dot电压探头线下标定实验和初级试验平台(PTS)单路样机激光触发开关输出电压测量中,使用该同轴积分器获取的测量波形没有波形畸变和高频干扰。