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31.
Variable Order and Distributed Order Fractional Operators 总被引:1,自引:0,他引:1
Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m
2) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m
2 memory may be chosen for a particular application. Memory retentiveness (m
2) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined. 相似文献
32.
In linear viscoelastic investigations the frequency dependence of the phase shift between stress and strain appears to be very characteristic of the molecular structure of the material. This function is also a good approximation of the slope of the double logarithmic plot of the absolute value of the shear modulusG
d
vs. the angular frequency. The product (G
d
/) sin 2 comes very close to the relaxation spectrumH(), with = 1/, in all physical states of the material.The experimentally observed separability of time and strain effects in nonlinear viscoelasticity of highly viscous isotropic polymer fluids imposes restraints to the form of the constitutive equation. A single integral superposition equation of the Boltzmann type containing the product of a time function and a nonlinear strain function gives good results in describing experimental data in shear as well as in elongation. The molecular structure affects both functions in a different way. A universal definition of the nonlinear tensorial strain measure has not yet been developed. There are some indications that a definition on the basis of the principal stretch ratios may be fruitful.Invited paper, presented at the First Conference of European Rheologists at Graz (Austria), April 14–16, 1982. 相似文献
33.
IntroductionThestabilityoftheintervalmatrixanduncertainsystemwithtimedelayhavebeenconsideredbyresearchersinthepapers [1 -1 3 ] .Thestabilityandαexponentialstabilityofthefollowingintervaldynamicalsystemwithsingletimedelay x(t) =N[P ,Q]x(t) +N[C ,D]x(t-τ)havebeenconsi… 相似文献
34.
35.
36.
The characterisation of flow through porous media is important for all solid–liquid separation and fluid transport realms.
The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result
of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research
on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The
two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores
and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due
to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function
of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by
a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight
times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly
increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated
that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy
ratios for lignite, as well as for other materials including sand, clay and kaolin. 相似文献
37.
38.
In this paper we survey some results on existence, and when possible also uniqueness, of solutions to certain evolution equations obtained by injecting randomness either on the set of initial data or as a perturbative term. 相似文献
39.
油页岩原位注热开采过程中,储层内部孔隙结构的连通性直接影响载热介质的流动行为和传热效率,同时对油气产物的扩散和流动行为起控制作用.本文利用低场核磁共振(LF NMR)技术,考察了不同热解终温(23~650℃)处理时,饱和水及束缚水状态下抚顺油页岩的T2谱,分析了可动流体T2截止值、束缚流体孔隙度、饱和流体孔隙度、渗透率等NMR孔隙参数,定量研究了随热解终温升高,抚顺油页岩孔隙结构的连通性演化规律.研究结果表明热解终温对抚顺油页岩孔隙连通性及渗透率的变化起控制作用,且可动流体孔隙度对总孔隙度的增加起主要促进作用,这说明热解终温升高加大了渗透率及油气产物的输运能力.本文为深入认识油页岩原位热解过程中孔隙结构的演化提供了依据. 相似文献
40.
Umair Ahmed Charles Turquand d’Auzay Masaya Muto Nilanjan Chakraborty Ryoichi Kurose 《Proceedings of the Combustion Institute》2019,37(3):2821-2830
The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (c), and the mixture fraction (ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of c and ξ can be parametrised by the standard β function. Furthermore, the log-normal distribution has been found to accurately represent |?c| and |?ξ|. It is also found that ?c and ?ξ remain aligned throughout the flame brush. Finally the joint PDF of |?c| and |?ξ| has been compared with the product of the PDF of |?c| and PDF of |?ξ| extracted from carrier phase DNS, and it has been found that |?c| and |?ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data. 相似文献