Characteristic function of sub-di usive transport processes

摘要：

Nuclear Magnetic Resonance is a powerful method to investigate transport proper- ties. Among other observables it allows us measuring the characteristic function of fluid particles displacements between two given instants. Such measurements are commonly interpreted on the basis of normal transport, that corresponds to Markovian processes for individual motions of fluid particles. We discuss asymptotic properties of the characteristic function of increments of two sub-diffusive processes, whose density satisfies fractional partial differential equations. That properties are linked with the behavior of NMR echoes induced by gradient impulses, of amplitude G and duration d when Gd tends to infinty. The echo limit can be estimated ana- lytically when d is very short, and linked to transport parameters. Then, numerical simulation generalizes the result to non-small values of d, that permit measuring the limit using moderate values of G.

关键词： Sub-diffusion Nuclear Magnetic Resonance Mittag-Lefler functions non-Markovian processes characteristic function

作者: V. Guillon S. H. Rakotonasy D. Bauer M. Fleury M.C.Néel

作者单位: IFP Energies nouvelles, 1 et 4, avenue de Bois Préau 92852-Rueil-Malmaison, France Université d’Avignon et des Pays de Vaucluse, UMR 1114 EMMAH,84018 Avignon Cedex, France Université d’Avignon et des Pays de Vaucluse, UMR 1114 EMMAH, 84018 Avignon Cedex, France

会议类型: 国际会议

会议名称: The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)

会议地点: 南京

会议语种:英文

页码: 1-5

在线出版日期: 2012-05-14（万方平台首次上网日期，不代表论文的发表时间）