2018
DOI: 10.1039/c8cp01863d
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Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

Abstract: We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We… Show more

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Cited by 57 publications
(40 citation statements)
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“…This is called an ordinary renewal process. If the processes started long before the measurement, we will have a modification of the PDF of the first waiting time [ 3 , 58 ]. How does this effect the large x behavior of ?…”
Section: Discussionmentioning
confidence: 99%
“…This is called an ordinary renewal process. If the processes started long before the measurement, we will have a modification of the PDF of the first waiting time [ 3 , 58 ]. How does this effect the large x behavior of ?…”
Section: Discussionmentioning
confidence: 99%
“…We have related the theory of extreme value statistics and the fluctuations of a particle diffusing in a disordered system with traps. As mentioned, the observation of a non-Gaussian packet P(x, t ) and superdiffusive MSD has been widely reported [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Here we showed that a modification of Fréchet's law is required to fully characterize these fluctuations.…”
Section: Discussion and Summarymentioning
confidence: 52%
“…Such processes are widespread; in particular, many works focused on the surprising discovery of the superdiffusion in dense environments [3][4][5][6][7][8]. This was originally investigated in the context of diffusion in disordered material [1][2][3][9][10][11][12], contamination spreading in porous media [13][14][15][16], simulation of biased particles in glass-forming systems [4], and supercooled liquids [6], pulled by a constant force.…”
Section: Introductionmentioning
confidence: 99%
“…An assortment of models more complex than the CTRW can be found in Refs. [37,38,44,[49][50][51][52][53]; they could be useful to improve the description.…”
Section: Summary and Discussionmentioning
confidence: 99%
“…Aging is intrinsic to the glassylike behavior of the lowintensity vibration driven unclogging dynamics [30,31]. This time dependency naturally arises from subdiffusive stochastic processes [37,38]. Anomalous diffusion in a one-dimensional stochastic variable model is characterized by a nonlinear scaling of the MSD with time:…”
Section: Ergodicity Analysismentioning
confidence: 99%