Brownian motion under dynamic disorder: effects of memory on the decay of the non-Gaussianity parameter

2018 ◽  
Vol 2018 (3) ◽  
pp. 033211 ◽  
Author(s):  
Neha Tyagi ◽  
Binny J Cherayil
Molecules ◽  
2021 ◽  
Vol 26 (14) ◽  
pp. 4119
Author(s):  
Gaetano Ricci ◽  
Sofia Canola ◽  
Yasi Dai ◽  
Daniele Fazzi ◽  
Fabrizia Negri

In this work, we investigate two recently synthesized naphthodithiophene diimide (NDTI) derivatives featuring promising n-type charge transport properties. We analyze the charge transport pathways and model charge mobility with the non-adiabatic hopping mechanism using the Marcus-Levich-Jortner rate constant formulation, highlighting the role of fluoroalkylated substitution in α (α-NDTI) and at the imide nitrogen (N-NDTI) position. In contrast with the experimental results, similar charge mobilities are computed for the two derivatives. However, while α-NDTI displays remarkably anisotropic mobilities with an almost one-dimensional directionality, N-NDTI sustains a more isotropic charge percolation pattern. We propose that the strong anisotropic charge transport character of α-NDTI is responsible for the modest measured charge mobility. In addition, when the role of thermally induced transfer integral fluctuations is investigated, the computed electron–phonon couplings for intermolecular sliding modes indicate that dynamic disorder effects are also more detrimental for the charge transport of α-NDTI than N-NDTI. The lower observed mobility of α-NDTI is therefore rationalized in terms of a prominent anisotropic character of the charge percolation pathways, with the additional contribution of dynamic disorder effects.


2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.


1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.


1971 ◽  
Vol 105 (12) ◽  
pp. 736-736
Author(s):  
V.I. Arabadzhi
Keyword(s):  

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