Next Article in Journal
An Experimental Test of the Classical Interpretation of the Kaluza Fifth Dimension
Previous Article in Journal
A Full-Fledged Analytical Solution to the Quantum Harmonic Oscillator for Undergraduate Students of Science and Engineering
Open AccessArticle

Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment

1
Department of Physics, Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente, 225, 22451-900 Rio de Janeiro, Brazil
2
Department of Physics, Federal University of Paraná, 81531-990 Curitiba, Brazil
*
Author to whom correspondence should be addressed.
Physics 2020, 2(4), 571-586; https://doi.org/10.3390/physics2040032
Received: 7 September 2020 / Revised: 7 October 2020 / Accepted: 12 October 2020 / Published: 19 October 2020
(This article belongs to the Section Statistical Physics and Nonlinear Phenomena)
Superstatistical approaches have played a crucial role in the investigations of mixtures of Gaussian processes. Such approaches look to describe non-Gaussian diffusion emergence in single-particle tracking experiments realized in soft and biological matter. Currently, relevant progress in superstatistics of Gaussian diffusion processes has been investigated by applying χ2-gamma and χ2-gamma inverse superstatistics to systems of particles in a heterogeneous environment whose diffusivities are randomly distributed; such situations imply Brownian yet non-Gaussian diffusion. In this paper, we present how the log-normal superstatistics of diffusivities modify the density distribution function for two types of mixture of Brownian processes. Firstly, we investigate the time evolution of the ensemble of Brownian particles with random diffusivity through the analytical and simulated points of view. Furthermore, we analyzed approximations of the overall probability distribution for log-normal superstatistics of Brownian motion. Secondly, we propose two models for a mixture of scaled Brownian motion and to analyze the log-normal superstatistics associated with them, which admits an anomalous diffusion process. The results found in this work contribute to advances of non-Gaussian diffusion processes and superstatistical theory. View Full-Text
Keywords: non-Gaussian diffusion; superstatistics; Langevin equation; scaled Brownian motion; random diffusivity non-Gaussian diffusion; superstatistics; Langevin equation; scaled Brownian motion; random diffusivity
Show Figures

Figure 1

MDPI and ACS Style

dos Santos, M.A.F.; Menon Junior, L. Log-Normal Superstatistics for Brownian Particles in a Heterogeneous Environment. Physics 2020, 2, 571-586.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Back to TopTop