Brownian non-Gaussian diffusion of self-avoiding walks

Abstract

Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center of mass grows linearly with time (Brownian behavior), the initial probability density function is strongly non-Gaussian and crosses over to Gaussianity only at large time. Full agreement between theory and simulations is achieved without the employment of fitting parameters. We discuss simulation techniques potentially capable of addressing the study of anomalous diffusion under complex conditions like adsorption- or Theta-transition.

Preface: Characterisation of Physical Processes from Anomalous Diffusion Data

“…Initial strong non-Gaussianity concurrent with Brownian scaling of the mean squared displacement is reported for self-avoiding random walks in Ref. [39].…”

Preface: characterisation of physical processes from anomalous diffusion data

“…the Korteweg-deVries equation, that provide a framework for solitonic solutions with power-law dispersion relations. Initial strong non-Gaussianity concurrent with Brownian scaling of the mean squared displacement is reported for self-avoiding random walks in [40].…”

Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories

“…Mathematically such motion is often modeled as so-called fractional Brownian motion (FBM) . There exist plenty of other models to explain the occurrence of anomalous diffusion, − apart from the mentioned SBM and FBM. We here also consider continuous-time random walk (CTRW), with random waiting times between successive jumps, ,, Lévy walks (LW), − and annealed transient time motion (ATTM) .…”