2024-03-28T12:16:19Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/1407682018-05-18T10:16:19Zcom_10261_5062com_10261_5col_10261_5064
Scaling forms of particle densities for Lévy walks and strong anomalous diffusion
Dentz, Marco
Le Borgne, Tanguy
Lester, Daniel R.
Barros, Felipe P. J. de
European Research Council
Piecewise linear techniques
Particle densities
Scaling behavior
We study the scaling behavior of particle densities for Lévy walks whose transition length r is coupled with the transition time t as |r|∞tα with an exponent α>0. The transition-time distribution behaves as ψ(t)∞t-1-β with β>0. For 1<β<2α and α≥1, particle displacements are characterized by a finite transition time and confinement to |r|<tα while the marginal distribution of transition lengths is heavy tailed. These characteristics give rise to the existence of two scaling forms for the particle density, one that is valid at particle displacements |r|蠐tα and one at |r|≲tα. As a consequence, the Lévy walk displays strong anomalous diffusion in the sense that the average absolute moments (|r|q) scale as tqν(q) with ν(q) piecewise linear above and below a critical value qc. We derive explicit expressions for the scaling forms of the particle densities and determine the scaling of the average absolute moments. We find that (|r|q)∞tqα/β for q<qc=β/α and (|r|q)∞t1+αq-β for q>qc. These results give insight into the possible origins of strong anomalous diffusion and anomalous behaviors in disordered systems in general. © 2015 American Physical Society.
2016-11-25T11:14:18Z
2016-11-25T11:14:18Z
2015-09-21
artículo
Physical Review - Section E - Statistical Nonlinear and Soft Matter Physics 92(3): Article number 032128 (2016)
http://hdl.handle.net/10261/140768
10.1103/PhysRevE.92.032128
http://dx.doi.org/10.13039/501100000781
eng
Postprint
10.1103/PhysRevE.92.032128
Sí
info:eu-repo/grantAgreement/EC/FP7/617511
openAccess
American Geophysical Union