PMID- 27300839
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20180330
LR  - 20180330
IS  - 2470-0053 (Electronic)
IS  - 2470-0045 (Linking)
VI  - 93
IP  - 5
DP  - 2016 May
TI  - Scaling analysis of random walks with persistence lengths: Application to 
      self-avoiding walks.
PG  - 052116
LID - 10.1103/PhysRevE.93.052116 [doi]
AB  - We develop an approach for performing scaling analysis of N-step random walks 
      (RWs). The mean square end-to-end distance, <R[over ⃗]_N;2>, is written in 
      terms of inner persistence lengths (IPLs), which we define by the ensemble 
      averages of dot products between the walker's position and displacement vectors, 
      at the jth step. For RW models statistically invariant under orthogonal 
      transformations, we analytically introduce a relation between <R[over ⃗]_N;2> 
      and the persistence length, lambda_N, which is defined as the mean end-to-end vector 
      projection in the first step direction. For self-avoiding walks (SAWs) on 2D and 
      3D lattices we introduce a series expansion for lambda_N, and by Monte Carlo 
      simulations we find that lambda_infinity is equal to a constant; the scaling corrections 
      for lambda_N can be second- and higher-order corrections to scaling for <R[over 
      ⃗]_N;2>. Building SAWs with typically 100 steps, we estimate the exponents 
      nu_0 and Delta_1 from the IPL behavior as function of j. The obtained results are 
      in excellent agreement with those in the literature. This shows that only an 
      ensemble of paths with the same length is sufficient for determining the scaling 
      behavior of <R[over ⃗]_N;2>, being that the whole information needed is 
      contained in the inner part of the paths.
FAU - Granzotti, C R F
AU  - Granzotti CR
AD  - Faculdade de Filosofia, Ciencias e Letras de Ribeirao Preto (FFCLRP), 
      Universidade de Sao Paulo (USP), Avenida Bandeirantes 3900, CEP 14040-901, 
      Ribeirao Preto, Sao Paulo, Brazil.
FAU - Martinez, A S
AU  - Martinez AS
AD  - Faculdade de Filosofia, Ciencias e Letras de Ribeirao Preto (FFCLRP), 
      Universidade de Sao Paulo (USP), Avenida Bandeirantes 3900, CEP 14040-901, 
      Ribeirao Preto, Sao Paulo, Brazil.
FAU - da Silva, M A A
AU  - da Silva MA
AD  - Faculdade de Ciencias Farmaceuticas de Ribeirao Preto (FCFRP), Universidade de 
      Sao Paulo (USP), Avenida Bandeirantes 3900, CEP 14040-901, Ribeirao Preto, Sao 
      Paulo, Brazil.
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
DEP - 20160509
PL  - United States
TA  - Phys Rev E
JT  - Physical review. E
JID - 101676019
EDAT- 2016/06/15 06:00
MHDA- 2016/06/15 06:01
CRDT- 2016/06/15 06:00
PHST- 2015/09/24 00:00 [received]
PHST- 2016/06/15 06:00 [entrez]
PHST- 2016/06/15 06:00 [pubmed]
PHST- 2016/06/15 06:01 [medline]
AID - 10.1103/PhysRevE.93.052116 [doi]
PST - ppublish
SO  - Phys Rev E. 2016 May;93(5):052116. doi: 10.1103/PhysRevE.93.052116. Epub 2016 May 
      9.