PMID- 27394124
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20170125
LR  - 20170125
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 145
IP  - 1
DP  - 2016 Jul 7
TI  - Winding angles of long lattice walks.
PG  - 014906
LID - 10.1063/1.4955161 [doi]
AB  - We study the winding angles of random and self-avoiding walks (SAWs) on square 
      and cubic lattices with number of steps N ranging up to 10(7). We show that the 
      mean square winding angle <theta(2)> of random walks converges to the theoretical 
      form when N --> infinity. For self-avoiding walks on the square lattice, we show that the 
      ratio <theta(4)>/<theta(2)>(2) converges slowly to the Gaussian value 3. For 
      self-avoiding walks on the cubic lattice, we find that the ratio <theta(4)>/<theta(2)>(2) 
      exhibits non-monotonic dependence on N and reaches a maximum of 3.73(1) for N  approximately  
      10(4). We show that to a good approximation, the square winding angle of a 
      self-avoiding walk on the cubic lattice can be obtained from the summation of the 
      square change in the winding angles of lnN independent segments of the walk, 
      where the ith segment contains 2(i) steps. We find that the square winding angle 
      of the ith segment increases approximately as i(0.5), which leads to an increase 
      of the total square winding angle proportional to (lnN)(1.5).
FAU - Hammer, Yosi
AU  - Hammer Y
AD  - Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, 
      Tel Aviv 69978, Israel.
FAU - Kantor, Yacov
AU  - Kantor Y
AD  - Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, 
      Tel Aviv 69978, Israel.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
SB  - IM
EDAT- 2016/07/11 06:00
MHDA- 2016/07/11 06:01
CRDT- 2016/07/11 06:00
PHST- 2016/07/11 06:00 [entrez]
PHST- 2016/07/11 06:00 [pubmed]
PHST- 2016/07/11 06:01 [medline]
AID - 10.1063/1.4955161 [doi]
PST - ppublish
SO  - J Chem Phys. 2016 Jul 7;145(1):014906. doi: 10.1063/1.4955161.