Michael Hörnquist 1997 J. Phys. A: Math. Gen. 30 7057 doi:10.1088/0305-4470/30/20/011
Michael Hörnquist
Show affiliationsWe use the concept of block variables to obtain a measure of order/disorder for some one-dimensional deterministic aperiodic sequences. For the Thue - Morse sequence, the Rudin - Shapiro sequence and the period-doubling sequence it is possible to obtain analytical expressions in the limit of infinite sequences. For the Fibonacci sequence, we present some analytical results which can be supported by numerical arguments. It turns out that the block variables show a wide range of different behaviour, some of them indicating that some of the considered sequences are more `random' than other. However, the method does not give any definite answer to the question of which sequence is more disordered than the other and, in this sense, the results obtained are negative. We compare this with some other ways of measuring the amount of order/disorder in such systems, and there seems to be no direct correspondence between the measures.
Issue 20 (21 October 1997)
Received 19 February 1997, in final form 22 May 1997
Michael Hörnquist 1997 J. Phys. A: Math. Gen. 30 7057
M Vasundhara et al 2005 J. Phys.: Condens. Matter 17 6025
R Saison 1968 Plasma Phys. 10 927
F Brochard-Wyart and P G de Gennes 1994 J. Phys.: Condens. Matter 6 A9
F V Bunkin et al 1987 J. Phys. B: At. Mol. Phys. 20 2937
Stefan Umbreit et al. 2005 ApJ 623 940
C Tsallis 1985 J. Phys. C: Solid State Phys. 18 6581
A H Bougourzi 1995 J. Phys. A: Math. Gen. 28 5831
R S Mane et al 2006 Nanotechnology 17 5393
E. D. Grundstrom et al. 2007 ApJ 656 431