674 research outputs found
Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
Planar diagrams from optimization
We propose a new toy model of a heteropolymer chain capable of forming planar
secondary structures typical for RNA molecules. In this model the sequential
intervals between neighboring monomers along a chain are considered as quenched
random variables. Using the optimization procedure for a special class of
concave--type potentials, borrowed from optimal transport analysis, we derive
the local difference equation for the ground state free energy of the chain
with the planar (RNA--like) architecture of paired links. We consider various
distribution functions of intervals between neighboring monomers (truncated
Gaussian and scale--free) and demonstrate the existence of a topological
crossover from sequential to essentially embedded (nested) configurations of
paired links.Comment: 10 pages, 10 figures, the proof is added. arXiv admin note: text
overlap with arXiv:1102.155
On the limiting power of set of knots generated by 1+1- and 2+1- braids
We estimate from above the set of knots, , generated by
closure of n-string 1+1- and 2+1-dimensional braids of irreducible length
() in the limit n>>1.Comment: 14 LaTeX pages, 2 PostScript figure
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