Attilio Stella - Università di Padova #
Topological polymer statistics #
 A fundamental problem in topological polymer statistics is that of
    determining the frequencies of realization of different knots in 
    stochastic models of closed random chains. A related issue is that
    of establishing up to what extent a fixed topology affects the
    thermodynamic behavior of the polymers when they are subject to 
    geometrical constraints interfering with this topology. Besides 
    filling a long standing gap in the field, addressing such issues 
    can help in applications, like the interpretation of topological 
    spectra of DNA ejected from viral capsids, or the study of polymer 
    translocation through membrane nanopores.
    Extensive simulations of interacting self-avoiding polygons on cubic
    lattice for various temperatures below the theta one, allow to determine
    the rich spectrum of different knots realized, and reveal the existence 
    of a finite size correction to the free energy of the globule depending 
    on the temperature and on the minimal crossing number of its knot. 
    This correction, apparently of entropic nature, can be shown to interfere 
    with the surface tension and to determine remarkable novel effects 
    in the process of translocation. The key role played by the minimal number 
    of crossings is also emerging in experiments where the globule 
    is separated into two interacting loops by a slipping link. Extremely 
    simple laws relate the average lengths of the loops in a large
    fluctuations regime.