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Numerical Knots: Models and Simulations

Polymers with spatial and geometrical constraints: theoretical and computational results

speaker: Enzo Orlandini (INFN e Dipartimento di Fisica, Università di Padova)

abstract: The understanding of the equilibrium properties of polymers subject to geometrical constraints is an area of primary interest in physics, mathematics, chemistry, mathematics and life sciences. The interest in the area has been recently boosted by a number of major experimental advancements based on single-molecule manipulation and advanced imaging techniques. These experiments provide a rapidly-growing amount of detailed characterizations of the interplay between the polymer entanglement and the geometrical confinement which call for a thorough understanding and interpretation by means of suitable mesoscopic models. For linear polymers some progress have been made in terms both of efficient stochastic simulations and of simple scaling arguments based on the competition between the polymer average size and the typical size of the confining region. The situation is less clear when rings are under confinement. In this case the presence of topological entanglements (knots or links) introduces a further length scale (topological) into the problem which, by competing with the other two lengths scales, may affect both the topological properties (when free to vary) of the rings and their overall shape (at fixed topology). In this talk we review some available theoretical and computational progress that have been made in the last few years on this subject. In particular we introduce and describe some stochastic methods for sampling coarse grained models of polymers under confinement and discuss their efficiency as the size of the confining region decreases. Finally, by focussing on the problem of linear and circular chains confined into slits we present recent results concerning i) the effect of confinement on the conformational properties of polymers with fixed topology and ii) the effect of spatial confinement on polymers' equilibrium topology.

Thu 9 Jun, 9:00 - 10:00, Aula Dini
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