On the motifs distribution in random hierarchical networks

The distribution of motifs in random hierarchical networks defined by nonsymmetric random block--hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al of network superfamilies by their motifs distributions, our artificial directed random hierarchical networks falls into the superfamily of natural networks to which the class of neuron networks belongs. This is the first example of ``handmade'' networks with the motifs distribution as in a special class of natural networks of essential biological importance.Comment: 7 pages, 5 figure

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.Comment: 56 pages, RevTeX, 20 Figure

Topologically Driven Compatibility Enhancement in the Mixtures of Rings and Linear Chains

The thermodynamics of the bicomponent melts of linear chains A and unknotted unentangled closed chains B (trivial rings) is considered within the framework of the usual Flory approach. It is shown that such melts exhibit a compatibility enhancement in comparison with the corresponding melts of linear chains. The reason for such effect is due to the topological entropy gain of mixing of A- and B-chains: if B-chains are unentangled since the A-chains play the role of a “diluent” softening the topological restrictions imposed on the B-chains. This result is in agreement with recent experimental findings of McKnight et al

The role of topological constraints in the kinetics of collapse of macromolecules

It is shown that the kinetics of collapse of a polymer coil consisting of N segments after an abrupt decrease of temperature is a two-stage process if N >> Ne. The first stage takes a time ∼ N2 and leads to the peculiar state — crumpled, or fractal, globule. Any part of a chain of any scale is itself a globule in this state ; these parts are segregated from each other in space due to the non-phantomness of a chain. The chain fold in the crumpled globule is a fractal line with fractal dimension 3, equal to the space dimension. The second stage is a chain knotting ; it is realized by means of reptation-like mechanism of motion, takes a time ∼ N3 and is accompanied by an increase of globule density.Une chaîne polymérique formée de N segments s'effondre à la suite d'un abaissement brutal de température. On montre que la cinétique de cet effondrement est un processus en deux étapes lorsque N est beaucoup plus grand que la longueur caractéristique de reptation Ne. La première étape dure un temps ∼ N2 et amène à un globule de structure froissée, ou fractale. Dans cet état, toute partie de la chaine forme elle-même un globule de ce type ; ces parties sont isolées les unes des autres parce que la chaîne ne forme pas un réseau fantôme. Les contours de la chmne dans le globule froissé forment une ligne fractale dont la dimension fractale est 3, égale à la dimension d'espace. La seconde étape accroît la densité des globules par pénétration des extrémités de la chaîne à travers les globules fractals ; elle est réalisée par reptation, dure un temps ∼ N3, et produit des noeuds dans le parcours de la chaîne